What Is the Minimum Height of a Rear-View Mirror to See the Entire Rear Window?

[sweetgirl86]

I have been trying to solve this problem using many equations, but am not getting the right answer. I guess I'm not using the right formula because I don't know it. Can someone please help.

The rear window in a car is approximately a rectangle, 1.17 m wide and 0.160 m high. The inside rear-view mirror is 0.600 m from the driver's eyes, and 1.23 m from the rear window. What is the minimum height of the rear-view mirror if the driver is to be able to see the entire height of the rear window in the mirror without moving her head?
do: 1.23m
di: 0.600m
ho: 0.160m
hi: ?

hi = (di/do)ho = (0.600/1.23)0.160m = 0.0780m

 

[sweetgirl86]

This is how i tried to solve it:

do: 1.23m
di: 0.600m
ho: 0.160m
hi: ?

hi = (di/do)ho = (0.600/1.23)0.160m = 0.0780m

 

[Farsight]

This sounds like triangles and simple ratios, sweetgirl. Unfold the reflection, then you've got a triangle .6m long within a triangle 1.23m + .6m long. Do you know if the first answer is

.16 x .6 / 1.83 = .05245

 

[Gokul43201]

This is how i tried to solve it:

do: 1.23m
di: 0.600m
ho: 0.160m
hi: ?

hi = (di/do)ho = (0.600/1.23)0.160m = 0.0780m

Where does this equation come from? It is wrong.

If you draw a diagram and identify the correct similar triangles, you will get the correct formula.

Physics is not about trying different formulas and hoping one of them works. It is about arriving at the correct formula by a combination of math and a knowledge of the fundamental principles.

In this case, since the rear-view mirror must be assumed to be planar, the principle that is relevant is the relationship between the angle of incidence and reflection. From there, it's just a geomtry problem.

Can you draw a diagram, label the various points and find the relationship from there? Have you come across the simpler problem where you are asked to find out how tall a mirror you need to completely view yourself? If not, it might be instructive to first attempt this simpler problem before going on to the one you have.

 

[sweetgirl86]

Thank You so much. I tried solving it the triangle way and go the right answer. And yes that's the right answer farsight. Thank you all so much. I solved the second part by myself :-).