19.21 Refraction

fig1

If you shine a laser pointer from air into a denser medium (like glass or water), the beam is bent – as shown in the picture above. This bending of light, as it passes from one medium to another, is called refraction.

It’s easy to see refraction using a laser pointer because it produces a clearly defined beam of light. But, if you want to see this for yourself, read about possible dangers in post 19.20.

Refraction can be explained by light being propagated as waves, as was diffraction in post 19.20. But, before we see the explanation, we need to know about some more experimental observations.

fig2

In the picture above, a dashed line has been drawn perpendicular to the interface between air and glass. The angle that the beam in air makes with this line is called the angle of incidence, θi. The angle that the beam in glass makes with this line is called the angle of refraction, θr. For any pair of media (like air and glass) sinθi/sinθr is a constant. In the example shown here, this constant is called the refractive index of glass in air.

fig3

The table above lists some values of the refractive index, n, for different media in air.

fig4

Now let’s try to explain refraction by assuming that light is propagated as waves (posts 19.9 and 19.20). The picture above shows a beam of light whose width is AB. In this picture, AB represents the wave-front at an instant in time; the wave-front at A meets the interface before the wave-front at B. The wave-front at B meets the interface, at C, some time, t, later. The length BC is given by tcair, where cair is the speed of light in air. While the wave-front moves from B to C in air, it moves from A to D in glass. The length AD is given by tcglass, where cglass is the speed of light in glass. If the waves move more slowly in glass than in air, the beam of light must bend, as shown in the picture, because AD is shorter than BC.

By definition, the wave-front AB is perpendicular to the direction of propagation, BC. The dashed line is perpendicular to the interface. So, if BC makes an angle of θi with the dashed line, the angle BCA must be 90oθi. Since the length of BC is tcair, the length of AC is tcair/cos(90oθi) = tcair/sinθi (see post 16.50). A similar argument shows that the length of AC is also given by tcglass/sinθr. So, assuming that light is propagated as waves, we predict that

tcair/sinθi = tcglass/sinθr.

Dividing both sides of this equation by tcglass/sinθr gives the result that

cair/cglass = sinθi/sinθr = n.

The final step comes from the definition of n.

So, if light is propagated as waves, we can explain how refraction occurs. We also predict that the refractive index of glass in air is equal to the speed of light in air divided by the speed of light in glass.  This prediction can be confirmed experimentally, providing further evidence that light is propagated as waves.

 

Related posts

19.20 Diffraction – light is propagated as waves
19.9 Electromagnetic waves
18.10 Waves

 

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