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Find sum of numbers from the average of numbers.

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1) The average of three numbers is 15. What is two times the sum of the three numbers?

Find the sum of the three numbers: We know the average is 15, so the sum of all three numbers is the average multiplied by the number of numbers (3): Sum = Average x Number of numbers = 15 x 3 = 45.

Double the sum: Now that you know the sum is 45, simply double it: 2 x Sum = 2 x 45 = 90.

Therefore, two times the sum of the three numbers is 90.

Find the factors of 12.

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2) How many factors does the number 12 have?

The number 12 has 6 factors. Here they are:

1, 2, 3, 4, 6, and 12

1/3rd of something is same as dividing by 3.

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3) John owns 1/3 of the CDs in the collection. If there are a total of 120 CDs, how many does John own?

120

360

To find out how many CDs John owns, you can multiply the total number of CDs by the fraction that John owns. In this case, John owns $3rd$ of the CDs in a collection of 120 CDs.

So, the calculation would be:

So, John owns 40 CDs from the collection of 120 CDs.

Equilateral triangle has 3 equal sides.

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4) What is the perimeter of an equilateral triangle, one side of which measures 6 inches?

18 inches

12 inches

6 inches

3 inches

It cannot be determined.

An equilateral triangle has all sides equal in length. Therefore, if one side measures 6 inches, the other two sides also measure 6 inches each.

To find the perimeter, we simply add the lengths of all three sides:

Perimeter = Side 1 + Side 2 + Side 3 Perimeter = 6 inches + 6 inches + 6 inches Perimeter = 18 inches

Therefore, the perimeter of the equilateral triangle is 18 inches.

Calculate amount contributed by others in terms of the amount contributed by James.

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5) Tyler, Sharice, and James want to put their money together in order to buy a $270 radio. If Sharice agrees to pay twice as much as James, and Tyler agrees to pay three times as much as Sharice, how much will Sharice contribute?

$30

$60

$90

$150

$180

To solve this, let's assign a variable to the amount James will contribute, say $J$ . According to the problem:

Sharice agrees to pay twice as much as James, so she will contribute $2 J$ .
Tyler agrees to pay three times as much as Sharice, which means he will contribute .

The total cost of the radio is $270, so the sum of their contributions is equal to this amount:

$J + 2 J + 6 J = 270$

Simplifying the equation:

$9 J = 270$

Now, we can solve for $J$ (the amount James will contribute) and then calculate $2 J$ (the amount Sharice will contribute). Let's do the calculation.

Sharice will contribute $60 towards the purchase of the $270 radio.

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6) The price of a jacket is reduced by half, and the resulting price is then reduced by 10%. The final price is what percentage of the original price?

10%

40%

45%

55%

60%

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7) In a jar of gumdrops, the ratio of green gumdrops to red gumdrops is 5:3. If only green and red gumdrops are in the jar and the total number of gumdrops is 56, how many green gumdrops are in the jar?

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8) A stop sign has eight equal sides and a perimeter of 64. What is the length of each individual side?

It cannot be determined.

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9) Two cardboard boxes have equal volume. The dimensions of one box are 3 x 8 x 10. If the length of the other box is 4 and the width is 6, what is the height of the second box?

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10) At a fund-raiser, 300 people each donated y dollars. In terms of y, what was the total number of dollars donated?

300

300y

$\cfrac { y }{300}$

$\cfrac { 300 }{ y }$

300+y

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11) If a harvest yields 120 bushels of corn, 40 bushels of wheat, and 80 bushels of soybeans, what percent of the total harvest is corn?

25%

30%

33%

40%

50%

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12) Which of the following is a multiple of 6?

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13) A 3-foot, 2-inch board is how many times bigger than a 2-foot board?

1.5

1.6

1.7

$\cfrac { 19 }{ 12 }$

$\cfrac { 17 }{ 12 }$

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14) What is the distance between (-14, -11) and (-20, -7) along the line connecting them?

$2\sqrt { 13 }$

$4\sqrt { 13 }$

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15) What is the perimeter of a regular pentagon whose sides measure three units?

7.5

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16) What is 60 expressed as the product of its prime factors?

(15)(6)

(5)(12)

(5)(3)(3)(2)

(4)(5)(3)

(2)(5)(3)(2)

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17) Mike bought 25 shares of Zooko stock at the closing price on Tuesday and sold them at the closing price on Friday. How much money did Mike lose on his investment?

$80

$200

$800

$2000

$95

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18) The hypotenuse of a right triangle is 10 and one leg is 6. Find the length of the other leg of the triangle.

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19) Calculate the area of the hexagon.
OP = $4\sqrt{3}$ , AB = 8

$96\sqrt { 3 }$

$32\sqrt { 3 }$

$16\sqrt { 3 }$

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20) If |3a - 1| = 5, which of the following is a possible value for a?

-2

-1

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21) A coat is on sale for $128 after a discount of 20%. Find the original price.

$102.40

$153.60

$160

$180

$148

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22) Rachel worked one Saturday from 7:30 A.M. until 3 P.M. at the rate of $4.65 per hour. How much did she receive?

$19.88

$22.53

$19.00

$22.00

$34.88

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23)

The graph shown above is of which inequality?

$-2< x<3$

$-2\le x<3$

$-2\le x\le 3$

$-2< x\le 3$

$-2< x$

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24) How many socks would you need to remove from a drawer containing 10 blue socks, 15 black socks, and 5 red socks, to insure that you have at least 2 matching socks?

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25) What is the sum of $\cfrac { a }{ b }$ and $\cfrac { b }{ a }$ ?

$\cfrac { a+b }{ ab }$

$\cfrac { \left( { a }^{ 2 }+{ b }^{ 2 } \right) }{ ab }$

$\cfrac { { \left( a+b \right) }^{ 2 } }{ ab }$

$\cfrac { \left( { a }^{ 2 }+{ b }^{ 2 } \right) }{ 2ab }$

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26) A gas tank is 1/3 empty. When full, the tank holds 18 gallons. How many gallons are in the tank now?

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27) Which of the following is the least?

$\cfrac { 1 }{ 4 }+\cfrac { 2 }{ 3 }$

$\cfrac { 3 }{ 4 }-\cfrac { 1 }{ 3 }$

$\cfrac { 1 }{ 12 } \div \cfrac { 1 }{ 3 }$

$\cfrac { 3 }{ 4 } \times \cfrac { 1 }{ 3 }$

$\cfrac { 1 }{ 12 } \times 2$

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28) If the sum of x and x + 3 is greater than 20, which is a possible value for x?

