Two parallel mirrors are separated by a certain distance

[november1992]

Homework Statement

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

Homework Equations

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.

 

[haruspex]

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

 

[november1992]

What is d_n?

 

[haruspex]

What is d_n?

My post was defining d_n to be the distance behind mirror 1 of its n^th image.

 

[november1992]

Your explanation confused me, but I got the answer right answer. I'm not sure why though.

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.

 

[haruspex]

Your explanation confused me

Then I'd better try to unconfuse you.
Let d_n to be the distance behind mirror 1 of its n^th 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.