Calculating a Mirror's Reflection

Date: 08/08/99 at 18:30:58
From: Brandon
Subject: Optics: find angle and point P

If you shine a light on a mirror to illuminate an object (<1 = <2), 
show how to find point P.

     object .        |
              \      |
                \ <1 |
                  \  |
                    \|P
                    /|
                  /  |
                /  <2|
        light /      | 
                   mirror

Date: 08/09/99 at 03:43:21
From: Doctor Floor
Subject: Re: Optics: find angle and point P

Hi, Brandon,

Thanks for your question.

Let's suppose that you are given the position of the light, the 
object, and the mirror.

Bring the object over to the position of its reflection in the mirror: 
drop the perpendicular altitude from the object to the mirror, and 
then make the altitude segment twice as long. Then draw a segment from 
the reflection of the object to the light. Of course the light should 
be shining straight to the reflection of the object. The segment meets 
the mirror at the point P you are looking for.

     object .        |        . reflection of object
              \      |      /
                \    |    /
                  \  |  /
                    \|/
                    /|P
                  /  |
                /    |
        light /      |
                   mirror


If you need more help, just write us back.

Best regards,
- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/