-10

-8

-2

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29) If a square has a perimeter of 88, what is the length of each side?

110

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30) If a Set R contains four positive integers whose average is 9, what is the greatest number Set R could contain?

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31) Which of the following is NOT a multiple of 4?

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32) For all real numbers m, *m = 10m - 10.

*7 =

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33) For all real numbers m, *m = 10m - 10. If *m = 120, then m =

120

130

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34) At Nifty Thrifty Buy ‘N Sell, an item that usually sells for $9 is on sale for $6. What approximate discount does that represent?

10%

25%

33%

50%

66%

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35) In Jackie’s golf club, 8 of the 12 members are right-handed. What is the ratio of left-handed members to right-handed members?

$1:2$

$2:1$

$2:3$

$3:4$

$4:3$

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36) The sum of five consecutive positive integers is 35. What is the square of the greatest of these integers?

100

37 / 125

37) ${ 2 }^{ 2 }\times { 2 }^{ 3 }\times { 2 }^{ 3 }$

${2}^{8}$

${2}^{10}$

${2}^{18}$

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38) If the area of a square is $100{s}^{2}$ , what is the length of one side of the square?

$100{s}^{2}$

$10{s}^{2}$

100s

10s

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39) If 10 books cost d dollars, how many books can be purchased for 4 dollars?

$\cfrac { 4d }{ 10 }$

$40d$

$\cfrac { d }{ 40 }$

$\cfrac { 40 }{ d }$

$\cfrac { 10d }{ 4 }$

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40) If g is an even integer, h is an odd integer, and j is the product of g and h, which of the following must be true?

j is a fraction.

j is an odd integer.

j is divisible by 2.

j is between g and h.

j is greater than 0.

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41) If a class of 6 students has an average grade of 78 before a seventh student joins, what must the seventh student get as a grade in order to raise the class average to 80?

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42) If 6 is a factor of a certain number, what must also be factors of that number?

1, 2, 3, and 6

2 and 3 only

6 only

2 and 6 only

1, 2, and 3

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43)

x =

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44) For what priced item does 40% off equal a $2.00 discount?

$5.00

$4.00

$10.00

$80.00

$40.00

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45) On Monday, Gerri ate 1/4 of an apple pie. On Tuesday, she ate 1/2 of what was left of the pie. What fraction of the entire pie did Gerri eat on both days?

$\cfrac { 3 }{ 8 }$

$\cfrac { 1 }{ 2 }$

$\cfrac { 5 }{ 8 }$

$\cfrac { 3 }{ 4 }$

$\cfrac { 7 }{ 8 }$

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46) If the area of a square is equal to its perimeter, what is the length of one side of that square?

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47) If 6x - 4 = 38, then x - 5 =

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48) $3{ ({ x }^{ 2 }{ y }^{ -4 }z) }^{ 4 }{ x }^{ 3 }y =$

$3{ x }^{ 11 }y^{ -15 }{ z }^{ 4 }$

$81{ x }^{ -1 }y{ z }^{ 4 }$

$81{ x }^{ 11 }y^{ -15 }{ z }^{ 4 }$

$3{ x }^{ 9 }y{ z }^{ 4 }$

$3{ x }^{ 3 }y^{ -5 }{ z }$

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49) What is NOT a prime factor of 360?

All of the above are prime factors of 360.

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50) What is the area of an equilateral triangle whose altitude is 4?

$4\sqrt{3}$

$8\sqrt{3}$

$\cfrac{16\sqrt{3}}{3}$

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51) At the start of the year, Terry invested $6,000 in South Bend Oil Corp. At the end of the year, his stock was worth $4,500. What was the percent decline in the value of his investment?

25%

$33\cfrac { 1 }{ 3 }$ %

$66\cfrac { 2 }{ 3 }$ %

75%

125%

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52) what is $\cfrac{a}{b} - \cfrac{b}{a}?$

$\cfrac { a -b }{ ab }$

$\cfrac { {a}^{2} -{b}^{2} }{ ab }$

$\cfrac { {a -b}^{2} }{ ab }$

$\cfrac { {a}^{2} -{b}^{2} }{ 2ab }$

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53) Tracy has a test average of 90 after five tests. She only knows the scores of four of her tests: they are 80, 87, 94, and 89. What was the score on her other test?

100

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54) What is 4 percent expressed as a decimal?

.04

.25

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55) Express in simplest form the following ratio:
15 hours to 2 days.

$7\cfrac { 1 }{ 2 }$

$\cfrac { 16 }{ 5 }$

$\cfrac { 5 }{ 8 }$

$\cfrac { 15 }{ 2 }$

$\cfrac { 5 }{ 16 }$

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56) .58 x .14 =

812

8.12

81.2

.812

.0812

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57) If 3a - 5 = 7, then a =

-4

$\cfrac { -2 }{ 3 }$

$\cfrac { 2 }{ 3 }$

$\cfrac { 5 }{ 3 }$

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58) A gumball machine contains five red and three blue gumballs. If one gumball is removed, what is the probability that it will be red?

$\cfrac { 5 }{ 3 }$

$\cfrac { 3 }{ 5 }$

$\cfrac { 5 }{ 8 }$

$\cfrac { 3 }{ 8 }$

$\cfrac { 8 }{ 3 }$

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59) How long is chord $\bar { AB }$ of circle O?

$\sqrt { 10 }$

$10\sqrt { 2 }$

100

$\sqrt { 50 }$

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60) $\left( 2{ x }^{ 2 }-3x+5 \right) +(3x-2)=$

$\left( 2{ x }^{ 2 }+3 \right)$

$\left( 2{ x }^{ 2 }+6x+3 \right)$

$\left( 2{ x }^{ 2 }+6x+7 \right)$

$\left( 2x+3 \right)$

$\left( 2{ x }^{ 2 }-6x+3 \right)$

61 / 125

61) Using the formula A = p + prt, find A when p = 500, r = .04, and t = $2\cfrac { 1 }{ 2 }$ .

700

600

550

500

450

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62)

Triangles ABE and ACD are similar. Find the length of DE.

63 / 125

63) The expression ${ (3{ K }^{ 2 }) }^{ 3 }$ is equivalent to

$9{ K }^{ 6 }$

$27{ K }^{ 6 }$

$27{ K }^{ 5 }$

$9{ K }^{ 5 }$

$3{ K }^{ 5 }$

64 / 125

64) Find the value of y in the proportion

$\cfrac{20}{12}=\cfrac{5}{y}$

$\cfrac { 3 }{ 8 }$

$8\cfrac { 1 }{ 3 }$

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65) If $\cfrac{3}{x}$ is subtracted from $\cfrac{4}{x}$ , the result is

$\cfrac { 7 }{ x }$

$\cfrac { -1 }{ x }$

$\cfrac { 1 }{ x }$

$\cfrac { 1 }{ {x}^{2} }$

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66) The markdown price of a computer game was $36.75, which represented 75% of the original selling price. What was the original selling price?

