How Far Are the Closest Four Images of the Candle in the Mirrored Room?

[meiler01]

Homework Statement

A student is standing in the middle of a room with two opposite walls that are separated by 10.0m and covered by plane mirrors. There is a candle in the room 1.5m from one mirrored wall (from the left wall). The student is facing the opposite (right) mirrored wall and sees many images of the candle. How far from the student are the closest four images of the candle that he/she can see?

Homework Equations

Distance of object= distance of image

The Attempt at a Solution

If the student is 5m from the right mirror, the candle is 8.5m from the right mirror; therefore, and image must be 8.5m behind the mirror. Add this to the 5m distance from the mirror to the student= 8.5 + 5 = 13.5m from the student

Also, the candle is 1.5m from the left mirror, which is 5m behind the student. If the image is 1.5m behind the mirror, it is 1.5m + 5 m = 6.5m behind the student. Since the student is 5m from the right mirror (she faces the right mirror), does she see the image an additional 6.5m behind the right mirror, thus 5+ 6.5m= 11.5m? Or do I need to add another 6.5 to account for the distance behind her = 6.5 + 6.5 + 5 = 18m?

I'm not sure of my logic thus far, and am therefore unsure of how to proceed for distances 3 and 4. Is this on the right track? How do I approach the additional images?

Thanks!

 

[ideasrule]

I'm not quite sure why you're adding 6.5 again, but the question only asks for images made by reflecting through the right mirror. Images formed in the left mirror don't count because the student can't see them.

Think about the problem this way: every image formed by every mirror acts exactly like a real candle, except that its light can pass through a mirror. The first image formed by the left mirror, for example, can be treated as a real candle being reflected by the right mirror, except that the candle's rays can pass through the left mirror unimpeded.