Image created by concave mirror, sight from a distance.

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rcmango
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Homework Statement



A science museum has created a huge concave mirror with a focal length of 5 m, and mounted it so that it covers the entire wall at one end of a long hallway. If you stand on a center line painted down the middle of the hallway, you're on the mirror's principal axis. You and a friend are standing on the center line, you're 8 m from the mirror, and your friend is 20 m from it. Can both you and your friend see the image of you created by the mirror? Explain.


Homework Equations



1/f-1/do = 1/di

The Attempt at a Solution



I will be standing to close to the mirror to see myself, my friend can see me and himself in the mirror though.

f is the focal length. (5m)
do: will be the distance between the mirror and me.
di: is the actual image from the mirror.

so 1/f = 1/di + 1/do (whats the name of this equation?)

solve for the image distance, di

1/f-1/do = 1/di

(f*do)/(do-f) = di
..5m*8m/(8-5) = 13.33333333_ m.

13.3 repeating meters is farther away than I'm standing, but definitely closer than what my friend is standing of 20 meters.
So he can see me and himself in the mirror.

If he can see me, than he should be able to see himself.
Is there a way to prove this without actually calculating his distance out using the formula above?
 
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rcmango said:
13.3 repeating meters is farther away than I'm standing, but definitely closer than what my friend is standing of 20 meters.
So he can see me and himself in the mirror.
So he can see you and your image. But can you see your own image? Can he see his own image?

If he can see me, than he should be able to see himself.
Why is that?
Is there a way to prove this without actually calculating his distance out using the formula above?
No. Use the formula to find the location of his image.
 
using (f*do)/(do-f) = di
5m*20m / 5m-20m = 6.25m

So he would be able to see himself because his image is in between the mirror and him. So is my image, its in between him and the mirror. However, I can't see myself because my image reflection is shown past where I'm standing.
 
rcmango said:
So he would be able to see himself because his image is in between the mirror and him. So is my image, its in between him and the mirror. However, I can't see myself because my image reflection is shown past where I'm standing.
Good!
 
Okay, so a counter question is this, why can't I turn around and see my image?
You're definitely free to turn around, but why won't that help you see your image?

another tutor asked me this. I was dumbfounded because I thought I was facing the mirror to begin with. So, help please.
 
rcmango said:
Okay, so a counter question is this, why can't I turn around and see my image?
You're definitely free to turn around, but why won't that help you see your image?

another tutor asked me this. I was dumbfounded because I thought I was facing the mirror to begin with. So, help please.

Where is the light coming from? Where is the light going to [If you can see it]?
 
Hmm, so your asking if perhaps I could see my image? Then the light would be going towards me, at me, but that is not happening?
 
rcmango said:
Hmm, so your asking if perhaps I could see my image? Then the light would be going towards me, at me, but that is not happening?

True