Two parallel mirrors are separated by a certain distance

1. Nov 28, 2012

november1992

1. The problem statement, all variables and given/known data

Two parallel mirrors are separated by a distance of d = 4 meter. A point object is placed at a position a = 0.4 meter from the mirror 1.

How deep is the second image of the object in the mirror 1?

How deep is the third image of the object in the mirror 1?

http://i.imgur.com/qvb5m.png

2. Relevant equations

3. The attempt at a solution

I found the distance of the second image to be 7.6m.
Since the first image reflected on the 2nd mirror would be a distance 3.6m away, I added the distance between the second and first mirror to that distance to find the second image on the 1st mirror.

I don't know how to find the 3rd image. There was a problem like this in my class, but the object was evenly spaced between the mirrors.

Last edited: Nov 28, 2012
2. Nov 28, 2012

haruspex

If the nth image behind mirror 1 is dn behind it, how far behind mirror 2 is its n+1th image?

3. Nov 29, 2012

november1992

What is dn?

4. Nov 29, 2012

haruspex

My post was defining dn to be the distance behind mirror 1 of its nth image.

5. Nov 29, 2012

november1992

I doubled the distance from the object to the first mirror and added that to the distance of the second image from the first mirror.

6. Nov 29, 2012

haruspex

Then I'd better try to unconfuse you.
Let dn to be the distance behind mirror 1 of its nth image there. So d1 = 0.4m, right?
The reflection of this in mirror 2 will make mirror 2's second image; at what distance behind mirror 2?
Meanwhile, mirror 2's first image was how far behind mirror 2? That reflected in mirror 1 makes mirror 1's 2nd image - where? And so on.
If you work in terms of variable names rather than numbers, you should quickly see the pattern and be able to make up a formula for the position of any image.