$27.56

$42.35

$45.94

$49.00

$45.35

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67) Use this chart to answer question

Weekly net income = $350
A. Food
B. Rent and Utilities
C. Entertainment
D. Clothing
E. Miscellaneous

How much money does Freddie spend on miscellaneous items each week?

$43.05

$19.05

$130.95

$18.55

$44.45

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68) What is the x-intercept of the line described by the equation y = 3x + 7?

-7

$\cfrac { -3 }{ 7 }$

$\cfrac { -7 }{ 3 }$

69 / 125

69) What is 60 expressed as the product of its prime factors?

(5)(13)

(5)(12)

(5)(3)(2)(2)

(4)(4)(3)

(15)(6)

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70) If |12a - 7| = 3, what is a possible value of a?

-3

$\cfrac { -1 }{ 3 }$

$\cfrac { 5 }{ 6 }$

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71) What is the graph of the inequality 4 ≤ x ≤ 7?

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72) ${ 11 }^{ 2 }-{ 9 }^{ 2 }$

-4

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73) Eric’s test scores were 98, 95, 84, 100, and 92. What would he need on his next test to have an average of 94?

100

It is not possible to get that average.

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74) Where does the line y = x - 3 cross the y-axis?

(0,3)

(0,-3)

(-3,0)

(-3,3)

(0,0)

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75)

If points A, B, C, and D are distinct collinear points, and $\bar { AC }$ is congruent to $\bar { BC }$ , and B lies between A and D, and the length of $\bar { AC }$ is 7, what is the length of $\bar { CD }$ ?

It cannot be determined.

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76) Which of the following is a multiple of both 4 and 5?

77 / 125

77) Four less than a number is two thirds of that number. What is the number?

$\cfrac { 12 }{ 5 }$

$\cfrac { 5 }{ 3 }$

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78) On a test with 25 questions, Mark scored an 84%. How many questions did Mark answer correctly?

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79) $\cfrac { 1 }{ 2 } +\cfrac { 2 }{ 3 } +\cfrac { 3 }{ 4 } -\cfrac { 1 }{ 2 } -\cfrac { 1 }{ 3 } +\cfrac { 1 }{ 4 } -\cfrac { 1 }{ 3 } =$

$\cfrac { 1 }{ 2 }$

$\cfrac { 2 }{ 3 }$

$\cfrac { 3 }{ 4 }$

80 / 125

80) The perimeter of a square with a side length of 4 is how much less than the perimeter of a rectangle with sides of length 6 and width 4?

81 / 125

81) Which of the following is most nearly 40% of $19.95?

$8.00

$4.00

$14.50

$12.00

$6.75

82 / 125

82) One fifth of a class chose electricity for the topic of a science project. If 2 students chose this topic, how many students are in the class?

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83) Don is 5 years older than Peter is. In 5 years, Don will be twice as old as Peter is now. How old is Peter now?

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84) If p pieces of candy cost c cents, 20 pieces of candy will cost

$\cfrac { pc }{ 20 }$ cents

$\cfrac { 20c }{ p }$ cents

20pc cents

$\cfrac { 20p }{ c }$ cents

20+p+c cents

85 / 125

85) Durant’s Trading Company earned profits of $750,000 in 1990. In 1998, their profit was $4,500,000. The profit from 1998 was how many times as great as it was in 1990?

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86)

If b = 45°, then ${ v }^{ 2 } =$

It cannot be determined.

87 / 125

87) A pet goat eats 2 pounds of oats and 1 pound of grass each day. When the goat has eaten a total of 30 pounds, how many pounds of grass has been eaten?

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88) If 3x - 9 = 18, what is x ÷ 9?

89 / 125

89) One half the difference between the number of degrees in a rectangle and the number of degrees in a triangle is

360

240

180

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90) A zoo has 4 times as many gorillas as tigers. There are 4 more tigers than there are zebras at the zoo. If z represents the number of zebras, in terms of z, how many gorillas are in the zoo?

z+4

z+8

4z+4

4z+16

91 / 125

91) If cats sleep $\cfrac{ 3 }{ 4 }$ of every day, how many full days would a cat sleep in a four-day period?

$\cfrac { 1 }{ 4 }$

$\cfrac { 3 } { 4 }$

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92) What is the least number that can be added to 2,042 to produce a result divisible by 9?

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93) An art club of 5 boys and 4 girls makes craft projects. If the girls average 2 projects each and the boys average 3 projects each, what is the total number of projects produced by this group?

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94) The area of a rectangle with width 3 and length 8 is equal to the area of a triangle with base 6 and height of

95 / 125

95) definition: For all real numbers r and s, $r\clubsuit s=(r\times s)-(r+s)$ .
$10\clubsuit 2=$

96 / 125

96) definition: For all real numbers r and s, $r\clubsuit s=(r\times s)-(r+s)$ .
If L( $4\clubsuit 3)=30$ ,then L =

97 / 125

97) Jessie scores an 88, 86, and 90 on her first 3 exams. What must she score on her fourth exam to receive an average of 91?

100

98 / 125

98) Solve for x: 3x - 8 = 10x - 13

$\cfrac { 5 }{ 7 }$

$\cfrac { -5 }{ 7 }$

-35

-3

99 / 125

99) If the price of a handbag is $75.00 before a discount of 15%, what is the final discounted price?

$11.25

$60.00

$63.75

$75.00

$86.25

100 / 125

100) Find the height of a triangle whose base is 15 inches and whose area is 75 square inches.

5 inches

5 square inches

10 inches

10 square inches

20 inches

101 / 125

101) What is .03 expressed as a percent?

30%

.3%

.03%

.003%

102 / 125

102) What is 72 expressed as the product of prime factors?

(2)(3)

(2)(3)(12)

(2)(2)(2)(3)(3)

(8)(9)

(6)(6)(2)

103 / 125

103) Fred invested $4,000 at a simple interest rate of 5.75%. What is the total value of his investment after one year?

$200

$230

$4,200

$4,230

$4,400

104 / 125

104) The area of a circle is the same as the area of a square whose side is 5 centimeters. The radius of the circle is closest to

25 centimeters.

3 centimeters.

3 square centimeters.

