### Mirrors and time

Type of mirror:

In this alternate version of the simulation, you can drag the tip of the object (red arrow) to change the object height and object distance, and you can drag the focal point (filled circle) to adjust the focal length.

This simulation builds on the simulation about ray diagrams and image formation using a mirror. In that simulation, it is not clear that time has any role to play in image formation. This simulation makes clear that time actually has a pretty important role.

A wavefront is sent out from the object - it is shown in red. (A wavefront consists of all points emitted by the object at the same time.) The wavefront heads over to the mirror, and reflects off the mirror. The mirror re-shapes the wavefront into another wavefront centered not on the tip of the object, but centered on the tip of the image. In the case of a real image, that wavefront then converges onto the tip of the image - each point on the wavefront reaches the image at the same time. This tells us that the light traveling from the tip of the object to the tip of the image via the mirror all takes the same amount of time, no matter which point on the mirror it reflected from. That's another way to define the image point - it's the only point in space for which light going from the tip of the object to the tip of the image via the mirror takes the same time for all points on the mirror. The wavefront then continues away from the image, diverging just as light does from a real object - this is why we see the image there when we look in the mirror.

What if the image is a virtual image, rather than a real image? The situation is similar, except in that case the mirror re-shapes the wavefront so the light appears to be diverging from the tip of the image. For a virtual image, the simulation sends out a reference wavefront (in purple) from the tip of the image. For the plane mirror, the real wavefront and the virtual wavefront arrive at the mirror simultaneously, merging into one. For the diverging mirror, or for the converging mirror when it creates a virtual image, the real and virtual wavefronts do not reach the mirror simultaneously, but you should still be able to see how the mirror re-shapes the wavefront so that it is centered on the tip of the image rather than on the tip of the object.

Note that in certain cases you may see a little distortion of the wavefront, coming from spherical aberration - a spherical mirror is not actually quite the right shape to produce perfect images (the shape really should be parabolic, instead.)

Simulation first posted on 3-5-2018. Written by Andrew Duffy