Infinite Number of Image Charges?

[bob012345]

Consider two opposing mirrors. If they are exactly parallel planes I think there is only a single image in each but if they are slightly angled there appears an "infinite" number of reflections. Similarly, suppose we have grounded conducting planes instead of mirrors with a charge in between them. I think if they are perfectly parallel there are exactly two image charges. But if they are slightly misaligned will there be an multiple series of image charges appearing to go to infinity? If so, will the actual number of images depend on the angle? Thanks.

p.s. Now I'm not sure if there are or aren't an infinite number of images when mirrors are exactly parallel. I can't see them since my own image blocks them.

p.s.2 On further reflection...Of course there must be.

 

[.Scott]

There are a seemingly infinite number of images whether or not the mirrors are parallel.
If you are looking straight into one of those mirrors, your first image will completely hide the others.
But stick your hand out to the side (with your arm bent - as if you were waving to yourself) and try counting how many images of your hand there are.

 

[Mister T]

Like a seeming infinite number of images occur in opposing mirrors, does a similar situation occur with opposing infinite grounded, conducting planes with a charge in between them?

Yes. It's called the method of images. (A far less known but similar method of images exists in magnetostatics.)

In both of your cases one gets images of images ad infinitum.

 

[bob012345]

Thanks. So for two perfectly parallel grounded, conducting planes with a charge in between, the number of image charges is infinite and any forces on the real charge cancel out. If the planes are angled the number of images is finite and should be dependent on the angle and there would be a net force on the charge acting towards the intersection of the two planes just as there is a force when a single charge is located near a single plane.