8 centimeters.

16 centimeters.

105 / 125

105) Solve for x: 7x - 3 = 4x + 6

-1

-4

106 / 125

106) The length of a side of a square is represented by x + 2, and the length of a side of an equilateral triangle is represented by 2x. If the square and the equilateral triangle have equal perimeters, find x.

107 / 125

107) A bag has five green marbles and four blue marbles. If one marble is drawn at random, what is the possibility that it is NOT green?

$\cfrac { 1 }{ 9 }$

$\cfrac { 4 }{ 9 }$

$\cfrac { 5 }{ 9 }$

$\cfrac { 5 }{ 20 }$

$\cfrac { 4 }{ 20 }$

108 / 125

108) The expression $\sqrt{162}$ is equivalent to:

$4\sqrt{2}$

$4+\sqrt{2}$

$9\sqrt{2}$

$3\sqrt{2}$

$9+\sqrt{2}$

109 / 125

109)

In the accompanying figure, the legs of a right triangle are 16 inches and 12 inches. Find the number of inches in the length of the line segment parallel to the 16-inch side and 3 inches from it.

110 / 125

110) On a map, 2 inches represent 15 miles. How many miles would 5 inches represent?

$37\cfrac{1}{2}$

111 / 125

111)

Three congruent squares are arranged in a row. If the perimeter of ABCD is 80, the area of ABCD is

240

320

640

300

160

112 / 125

112) Express as a ratio in simplest form: 5 feet to 3 inches

$\cfrac { 5 }{ 3 }$

$\cfrac { 3 }{ 5 }$

$\cfrac { 60 }{ 3 }$

$\cfrac { 1 }{ 20 }$

$\cfrac { 20 }{ 1 }$

113 / 125

113) What is the slope of the line that passes through the point (2,6) and the point (7, 27)?

$\cfrac { -13 }{ 5 }$

$\cfrac { 5 }{ 13 }$

$\cfrac { -1 }{ 5 }$

$\cfrac { 13 }{ 5 }$

$\cfrac { 21 }{ 7 }$

114 / 125

114) $423,252\times 835,234$ =

353,534,359,987

983,414,460,968

989,353,414,426

353,514,425,972

353,514,460,968

115 / 125

115) If points A, B, C, and D are collinear, and C is the midpoint of $\bar { AB }$ , and B is the midpoint of $\bar { AD }$ , and the length of $\bar { AD }$ is 24, what is the length of $\bar { CD }$ ?

It cannot be determined.

116 / 125

116) If x = 4 on the graph of y = -5x + 4, what does y equal?

-1

-5

-16

117 / 125

117) What is the graph of the inequality 6 < $x\le 9$ ?

118 / 125

118) What is $3 { x }^{ 5 }$ divided by $4 { x }^{ 7 }$ ?

$7 { x }^{ 12 }$

$12 { x }^{ 12 }$

$\cfrac { 3 }{ 4{ x }^{ 2 } }$

$12 { x }^{ 35 }$

$\cfrac { 4{ x }^{ 2 } }{ 3 }$

119 / 125

119) Express .075 as a percent.

75%

7.5%

.75%

.075%

120 / 125

120) A scale model of a cube has sides that are one fortieth of the length of the original. If the scale model required three gallons of paint to coat, how much paint is required to coat the original with the same thickness of paint?

$\cfrac { 40 }{ 3 }$ gallons

7,280 gallons

4,800 gallons

240 gallons

120 gallons

121 / 125

121) Dinner (plus tax and tip) cost $93.60. The tax rate is 5% and Mr. Simmons left a 15% tip. Both tax and tip are calculated on the base amount of the check. What was the base amount of Mr. Simmons’s bill?

$78.00

$113.32

$77.41

$112.00

$81.30

122 / 125

122) What is the area of a square whose diagonal is 6?

$6 \sqrt{2}$

123 / 125

123) Which fraction lies between $\cfrac {2}{3}$ and $\cfrac {4}{5}$ ?

$\cfrac { 5 }{ 6 }$

$\cfrac { 17 }{ 20 }$

$\cfrac { 7 }{ 10 }$

$\cfrac { 13 }{ 15 }$

$\cfrac { 9 }{ 10 }$

124 / 125

124) The circumference of a circle whose diameter is 7 inches is approximately

22 inches.

28 inches.

38 inches.

154 inches.

14 inches.

125 / 125

125)

Josie bought 16 shares of Zariche stock at the closing price Monday and sold them at the closing price on Friday. What was Josie’s profit on this investment?

$60

$96

$600

$960

None of the above

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Math Test Quiz

1 / 50

1) A convergent lens can produce which of the following from a single object in front of the lens? Select two answers.

Real and upright image

Virtual and upright image

Real and inverted image

Virtual and inverted image

The image is virtual and upright, or it is inverted and real. If the distance of the object is less than one focal length from the convergent lens, the image is virtual and upright. If the distance of the object is more than one focal length from the convergent lens, the image is inverted and real.

2 / 50

2) Which of the following statements are true concerning isolated fundamental particles? Select two answers.

An isolated fundamental particle cannot have charge.

An isolated fundamental particle cannot have potential energy.

An isolated fundamental particle cannot have internal energy.

An isolated fundamental particle cannot have mass.

An isolated fundamental particle cannot have potential energy. An isolated fundamental particle cannot have mass. Potential energies are energies of relationship and therefore cannot belong to an isolated particle with no internal structure. Likewise, internal energy refers to energies (both kinetic and potential) carried by the various internal constituents of nonfundamental particles.

3 / 50

3) For an RC circuit, which of the following is the correct analogy for the instantaneous current behavior in a pathway containing a capacitor? Choose the option that would give the correct instantaneous current values in the capacitor’s path.

Uncharged capacitor—closed switch; fully charged capacitor— open switch. An uncharged capacitor will initially appear to be a simple wire as the first charge to hit one side of the capacitor draws its opposite on the other side. On the other hand, a fully charged capacitor accepts no additional charges and blocks any current from entering its pathway. These two states are connected by an exponential function:

$I=( V/R) e^{-t/RC}$

Remember to compare t = 0 to t >> RC.

4 / 50

4) Some objects can be made to exhibit an interference pattern with the two-slit experiment, and some objects cannot. What is the difference between those that can and those that cannot?

Objects are either fundamentally a wave or fundamentally a particle.

All objects can exhibit either wave-like properties or particle-like properties depending on the situation.

Whether an interference pattern can be observed depends on the object’s de Broglie wavelength.

All objects can be made to exhibit an interference pattern under the right circumstances.

