Standing Between 2 Plane Mirrors

[Neophyte7]

If I stand between two plane mirrors on opposite walls in a room, I observe multiple images. When I stand 5 m from the mirror on the left wall, and 10 m from the mirror on the right wall, what are the distances (in meters) from me to the first three images seen in the mirror on the LEFT?

I know how to calculate the distance of an object with one mirror, but two throws me off because of the multiple reflections. My teacher hasn't discussed this and I can't find anything like it in my textbook.

Can anyone help?

 

[HallsofIvy]

Just do it "one step at a time". Since you are 5 m from the mirror on the left, the "first" image in that mirror is 5 m "inside" the mirror and so 10 m from you. Since you are 10 m from the mirror on the right, the first image in that mirror is 10 m "inside" that mirror and so 20 m from you and 25 m from the mirror on the left. Therefore the "second" image in the mirror on the left is 25 m "inside" that mirror. Etc.

 

[Neophyte7]

Thanks! That made sense when you broke it down like that.