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Why is the index of refraction always greater than or equal to 1?

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Does the fact that the light flash from lightning reaches you before its sound prove that the speed of light is extremely large or simply that it is greater than the speed of sound? Discuss how you could use this effect to get an estimate of the speed of light.

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Will light change direction toward or away from the perpendicular when it goes from air to water? Water to glass? Glass to air?

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Explain why an object in water always appears to be at a depth shallower than it actually is? Why do people sometimes sustain neck and spinal injuries when diving into unfamiliar ponds or waters?

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Explain why a person’s legs appear very short when wading in a pool. Justify your explanation with a ray diagram showing the path of rays from the feet to the eye of an observer who is out of the water.

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Why is the front surface of a thermometer curved as shown?

A triangular shaped transparent thermometer is shown.
The curved surface of the thermometer serves a purpose.
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Suppose light were incident from air onto a material that had a negative index of refraction, say –1.3; where does the refracted light ray go?

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Problems&Exercises

What is the speed of light in water? In glycerine?

2 . 25 × 10 8 m/s size 12{2 "." "25" times "10" rSup { size 8{8} } " m/s"} {} in water

2 . 04 × 10 8 m/s size 12{2 "." "04" times "10" rSup { size 8{8} } " m/s"} {} in glycerine

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What is the speed of light in air? In crown glass?

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Calculate the index of refraction for a medium in which the speed of light is 2 . 012 × 10 8 m/s size 12{2 "." "012"´"10" rSup { size 8{8} } " m/s"} {} , and identify the most likely substance based on [link] .

1 . 490 size 12{1 "." "491"} {} , polystyrene

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In what substance in [link] is the speed of light 2 . 290 × 10 8 m/s size 12{2 "." "290"´"10" rSup { size 8{8} } " m/s"} {} ?

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There was a major collision of an asteroid with the Moon in medieval times. It was described by monks at Canterbury Cathedral in England as a red glow on and around the Moon. How long after the asteroid hit the Moon, which is 3 . 84 × 10 5 km size 12{3 "." "84"´"10" rSup { size 8{5} } " km"} {} away, would the light first arrive on Earth?

1 . 28 s size 12{1 "." "28"" s"} {}

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A scuba diver training in a pool looks at his instructor as shown in [link] . What angle does the ray from the instructor’s face make with the perpendicular to the water at the point where the ray enters? The angle between the ray in the water and the perpendicular to the water is 25 . size 12{"25" "." 0°} {} .

A scuba diver and his trainer look at each other. For the trainer, the scuba diver appears less deep than he actually is, and to the diver, the trainer appears much higher than she actually is. To the trainer, the scuba diver's feet appear to be at a depth of two point zero meters. The incident ray from the trainer strikes the water surface at a point, the point of incidence, and the trainer is at a horizontal distance of two point zero meters from a perpendicular drawn at the point of incidence.
A scuba diver in a pool and his trainer look at each other.
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Components of some computers communicate with each other through optical fibers having an index of refraction n = 1 . 55 size 12{n=1 "." "55"} {} . What time in nanoseconds is required for a signal to travel 0.200 m through such a fiber?

1.03 ns size 12{ {}=1 "." "03"" ns"} {}

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(a) Using information in [link] , find the height of the instructor’s head above the water, noting that you will first have to calculate the angle of incidence. (b) Find the apparent depth of the diver’s head below water as seen by the instructor.

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Suppose you have an unknown clear substance immersed in water, and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of 45 . size 12{"45" "." 0°} {} , and you observe the angle of refraction to be 40 . size 12{"40" "." 3°} {} . What is the index of refraction of the substance and its likely identity?

n = 1 . 46 size 12{n=1 "." "46"} {} , fused quartz

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On the Moon’s surface, lunar astronauts placed a corner reflector, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. What percent correction is needed to account for the delay in time due to the slowing of light in Earth’s atmosphere? Assume the distance to the Moon is precisely 3 . 84 × 10 8 m size 12{3 "." "84"´"10" rSup { size 8{8} } " m"} {} , and Earth’s atmosphere (which varies in density with altitude) is equivalent to a layer 30.0 km thick with a constant index of refraction n = 1 . 000293 size 12{n=1 "." "000293"} {} .

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Suppose [link] represents a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass ( Δ x size 12{Dx} {} ), given that the incident angle is 40 . size 12{"40" "." 0°} {} and the glass is 1.00 cm thick.

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[link] shows a ray of light passing from one medium into a second and then a third. Show that θ 3 size 12{q rSub { size 8{3} } } {} is the same as it would be if the second medium were not present (provided total internal reflection does not occur).

The figure illustrates refraction occurring when light travels from medium n1 to n3 through an intermediate medium n2. The incident ray makes an angle theta 1 with a perpendicular drawn at the point of incidence. The light ray bends towards the perpendicular line making an angle theta 2 as it moves from n1 to n2. The refracted ray 1 becomes the incident ray for the second refraction at n3 and on falling on to the third medium makes an angle theta 2, and the refracted ray 2 moves away from a perpendicular drawn at the point of incidence on n3. The shift in the path of the incident ray is delta x.
A ray of light passes from one medium to a third by traveling through a second. The final direction is the same as if the second medium were not present, but the ray is displaced by Δ x size 12{Dx} {} (shown exaggerated).

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Unreasonable Results

Suppose light travels from water to another substance, with an angle of incidence of 10 . size 12{"10" "." 0°} {} and an angle of refraction of 14 . size 12{"14" "." 9°} {} . (a) What is the index of refraction of the other substance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

(a) 0.898

(b) Can’t have n < 1 . 00 size 12{n<1 "." "00"} {} since this would imply a speed greater than c size 12{c} {} .

(c) Refracted angle is too big relative to the angle of incidence.

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Construct Your Own Problem

Consider sunlight entering the Earth’s atmosphere at sunrise and sunset—that is, at a 90º size 12{"90"°} {} incident angle. Taking the boundary between nearly empty space and the atmosphere to be sudden, calculate the angle of refraction for sunlight. This lengthens the time the Sun appears to be above the horizon, both at sunrise and sunset. Now construct a problem in which you determine the angle of refraction for different models of the atmosphere, such as various layers of varying density. Your instructor may wish to guide you on the level of complexity to consider and on how the index of refraction varies with air density.

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Unreasonable Results

Light traveling from water to a gemstone strikes the surface at an angle of 80 . size 12{"80" "." 0°} {} and has an angle of refraction of 15 . size 12{"15" "." 2°} {} . (a) What is the speed of light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

(a) c 5 . 00 size 12{ { {c} over {5 "." "00"} } } {}

(b) Speed of light too slow, since index is much greater than that of diamond.

(c) Angle of refraction is unreasonable relative to the angle of incidence.

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Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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