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posted by  cstina on 7/8/2008 8:56:44 PM  |  status: Live  

mirror problem - DUE TOMORROW!

Course Textbook Chapter Problem
Algebra Based Physics Physics (3rd) by Walker 26 12P
Question Details:
The rear window in a car is approximately a rectangle, 1.3 meters wide and .30 meters high. The inside rearview mirror is a .50 m from the drivers eyes, and 1.5 meters from the rear window. What are the minimum dimensions for the rearview mirror if the driver is to be able to see the entire width and height of the rear window in the mirror without moving her head?
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posted by Cdutch88 on 7/8/2008 9:16:27 PM  |  status: Live
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cstina's comment:
"thanks!"
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Looking at the diagram, you can see that the reflection of the window in the mirror will appear 1.5+0.5 = 2.0 meters in front of the driver.

The smallest dimensions of the rearview mirror will enable the driver to just barely see the left side of the reflection of the mirror when she looks in the left side of the mirror. Similarly, the driver will just barely see the top of the reflection of the mirror when she looks in the top of the mirror and so on for all four sides. Thus, for each of these sides, you can picture a triangle within a triangle, creating two similar triangles. The length of the rearview mirror is the length of the smaller base and the length of the window is the length of the larger base. Using the properties of similar triangles, you can see that since
height1/height2 = base1/base2,
0.5/2.0 = width1/1.3 => 0.325 meters
0.5/2.0 = height1/0.30 => 0.075 meters


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posted by jecstir on 7/8/2008 9:16:44 PM  |  status: Live
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cstina's comment:
"thanks!"
Response Details:
draw a triagle ... with the eye in the center of the mirror
 
ok so the equation should be for the width an comarison relating the distances... 1.5/1.3=.5/x
which is half of the mirror.... which is .433333.... so the width should be .86666m
same with the height....
1.5/.3=.5/x
=.1m that is the height of half of it.... which is .2 meters for the entirety
that seems excesive for the lengths of a rear view mirror.... maybe the factor of 2 is wrong...
it is either .4333 or .8666
but whatever the case.... the angle of refraction is the same as the angle of reflection... meaning whatever angle you look at a mirror... the light you see will be coming 2 times that angle..... like an isoceleleleles triangle .... so if you were looking at the mirror from the bottom left corner... then you would not multiply the numbers by two... but if you were looking from the center of the mirror you would
...rate plz!
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