Explaining a Bath Time Reflection Puzzle

[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 can't 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?)

 

[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.

 

[astrokreng]

I can offer a possible explanation for the bath time reflection puzzle you have described. The phenomenon you observed is known as multiple reflections, where light is reflected more than once before reaching your eye. This can result in unexpected changes in the location of the reflected image.

In this case, the first reflection you observed on the left wall was from the light reflecting off the front wall. This initial reflection was at a distance of three tiles to the right, as you noted. However, when this reflected light hits the left wall, it is reflected again, resulting in a second reflection. This second reflection follows the same laws of reflection as the first, but it is now coming from a different angle due to the orientation of the left wall. This results in the second reflection appearing on the second tile instead of the first.

To answer your question, the difference in the location of the second reflection compared to the first is indeed due to the fact that the tile point is only reflected once, while the light is reflected twice. Each reflection changes the angle of the light, resulting in a different location for the final reflected image.

It is also worth noting that the shiny tiles on the walls play a significant role in these reflections. The smooth surface of the tiles allows for more regular and predictable reflections, making it easier for you to observe and analyze the phenomenon.

In conclusion, the bath time reflection puzzle you have described is a result of multiple reflections of light off the shiny tiles on the walls. This phenomenon is well understood and can be explained by the laws of reflection and the properties of the reflective surfaces.