Whether an interference pattern can be observed depends on the object’s de Broglie wavelength. The de Broglie wavelength is the connection between classically particle-like objects and their wave like properties. Interference patterns have been successfully shown for many particles. Macroscopic objects, however, have such large masses that their de Broglie wavelengths make observing a diffraction pattern impossible:

$\lambda =h/p$

5 / 50

5) When examining the spectrum for a specific element, a bright spectral line with the highest frequency represents

an electron excited to the atom’s highest energy state

an electron falling from the highest energy state in the atom to the next to highest state

an electron excited from its ground state to the next to lowest energy state

an electron falling from a higher energy state to a much lower energy state

An electron falling from a higher energy state to a much lower energy state. Light is emitted (bright spectral line) when an electron falls from an excited state to a lower energy state. The greater the energy difference is (as opposed to the starting energy state), the higher the frequency of light emitted (E = hf).

6 / 50

6) A radioactive isotope undergoes gamma decay. Afterward, the nucleus

contains fewer nucleons

has the same number of nucleons but a different ratio of protons/neutrons

has the same mass number but a lower mass

undergoes beta decay

The nucleus has the same mass number but a lower mass. Since the nucleus has emitted a photon of electromagnetic energy, the net charge on the nucleus must remain the same. Since energy left the nucleus, the mass of the nucleus as a whole must be decreased by $E/c^{2}$ .

7 / 50

7) When examining a two-slit diffraction pattern, which of the following would you notice as the slits were brought closer together?

The interference pattern would contain more maximums. They would be more closely spaced.

The location of the central interference peak would shift.

The interference pattern would spread out.

The interference peaks themselves would each become sharper (narrower).

The interference pattern would spread out.

$D sin \theta =m\lambda$

Wavelength does not change. So as D gets smaller, sin θ must increase. Therefore, the locations of the bright, constructive interference fringes (integer m’s) are found at greater angles.

8 / 50

8) A radio telescope uses a curved reflecting material to focus radio signals from orbiting satellites or distant objects in space onto a detector. Which of the following would be the biggest problem with designing a radio telescope with a convex reflecting dish?

The image produced is virtual.

The image produced is inverted.

The detection equipment would have to be placed in the line of sight.

There is no real problem with designing a convex reflecting dish for radio waves.

The image is virtual. Convex mirrors are diverging. This means the real, reflected rays do not come to an actual focus. The focus is virtual and located behind the mirror. So any detection equipment placed at the focus would not actually receive a signal!

9 / 50

9) A beam of light incident at 50 degrees travels from a medium with an index of refraction of 2.5 into one with an index of refraction of 1.1. The refracted angle of light that emerges is

20 degrees

50 degrees

90 degrees

There is no solution.

There is no solution. This is a situation of total internal reflection. Since 50 degrees is beyond the critical angle for this pair of materials, all of the light will be reflected and none will be refracted. Remember that a 90-degree “refraction” happens right at the critical angle.

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10) A light beam is traveling in a vacuum and then strikes the boundary of another optically dense material. If the light comes to the interface at an angle of incidence of 30 degrees on the vacuum side, it will emerge with an angle of refraction

equal to 30 degrees

less than 30 degrees

greater than 30 degrees

The relative indices of refraction must be known in order to find the solution.

Less than 30 degrees. Since the second medium is slower, it will have a larger n value, thereby requiring a smaller sin θ value. So a smaller angle is needed:

$N_{1} sin \theta _{1} =N_{2} sin \theta _{2}$

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11) A charge is accelerated by an electric field. While the charge is accelerating, which of the following is occurring?

A static magnetic field is created.

A new, static electric field is created.

Only a varying magnetic field is created.

An electromagnetic wave is created.

An electromagnetic wave is created. When a charge is accelerating, the changing velocity of the charge creates a changing magnetic field. The changing magnetic field induces a changing electric field. This dual oscillation is self-perpetuating and is known as electromagnetic radiation (or light when the frequency of oscillation lies within the visible range).

12 / 50

12) A conducting loop of wire is held steady parallel to the ground within a strong magnetic field directed upward. The setup is viewed from above. As the loop of wire is quickly pulled out of a magnetic field, what will the loop experience?

A temporary clockwise current that dies out soon after the loop is out of the field

A temporary counterclockwise current that dies out soon after the loop is out of the field

A temporary clockwise current that dies out as soon as the loop is out of the field

A temporary counterclockwise current that dies out as soon as the loop is out of the field

A temporary counterclockwise current that dies out as soon as the loop is out of the field. Only while the flux of the field through the loop is changing will there be an induced emf causing the current. The induced current will be such that its magnetic field will oppose the change. Since the magnetic field flux upward through the loop is getting smaller as the loop is pulled out, the induced current will create an additional upward magnetic field. The right-hand rule for current indicates a counterclockwise current is needed.

13 / 50

13) Two parallel wires carrying current near each other exert magnetic forces on each other. If the direction and magnitude of the current in both wires is reversed and doubled, what will happen to the magnetic forces?

They will reverse directions and double in magnitude.

They will reverse directions and quadruple in magnitude.

They will remain in the same directions and double in magnitude.

They will remain in the same directions and quadruple in magnitude.

They will remain in the same directions and quadruple in magnitude. Reversing the direction of one current will switch the direction of its magnetic field. However, when using the right-hand rule and since the direction of the moving charges within the reversed field is also reversed, the same direction of force is found. Doubling the source current will double the field strength, which then is acting on twice as much current and creating four times the force.

$B\varpropto I_{1}$

$F\varpropto I_{2} B$

$F\varpropto I_{1} I_{2}$

14 / 50

14) A very long wire carries a steady current. Which of the following statements describes the magnetic field at a distance of R from the wire?

The magnetic field is zero.

The magnetic field loops around the wire and gets weaker proportional to $1/R^{2}$ as one moves to larger R values.

The magnetic field loops around the wire and gets weaker proportional to 1/R as one moves to larger R values.

The magnetic field extends radially outward and gets weaker proportional to $1/R^{2}$ as one moves to larger R values.

The magnetic field loops around the wire and gets weaker proportional to 1/R as one moves to larger R values. The moving charges in the wire create loops of magnetic field around them. As R increases, the field strength decreases proportional to 1/R rather than $1/R^{2}$ because the source of the field is a line rather than a point.

