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25.3 The law of refraction  (Page 5/9)

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A larger change in direction

Suppose that in a situation like that in [link] , light goes from air to diamond and that the incident angle is 30 . 0º size 12{"30" "." 0°} {} . Calculate the angle of refraction θ 2 size 12{q rSub { size 8{2} } } {} in the diamond.

Strategy

Again the index of refraction for air is taken to be n 1 = 1 . 00 size 12{n rSub { size 8{1} } =1 "." "00"} {} , and we are given θ 1 = 30 . 0º size 12{q rSub { size 8{1} } ="30" "." 0°} {} . We can look up the index of refraction for diamond in [link] , finding n 2 = 2 . 419 size 12{n rSub { size 8{2} } =2 "." "419"} {} . The only unknown in Snell’s law is θ 2 size 12{q rSub { size 8{2} } } {} , which we wish to determine.

Solution

Solving Snell’s law for sin θ 2 size 12{q rSub { size 8{2} } } {} yields

sin θ 2 = n 1 n 2 sin θ 1 . size 12{"sin"θ rSub { size 8{2} } = { {n rSub { size 8{1} } } over {n rSub { size 8{2} } } } "sin"θ rSub { size 8{1} } } {}

Entering known values,

sin θ 2 = 1 . 00 2 . 419 sin 30 . 0º = ( 0 . 413 ) ( 0 . 500 ) = 0 . 207 . size 12{"sin"q rSub { size 8{2} } = { {1 "." "00"} over {2 "." "419"} } "sin""30" "." 0"°=" left (0 "." "413" right ) left (0 "." "500" right )=0 "." "207"} {}

The angle is thus

θ 2 = sin − 1 0 . 207 = 11 . 9º . size 12{θ rSub { size 8{2} } ="sin" rSup { size 8{ - 1} } 0 "." "207"="11" "." 9°} {}

Discussion

For the same 30º angle of incidence, the angle of refraction in diamond is significantly smaller than in water ( 11.9º rather than 22º —see the preceding example). This means there is a larger change in direction in diamond. The cause of a large change in direction is a large change in the index of refraction (or speed). In general, the larger the change in speed, the greater the effect on the direction of the ray.

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Test prep for ap courses

When light travels from air into water, which of the following statements is accurate?

  1. The wavelength decreases, and the speed decreases.
  2. The wavelength decreases, and the speed increases.
  3. The wavelength increases, and the speed decreases.
  4. The wavelength increases, and the speed increases.

(a)

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When a light ray travels from air into glass, which of the following statements is accurate after the light enters the glass?

  1. The ray bends away from the normal, and the speed decreases.
  2. The ray bends away from the normal, and the speed increases.
  3. The ray bends toward the normal, and the speed increases.
  4. The ray bends toward the normal, and the speed decreases.
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Diagram shows two arrows running from point A to the top of a shaded box. Where they meet the shaded box, two new arrows emerge inside the box. These arrows meet at a point B inside the box.

Two different potential paths from point A to point B are shown. Point A is in the air, and point B is in water. For which of these paths (upper or lower) would light travel from point A to point B faster? Which of the paths more accurately represents how a light ray would travel from point A to point B? Explain.

Since light bends toward the normal upon entering a medium with a higher index of refraction, the upper path is a more accurate representation of a light ray moving from A to B.

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Students in a lab group are given a plastic cube with a hollow cube-shaped space in the middle that fills about half the volume of the cube. The index of refraction of the plastic is known. The hollow space is filled with a gas, and the students are asked to collect the data needed to find the index of refraction of the gas. The students take the following set of measurements:

Angle of incidence of the light in the air above the plastic block: 30°

Angle of refraction of the beam as it enters the plastic from the air: 45°

Angle of refraction of the beam as it enters the plastic from the gas: 45°

The three measurements are shared with a second lab group. Can the second group determine a value for the index of refraction of the gas from only this data?

  1. Yes, because they have information about the beam in air and in the plastic above the gas.
  2. Yes, because they have information about the beam on both sides of the gas.
  3. No, because they need additional information to determine the angle of the beam in the gas.
  4. No, because they do not have multiple data points to analyze.
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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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