Light: Reflections and Phases

Reflections at the interface between media often produce phase differences, whereas transmission occurs with no change of phase. Here we begin by looking a reflections in one dimension using strings, then show the analogous behaviour of light reflected at an interface between media with different refactive indices. This page supports the multimedia tutorial Interference.

light reflected and refracted at glass-air interface

Reflection and transmission in one dimension

Let's begin by revising reflections in one dimension using waves in strings. (You may wish to revise the multimedia tutorial Travelling Waves I.) These film clips show a transverse pulse travelling from light to heavy string (left) and heavy to light (right).

Left: a wave pulse travelling from a light string (low mass per unit length, μ) to heavy string (high μ). Right: from heavy to light string.

For the wave travelling from the light string towards the heavy, we see that the reflected wave has a phase change of π. Going from heavy towards light, the phase change of the reflected pulse is zero. In both cases, the transmitted wave has no phase change.

Further, look at the wave speed. In both cases, the tension F in both strings was the same (10 newtons). The speed of the wave in a string is (F/μ)1/2 so the string with low μ therefore has a higher wave speed.

Reflection and refraction (transmission) of light

Here a ray of light in air meets the interface with glass. Part of the incident energy is reflected and part is refracted. What do we expect for the phases here?

The refractive index for glass is very nearly 1. That for glass is somewhat higher: n ~ 1.5 here. (See Geometrical optics for an introduciton.) So the speed of light in glass (by definition c/n) is slower than that in air. Glass is analogous to the heavy string in the clips above.

So, going from air towards glass (low n towards high n), we expect light to be reflected with a phase change of π. Going from glass towards air, we expect reflection with a phase change of zero. And, in both cases, the transmitted wave has a phase change of zero.

(Although we don't show it here, we also get these predictions for the phases by imposing the boundary conditions on the electric field and displacment at the interface: the speed of light is slower in glass because its dielectric permettivity is higher.)

Before we test these predictions, let's look at the wave behaviour in the following animations.

 

Wave animation: air towards glass

Wave animation: air towards glass

Note that, in glass, the speed of light is slower (n higher) than in air. At the interface, the oscillation in the fields has the same frequency so both waves have the same frequency. Therefore the wavelength in glass is smaller. The transmitted wave has no phase change, but the wave reflected in air has a phase change of π. (See Geometrical optics for futher discussion of reflection, refraction and phases.)

Wave animation: glass towards air

Wave animation: glass towards air

The wave transmitted from glass to air has no phase change, and neither does the reflected wave.

Does it work? and Further information

Reflections in strings and in optical media are mathematically analogous: Newton's laws for the string and Maxwell's equations for light. But the ultimate test is of course experiment. We can use the reflection conditions discussed here to predict the interference patterns that would be produced by reflection under different conditions and see whether that confirms or disproves the hypothesis. Here are examples:
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