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# Refraction: Snell’s Law

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Refraction: Snell’s Law
Example : Refraction through flat glass. Light traveling in air strikes a flat piece of uniformly thick glass at an incident angle of 60°, as shown. If the index of refraction of the glass is 1.50, (a) what is the angle of refraction θA in the glass; (b) what is the angle θB at which the ray emerges from the glass? Solution: a. Applying Snell’s law gives sin θA = 0.577, or θA = 35.3°. b. Snell’s law gives sin θB = 0.866, or θB = 60°. The outgoing ray is parallel to the incoming ray.

Refraction: Snell’s Law
Example : Apparent depth of a pool. A swimmer has dropped her goggles to the bottom of a pool at the shallow end, marked as 1.0 m deep. But the goggles don’t look that deep. Why? How deep do the goggles appear to be when you look straight down into the water? Solution: The ray diagram appears in Figure Refraction causes the goggles to appear to be less deep than they actually are. Snell’s law plus a small-angle approximation (sin θ ≈ tan θ ≈ θ) gives d’ ≈ d/n1 = 0.75 m.

Total Internal Reflection; Fiber Optics
If the angle of incidence is larger than this, no transmission occurs. This is called total internal reflection. Figure Since n2 < n1, light rays are totally internally reflected if the incident angle θ1 > θc, as for ray L. If θ1 < θc, as for rays I and J, only a part of the light is reflected, and the rest is refracted.

Total Internal Reflection; Fiber Optics
Conceptual Example 32-11: View up from under water. Describe what a person would see who looked up at the world from beneath the perfectly smooth surface of a lake or swimming pool. Figure (a) Light rays, and (b) view looking upward from beneath the water (the surface of the water must be very smooth). Example 32–11. Solution: The critical angle for an air-water interface is 49°, so the person will see the upwards view compressed into a 49° circle.

Total Internal Reflection; Fiber Optics
Binoculars often use total internal reflection; this gives true 100% reflection, which even the best mirror cannot do. Figure Total internal reflection of light by prisms in binoculars.

Total Internal Reflection; Fiber Optics
Optical fibers also depend on total internal reflection; they are therefore able to transmit light signals with very small losses. Figure Light reflected totally at the interior surface of a glass or transparent plastic fiber.

ConcepTest 32.4a Refraction I
Parallel light rays cross interfaces from air into two different media, 1 and 2, as shown in the figures below. In which of the media is the light traveling faster? 1) medium 1 2) medium 2 3) both the same 1 air air Answer: 1 2

ConcepTest 32.4a Refraction I
Parallel light rays cross interfaces from air into two different media, 1 and 2, as shown in the figures below. In which of the media is the light traveling faster? 1) medium 1 2) medium 2 3) both the same The greater the difference in the speed of light between the two media, the greater the bending of the light rays. 1 air air 2 Follow-up: How does the speed in air compare to that in #1 or #2?

ConcepTest 32.4b Refraction II
1) n1 > n2 > n3 2) n3 > n2 > n1 3) n2 > n3 > n1 4) n1 > n3 > n2 5) none of the above Parallel light rays cross interfaces from medium 1 into medium 2 and then into medium 3. What can we say about the relative sizes of the index of refraction of these media? 1 3 2 Answer: 5

ConcepTest 32.4b Refraction II
1) n1 > n2 > n3 2) n3 > n2 > n1 3) n2 > n3 > n1 4) n1 > n3 > n2 5) none of the above Parallel light rays cross interfaces from medium 1 into medium 2 and then into medium 3. What can we say about the relative sizes of the index of refraction of these media? The rays are bent toward the normal when crossing into #2, so n2 > n1. But rays are bent away from the normal when going into #3, so n3 < n2. How to find the relationship between #1 and #3? Ignore medium #2! So the rays are bent away from the normal if they would pass from #1 directly into #3. Thus, we have: n2 > n1 > n3 . 1 3 2

ConcepTest 32.5a Gone Fishin’ I
To shoot a fish with a gun, should you aim directly at the image, slightly above, or slightly below? 1) aim directly at the image 2) aim slightly above 3) aim slightly below Answer: 3

ConcepTest 32.5a Gone Fishin’ I
To shoot a fish with a gun, should you aim directly at the image, slightly above, or slightly below? 1) aim directly at the image 2) aim slightly above 3) aim slightly below Due to refraction, the image will appear higher than the actual fish, so you have to aim lower to compensate.

ConcepTest 32.5b Gone Fishin’ II
To shoot a fish with a laser gun, should you aim directly at the image, slightly above, or slightly below? 1) aim directly at the image 2) aim slightly above 3) aim slightly below Answer: 1

ConcepTest 32.5b Gone Fishin’ II
To shoot a fish with a laser gun, should you aim directly at the image, slightly above, or slightly below? 1) aim directly at the image 2) aim slightly above 3) aim slightly below laser beam light from fish The light from the laser beam will also bend when it hits the air-water interface, so aim directly at the fish.

ConcepTest 32.6 Parallel Lines
1) shifted to the right 2) shifted to the left 3) spaced farther apart 4) spaced closer together 5) no change – same as before An observer views two closely spaced lines through an angled piece of glass. To the observer, the lines appear: Answer: 2

ConcepTest 32.6 Parallel Lines
1) shifted to the right 2) shifted to the left 3) spaced farther apart 4) spaced closer together 5) no change – same as before An observer views two closely spaced lines through an angled piece of glass. To the observer, the lines appear: The light rays get refracted twice, so they remain parallel, but they shift to the left, as seen in the figure. Their relative spacing does not change, just the overall position. Follow-up: What happens when the top glass moves toward the bottom glass?

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