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Old Aug 27th 2010, 07:12 AM   #1
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Image of your toes.

It is 160cm from your eyes to your toes. You're standing 200cm in front of a tall mirror. How far is it from your eyes to the image of your toes?

I haven't had to think about physics in years. Could someone please explain the answer and how to get it? Thank you.

I'm trying to use trig functions to figure it out but I feel that as usual, I'm making this tougher than it is. I only have one angle at 90 and two side lengths so i'm not sure where to go from there.

Last edited by rms390; Aug 27th 2010 at 07:14 AM.
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Old Sep 18th 2010, 03:53 PM   #2
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Originally Posted by rms390 View Post
It is 160cm from your eyes to your toes. You're standing 200cm in front of a tall mirror. How far is it from your eyes to the image of your toes?

I haven't had to think about physics in years. Could someone please explain the answer and how to get it? Thank you.

I'm trying to use trig functions to figure it out but I feel that as usual, I'm making this tougher than it is. I only have one angle at 90 and two side lengths so i'm not sure where to go from there.
It's not all that hard. For you to see an image of your toes in the mirror, light must go from your toes to the mirror and back to your eyes. The "physics" information needed here is that the light will make the same angle with the mirror both "coming" and "going". so you have an isosceles triangle. If you draw a line from the image of your toes perpendicular to your body, it strikes your body exactly half way between your toes and your eyes and makes a right triangle. You don't need trig functions, just the Pythagorean theorem. The "distance from your eyes to the image" (which is the same as the "distance from your toes to the image") is the length of the hypotenuse where the two legs have lengths 200cm (from your body to the mirror) and 80 cm (half the distance from your toes to your eyes). $\displaystyle c^2= 200^2+ 80^2$.
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Old Sep 22nd 2010, 09:07 AM   #3
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actually, the image is formed behind the mirror (not in the mirror) so the distance is twice what HallsofIvy said
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