Geometric Optics problem!

by blumfeld0
Tags: geometric, optics
blumfeld0 is offline
Apr30-08, 12:29 AM
P: 148
1. The problem statement, all variables and given/known data
If a plane mirror is hung at an angle of 30 degrees from the vertical toward the viewer. what is the minimum length that will allow the viewer to see the full body image if the line of vision can not be depressed below the horizontal. you may assume that the eyes are at the top of your head.

2. Relevant equations

3. The attempt at a solution

I have done a very similar problem where I know the height of the person. in that problem we did NOT assume that the eyes were on top of the head.
then the minimum length i need for the PLANE FLAT mirror (not tilted at an angle of 30 degrees) is HALF the height of the person.
so if the height of the person was 2 ft then the minimum length we need would be 1 ft for the mirror to see the full image of the person.

so my question is in this problem the mirror is tilted by 30 degrees. how does affect anything??
i do not think it does but i can not prove. i THINK the answer should still be half the height of object (person) but i might be wrong.

any ideas or solution so i can understand.

thank you
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blumfeld0 is offline
Apr30-08, 07:31 PM
P: 148
After taking to someone they said that the 30 degrees will make a difference? That is counter to what I thought.
So I am guessing that the minimum length of the mirror will be

L = (2/Sqrt[3]) * height of person

I used Cos[30]= height/Length of mirror

is that even close?
if not any suggestions would be greatly appreciated

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