15 / 50

15) The primary difference between a permanent magnet (an object with identifiable north and south poles) and magnetic material that does not have identifiable north and south poles is

electron configuration

magnetic domain alignment

magnetic materials have no poles at all

magnetic materials are lacking one of the two poles

Magnetic domain alignment. Electron configuration is the difference between a nonmagnetic and a magnetic material. Any magnetic material can be made to have overall north and south poles by lining up all of the individual magnetic domains within the material. (Each domain has its own north and south poles.) Magnetic poles do not exist in isolation as all magnetic field lines loop back on themselves.

16 / 50

16) If each of the batteries in the circuit below supplies a voltage V and if each resistor has resistance R, what will be the reading on the meter pictured?

APPHY2-489

V/3

2V/3

2V/3R

V/3. The meter pictured is a voltmeter. The voltage supplied by the battery will be split evenly among the three identical resistors.

17 / 50

17) A standard RC (resistor-capacitor) circuit takes approximately two seconds to charge the capacitor fully. If the resistor is 100 ohms and the voltage across the RC combination is 12 volts, what is the current through the fully charged capacitor?

One must know the capacitance of the capacitor in order to answer this question.

0.12 A

0.06 A

0 A

A fully charged capacitor cannot accept any more charge; therefore, the current going into it is zero.

18 / 50

18) Which of the following pictures is an incorrect representation of the electric field near various charged conductors?

Field lines should point away from the positive and toward the negative, which all the pictures show. Field lines should never cross, and none of these diagrams has that. Field lines should also be perpendicular to the surface of conductors. Picture () violates this principle.

19 / 50

19) One large conducting sphere with a net charge of +8 microcoulombs is put into contact with a slightly smaller conducting sphere that initially has a charge of –6 microcoulombs. Which statement best describes the charge distribution after the two spheres are separated?

They are both neutral.

The larger sphere has +8 microcoulombs of charge, while the smaller retains –6 microcoulombs of charge.

Both spheres have +1 microcoulomb of charge.

The larger sphere has slightly more than +1 microcoulomb of charge, while the smaller sphere has slightly less than +1 microcoulomb of charge.

The larger sphere has slightly more than +1 microcoulomb of charge, while the smaller sphere has slightly less than +1 microcoulomb of charge. When the spheres contact each other, electrons move off of the smaller sphere to the larger sphere and attempt to neutralize both spheres. Since this is a net +2 microcoulombs of charge, the electrons distribute themselves over both surface areas of the spheres, keeping the positive charges as far from each other as possible. Since the larger sphere has more surface area, it captures a greater portion of the excess charge than does the smaller sphere.

20 / 50

20) Two identical spheres originally in contact undergo induced charge separation. The two spheres are slowly separated until a gap of 12 cm is separating their surfaces. The net force of attraction between the two oppositely charged large spheres after they have been separated by 12 cm is measured. The entire experiment is then repeated with two smaller but otherwise similar spheres.

APPHY2-485.1 APPHY2-485.2

The force between the smaller spheres compared with the force between the larger spheres is best described as

the same since the charges and separations are the same

smaller since the charges on each small sphere are closer together

bigger since the centers of the spheres are closer

the same since the average force felt by any one particular charge is the same in both cases

Bigger since the centers of the spheres are closer. Remember $kq_{1} q_{2} /r^{2}$ .

The charges (q1 and q2) are the same, and k is a constant. So the only variation in the two situations is the average r between the spheres. In the case of the two smaller spheres, the average distance (represented by the centers of the spheres) is actually closer. Therefore, the force is stronger in that case.

21 / 50

21) Consider the following process for a gas. Which of the following statements is true concerning this process?

APPHY2-484

Path D (from point 4 to point 1) is isobaric.

No work was done to or by the gas during path A (from point 1 to point 2).

No net work was done to or by the gas during the entire cycle (from point 1 back to point 1 through A, B, C, D).

No work was done to or by the gas during path B (from point 2 to point 3).

No work was done to or by the gas during path B (from point 2 to point 3). The term isobaric indicates constant pressure, so choice (Path D (from point 4 to point 1) is isobaric.) is false. During path B, the gas expands and therefore does work to its surroundings. So choice (No work was done to or by the gas during path A (from point 1 to point 2).) is false. Over the entire process, the area of the enclosed area is the work done by the gas. Since this area does not equal zero, choice (No net work was done to or by the gas during the entire cycle (from point 1 back to point 1 through A, B, C, D).) is false. Process No work was done to or by the gas during path B (from point 2 to point 3). involves an expansion or contraction (displacement) of the gas. Therefore, no work is done during the part of the process.

22 / 50

22) Which of the following is the best explanation of the statement, “A roomful of neon gas has a lower average speed than 1 mole of helium gas at the same temperature and pressure.”

This is not a correct statement.

There is more than 1 mole of neon gas in an average room.

Helium atoms have more degrees of freedom than do neon atoms.

Helium has a lower mass per particle than neon.

Helium has a lower mass per particle than neon. Average kinetic energy is directly related to temperature. Since both gases are at STP (standard temperature and pressure), their average kinetic energies are the same. However, since helium has a lower mass, it must have a higher velocity to obtain the same kinetic energy (½ $mv^{2}$ ).

23 / 50

23) The Sun’s rays strike a black surface that is directly on top of a liquid. The liquid is then observed to swirl as it transfers the heat to the bottom layers of the liquid. The correct sequence of transfers in thermal energy in this story is

Radiative → convective → conductive

Radiative → conductive → convective

Convective → conductive → convective

Convective → conductive → radiative

Radiative → conductive → convective. Radiative transfer is the transfer of energy via electromagnetic radiation (such as sunlight). Conductive transfer is the transfer of thermal energy via direct contact (such as a floating object in contact with the water). Convective transfer is the transfer of thermal energy due to the movement of a fluid (like currents in the water).

24 / 50

24) Fluid is poured into an open U-shaped tube as shown below. If a person blows across the top of the right-hand side’s opening, what will happen to the fluid in the tube?

APPHY2-481

It will remain the same.

It will rise on the right-hand side and lower on the left-hand side.

It will rise on both sides.

It will rise on the left-hand side and lower on the right-hand side.

It will rise on the right-hand side and lower on the left-hand side. Blowing over the right-hand side will lower the pressure at that height:

$\cfrac{1}{2} pv^{2} +pgh+P=constant$

Remember that h remains the same while v is raised, forcing P lower. This causes an imbalance in pressure between the right-hand side (lower pressure) and left-hand side (higher pressure). This difference in pressure causes a net force pushing the fluid upward on the right and downward on the left.

