Parabolic Mirrors/Whispering Gallery

Parabolic Mirrors/Whispering Gallery:

Waves emitted from a wave source travel outward in all directions. For example, the light from a candle or light bulb travels outward in all directions (which is why you can see it from whichever direction you are standing to look at it). The same is true for sound waves, which is why you can hear your friend speaking at any point as you walk around her.

(A sketch of circular wavefronts around a source…)

As we get further away from the wave source, the strength, or intensity, of the waves decreases. The waves are spreading out. This is why a light bulb appears fainter as you walk away from it, and why it is harder to hear your teacher if you are at the back of the classroom rather than the front.

You will perhaps be familiar with concave mirrors, which focus incoming light waves. We can use a certain shape of concave mirror to focus waves from a distant source back to a point – this is a parabolic mirror.

(A sketch of focusing of light rays goes here…)

We can use this property in an interesting way, by placing two parabolic mirrors facing each other, and by putting a light or sound source at the focus of one of them. The waves from the source are initially emitted in all directions, but those that are reflected from the mirror subsequently travel in a roughly parallel track. By placing a second parabolic mirror some distance away in the path of these waves, we can refocus them back to a point.

(A sketch of both mirrors and the rays goes here…) In this way, we can collect and concentrate a sizeable fraction of the waves emitted by the source (and the energy they carry) at our second focus point. With sound waves, this allows one person speaking at the focal point of our first reflector to be clearly heard by a friend standing at the focal point of the second reflector, even if they are separated by a large distance. Someone walking between the two friends would probably not be able to hear their conversation since the sound waves are spread out at this point (look how far apart the rays are on the drawing above). This has been called a Whispering Gallery, and allows you to speak to someone a large distance away without other people overhearing you! We can do a similar thing with light waves, by putting a light bulb at the focus of our first mirror, and using the energy of the light focused at the second mirror to light a match!

This is a nice example of the application of the laws of reflection for waves.