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The figures compare the working of a lawn mower to that of the refraction phenomenon. In figure (a) the lawn mower goes from a sidewalk to grass, it slows down and bends towards a perpendicular drawn at the point of contact of the mower with the surface of separation. An imaginary line along the mower when it is on sidewalk is taken to be the incident ray and the angle which the mower makes with the perpendicular is taken to be theta one. As it goes into the grass, the mower turns and the imaginary line moves towards the perpendicular line drawn and makes an angle theta two with it. The imaginary line drawn along the mower when the mower is in the grass is taken to be the refracted ray. Sidewalk is taken to be a medium of refractive index n one and that of grass to be taken as n two. In figure (b), the situation is the reverse of what has happened in figure (a). The mower moves from grass to sidewalk and the ray of light moves away from the perpendicular when it speeds up.
The change in direction of a light ray depends on how the speed of light changes when it crosses from one medium to another. The speed of light is greater in medium 1 than in medium 2 in the situations shown here. (a) A ray of light moves closer to the perpendicular when it slows down. This is analogous to what happens when a lawn mower goes from a footpath to grass. (b) A ray of light moves away from the perpendicular when it speeds up. This is analogous to what happens when a lawn mower goes from grass to footpath. The paths are exactly reversible.

The amount that a light ray changes its direction depends both on the incident angle and the amount that the speed changes. For a ray at a given incident angle, a large change in speed causes a large change in direction, and thus a large change in angle.

Take-home experiment: a broken pencil

A classic observation of refraction occurs when a pencil is placed in a glass half filled with water. Do this and observe the shape of the pencil when you look at the pencil sideways, that is, through air, glass, water. Explain your observations. Draw ray diagrams for the situation.

Section summary

  • The changing of a light ray’s direction when it passes through variations in matter is called refraction.
  • The speed of light in vacuum c = 2 . 9972458 × 10 8 m/s 3 . 00 × 10 8 m/s . size 12{c=2 "." "9972458" times "10" rSup { size 8{8} } " m/s" approx 3 "." "00" times "10" rSup { size 8{8} } " m/s"} {}
  • Index of refraction n = c v size 12{n= { {c} over {v} } } {} , where v size 12{v} {} is the speed of light in the material, c size 12{c} {} is the speed of light in vacuum, and n size 12{n} {} is the index of refraction.

Conceptual questions

Diffusion by reflection from a rough surface is described in this chapter. Light can also be diffused by refraction. Describe how this occurs in a specific situation, such as light interacting with crushed ice.

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

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.

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

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?

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.

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.

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?

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

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

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

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"} {} ?

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"} {}

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"} {}

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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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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