25 / 50

25) The exact same boat will ride higher (have more volume exposed to the air) while floating on a fluid if

the fluid’s density is raised

the fluid’s temperature is raised

the boat’s density is raised

the boat shifts its cargo to a lower deck

The fluid’s density is raised. The buoyancy force that lifts the boat upward is proportional to the weight of the fluid displaced. The boat will rise or sink until the buoyant force and the boat’s weight cancel. Raising the fluid’s temperature will usually make the fluid less dense, requiring a greater displacement of water (i.e., the boat will ride lower). Raising the boat’s density will increase its weight, requiring a greater displacement of water. Finally, shifting the cargo around will have no effect as the weight and shape of the boat remain unaffected.

26 / 50

26) Compare the two columns of water pictured below. They have the same height. Which of the following statements compares the total weight and the pressure at the bottom of the columns?

APPHY2-479

Weight and pressure are greater for the wider column.

Weight and pressure are the same for both.

Weight is greater for the wider column, while pressure is the same.

Weight is the same, while pressure is greater for the wider column.

Weight is greater for the wider column, while pressure is the same. Although the wider column has a greater volume of water and therefore more mass, the fact that the height remains constant means any unit area on the bottom of the column will experience the same force/area (pressure).

27 / 50

27) In a certain process, 400 J of heat is transferred to a system and the system simultaneously does 100 J of work. The change in internal energy of the system is

500 J

300 J

–100 J

–300 J

Q = +400 J; W =–100 J; ΔU = Q + W

28 / 50

28) If one of the two slits in a Young’s double-slit demonstration of the interference of light is covered with a thin filter that transmits only half the light intensity, which of the following occurs?

The bright lines are brighter and the dark lines are darker.

The bright lines and the dark lines are all darker.

The bright lines and the dark lines are all brighter.

The dark lines are brighter and the bright lines are darker.

This is still a double slit pattern because there is still light making it through both slits. One of the light sources has reduced its amplitude; which means when it meets the second light source it will cause less interference than it originally did. This means less constructive interference and less destructive interference also. So bright spots become less bright, and dark spots become brighter.

29 / 50

29) APPHY2-477

Plane sound waves of wavelength 0.12 m are incident on two narrow slits in a box with nonreflecting walls, as shown. At a distance of 5.0 m from the center of the slits, a first-order maximum occurs at point P, which is 3.0 m from the central maximum. The distance between the slits is most nearly

0.09 m

0.16 m

0.20 m

0.24 m

Since the slits are narrow, we can use m λ = d sin θ, but since θ is clearly large we cannot use the x/L small angle approximation. From the given diagram, the geometry shows sin θ = o/h = 3/5 .. rather than finding θ, we will just use this value for sin θ and plug in … m λ =d sin θ … (1) (0.12) = d (3/5)

30 / 50

30) APPHY2-476

In an experiment to measure the wavelength of light using a double slit apparatus, it is found that the bright fringes are too close together to easily count them. To increase only the spacing between the bright fringes, one could

increase the slit width

decrease the slit width

increase the slit separation

decrease the slit separation

Based on m λ = dx / L we want to increase x. d is separation of slits and less d means more x

31 / 50

31) Two sources, in phase and a distance d apart, each emit a wave of wavelength λ. See figure below. Which of the choices for the path difference $\vartriangle L=L_{1} -L_{2}$ will always produce destructive interference at point P?

$d sin \theta$

$( x/L_{2}) d$

$\lambda /2$

$2\lambda$

By definition, when the path difference equals ½ λ or any odd multiple of ½ λ’s for sources of the same λ, there will be destructive interference.

32 / 50

32) In a Young's double-slit experiment, the slit separation is doubled. To maintain the same fringe spacing on the screen, the screen-to-slit distance D must be changed to

$D/2$

$\cfrac{D}{\sqrt{2}}$

$\sqrt{2} D$

$2D$

From mλ = dx/ L, d x2 needs L x2 also.

33 / 50

33) A diffraction grating of 1,000 lines/cm has red light of wavelength 700 nm pass through it. The distance between the first and third principal bright spots on a screen 2 m away is

14 cm

28 cm

42 cm

140 cm

1000 lines/cm gives a line spacing $d=1/1,000 cm/line=1\times 10^{-5} m/line$ . $\lambda =7\times 10^{-7} m$ . With diffraction gratings, we usually assume the small angle approximation does not work, so we find θ then use the geometry with tan θ or another trig function to find Y. Do this for each spot.

m=1. m λ = d sin θ $( 1)\left( 7\times 10^{-7}\right) =\left( 1\times 10^{-5}\right) sin \theta$ θ = 4.01° … tan θ = o/a … $Y_{1} =0.14m$

Repeat for m = 3 … $Y_{3} =0.43m$ . Subtract $Y_{3} -Y_{1}$ to find the distance between = 0.29 m

Note: Since the angle θ here actually came out to be small, the x/L small angle approximation could be used and the spacing x between spots could be assumed to be equal as well, so you could simply find x for the first spot and double it to find the spacing 1 to 3.

34 / 50

34) In Young’s double slit experiment, the second order bright band of one light source overlaps the third order band of another light source. If the first light source has a wavelength of 660 nm, what is the wavelength of the second light source?

1,320 nm

990 nm

440 nm

330 nm

Using m λ = d sin θ, the value of sin θ is the same for both sources since the location of the spot is the same, but the first source is at m=2, and the second source is at m=3. Equating d sin θ for each gives $m_{1} \lambda _{1} =m_{2} \lambda _{2}$ … $( 2)( 660) =3 ( \lambda _{2})$ … $\lambda _{2} =440nm$ .

35 / 50

35) APPHY2-471

A ray of light in air is incident on a 30-°60°-90° prism, perpendicular to face ab, as shown in the diagram. The ray enters the prism and strikes face ac at the critical angle. What is the index of refraction of the prism?

$\cfrac{1}{2}$

$\sqrt{\cfrac{3}{2}}$

$\cfrac{2\sqrt{3}}{3}$

$2$

From the diagram, the angle at the bottom of the small top triangle is 30° so when we draw the normal line on that slanted interface, the angle of incidence there is 60°. We are told this is the critical angle which means the angle of refraction of the scenario is 90°. Now we use

$n_{i} sin \theta _{c} =n_{r} sin( 90)$ … $n_{i} sin( 60) =( 1)( 1)$ … $n_{i} =1/sin 60$ … $n_{i} =\cfrac{1}{\left(\frac{\sqrt{3}}{2}\right)}$

Rationalizing gives us the answer.

36 / 50

36) APPHY2-469

An object O is located at point P to the left of a converging lens, as shown in the figure. $F_{1}$ and $F_{2}$ are the focal points of the lens.

Which of the following characterizes the image when the object is in the position shown?

