# Bathroom Optics

1. Jul 28, 2009

### YellowPeril

This is a picture of me in my bath. (dont worry, it is purely diagramatic!). I face a wall to the front of the bath. There is also a wall to the left hand side of me. Both with shiny tiles. Their is a light above me and slightly behind to my right. While relaxing, I took note of the light bulb reflections on the wall and it's geometry (using the reflection of the front wall tiles on the left side wall as a coordinate reference point). What I noticed I cant explain precisely. The light reflects onto the front wall and I see the reflection. Using the tiles as coordinates, the first reflection is about a distance of three tiles to the right. When I look to my left I see the light reflection of the front wall reflected as a second reflection on the left wall. I also see the front wall tiles reflected on the left wall. What puzzles me is that the second reflection now falls on the second tile instead of the first. (See diagram). Can you explain this.

To put the problem more succinctly, the first reflection is coincident with a point which has a x cartesian coordinate of three (Third tile). The third tile also has a x cartesian coordinate of three. However on the reflection the third tile has a x cartesian coordinate of three but the x cartesian coordinate of the lights second reflection is 2. I.e. Two points that were coincident are no longer coincident.

(Is the difference due to the fact that the tile point is reflected only once while the light it reflected twice?)

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• ###### Bath.bmp
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2. Jul 28, 2009

### negitron

Parallax--remember that the images of the light are not ON the surface of the reflecting tiles, but some distance behind it. Your point of observation is not directly flat against the wall to your left; if it were, the images would line up the way you expect. Try it.