Real, inverted, and smaller than the object

Real, upright, and larger than the object

Real, inverted, and larger than the object

Virtual, upright, and larger than the object

This is a magnifying glass, which can be memorized or the math can be done to prove the answer.

37 / 50

37) APPHY2-469

An object O is located at point P to the left of a converging lens, as shown in the figure. $F_{1}$ and $F_{2}$ are the focal points of the lens.

If the focal length of the lens is 0.40 m and point P is 0.30 m to the left of the lens, where is the image of the object located?

1.2 m to the left of the lens

0.17 m to the left of the lens

At the lens

0.17 m to the right of the lens

Using the math, $1/f=1/d_{o} +1/d_{i}$ , $d_{i} =-1.2$ . Its virtual so its on the same side as the object, which puts the image on the left side of the lens.

38 / 50

38) APPHY2-468

A ray of light in glass that is incident on an interface with ice, as shown, is partially reflected and partially refracted. The index of refraction n for each of the two media is given in the figure. How do the angle of reflection and the angle of refraction compare with the angle of incidence θ?

39 / 50

39) APPHY2-467

Multiple Correct: As shown, a beam of white light is separated into separate colors when it passes through a glass prism. Red light is refracted through a smaller angle than violet light because red light has a: Select two answers.

slower speed in glass than violet light

faster speed in glass than violet light

slower speed in the incident beam than violet light

lower index of refraction in glass than violet light

Bending of a wave (refraction) is due to the speed change at an angle. The more the speed changes, the more the bending. Hence, the violet bends more so must have a larger speed change (more slowing), so the red is faster. Additionally, we can note that since the violet slows and bends more, the index of refraction in glass for a violet light is higher than the index for a red light.

40 / 50

40) Which of the following statements are true for both sound waves and electromagnetic waves?

They can undergo refraction.
They can undergo diffraction.
They can produce a two-slit interference pattern.
They can produce standing waves.

I and II only

III and IV only

I, II, III and IV

II, III, and IV only

All waves demonstrate the listed choices.

41 / 50

41) A large lens is used to focus an image of an object onto a screen. If the left half of the lens is covered with a dark card, which of the following occurs

The left half of the image disappears

The right half of the image disappears

The image becomes blurred

The image becomes dimmer

When light from multiple locations pass through a given part of a lens to form an image, only a small portion of a lens is needed to form the image. The more of a lens, the more light rays that can be bent by it to each image location. This simply makes the image brighter. By covering half the lens, all of the incoming rays still bend all the same ways but there are less total ray being bent to given locations on the image so it is dimmer. This can easily be seen by looking at a lens that has only horizontal rays approaching it. All of these rays converge to the focal point; covering a portion of the lens still focuses the rays on the focal point, just less of them.

42 / 50

42) APPHY2-463

A light ray R in medium I strikes a sphere of medium II with angle of incidence θ, as shown above. The figure shows five possible subsequent paths for the light ray.

Which path is possible if medium I is glass and medium II is air?

This should be the opposite of the scenario in the last question.

43 / 50

43) APPHY2-463

A light ray R in medium I strikes a sphere of medium II with angle of incidence θ, as shown above. The figure shows five possible subsequent paths for the light ray.

Which path is possible if medium I is air and medium II is glass?

path A

path C

path D

path E

Medium I (air) is surrounding the sphere on both sides. As it enters the sphere, it goes less–more so bends towards the normal line (leaving D or E as the possibly answers). When the ray reaches the far edge of the sphere, it goes from more–less so should bend away from the normal line. Note the normal line drawn below.

APPHY2-463 expl

44 / 50

44) APPHY2-462

A thin film with index of refraction n1 separates two materials, each of which has an index of refraction less than $n_{f}$ . A monochromatic beam of light is incident normally on the film, as shown above. If the light has wavelength λ within the film, maximum constructive interference between the incident beam and the reflected beam occurs for which of the following film thicknesses?

2λ

λ/2

λ/4

The film has a higher n compared to both sides, such as soap surrounded by air. So as the light ray hits the first boundary it makes a ½ λ phase flip, but does not make the flip at the second boundary. To be constructive, we need to cover a total of ½ λ extra phase shift due to traveling in the film thickness. So the thickness should be ¼ $\lambda _{film}$ .

45 / 50

45) An object is placed in front of a converging thin lens at a distance from the center of the lens equal to half the focal length. Compared to the object, the image is

upright and larger

upright and smaller

inverted and larger

inverted and smaller

When an object is placed in front of the focal point of a converging lens, the lens acts as a magnifying glass.

46 / 50

46) APPHY2-460

A beam of white light is incident on a triangular glass prism with an index of refraction of about 1.5 for visible light, producing a spectrum. Initially, the prism is in a glass aquarium filled with air, as shown above. If the aquarium is filled with water with an index of refraction of 1.3, which of the following is true?

A spectrum is produced, but the deviation of the beam is opposite to that in air.

The positions of red and violet are reversed in the spectrum.

The spectrum produced has greater separation between red and violet than that produced in air.

The spectrum produced has less separation between red and violet than that produced in air.

The larger the difference between n’s the more the rays bend. When the water is added, the difference between n’s is less so the amount of bending is less.

47 / 50

47) APPHY2-459

A light ray passes through substances 1, 2, and 3, as shown. The indices of refraction for these three substances are n1, n2, and n3, respectively. Ray segments in 1 and 3 are parallel. From the directions of the ray, one can conclude that

$n_{3}$ must be the same as $n_{1}$

$n_{2}$ must be less than $n_{1}$

$n_{2}$ must be less than $n_{3}$

all three indices must be the same

If the angle in equals the angle out in a 3 tier medium arrangement, then the substances on the outsides must be the same.

48 / 50

48) APPHY2-458

An object is placed at a distance of 1.5f from a converging lens of focal length f, as shown. What type of image is formed and what is its size relative to the object?

Draw the ray diagram, or makeup some numbers and do the math.

49 / 50

49) A physics student places an object 6.0 cm from a converging lens of focal length 9.0 cm. What is the magnitude of the magnification of the image produced?

0.6

1.5

2.0

3.0

Using the math, $1/f=1/d_{o} +d_{i}$ , $d_{i} =-18$ … then $M=-d_{i} /d_{o}$ … M = 3

50 / 50

50) When light passes from air into water, the frequency of the light remains the same. What happens to the speed and the wavelength of light as it crosses the boundary in going from air into water?

When light goes in higher indices of refraction, it slows down. Since v = f λ and f remains constant, when v decreases λ decrease with it.

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