Reflection of a reflection (TPR Physics passage 55))

[ModerateMouse]

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If light from a light source is reflected in one mirror (P), and then this reflection is reflected in another (M), at what distance behind the second mirror will the light source appear to be to an observer?

My reasoning:

1)to someone looking at mirror P, the object appears a distance a behind it.
2)this image is then reflected in M, and now appears L+a+a behind this mirror

TPR says that "seen trough the eyepiece, the light source will appear to be located at a distance of L+a behind Mirror M."

(mirror P is 'partially silvered', so light coming up is reflected but light returning from M passes through to the eyepiece)

Here is a link to a website using my method for locating images in a 2 mirror system.

 

[TieuBachHo]

The eyepiece is located BEHIND the mirror P, you can not see its reflection on P. This is actually only one mirror problem, not two. It's a trick to get you to think that there are two. Your eye can only see the real reflection of the light source behind the mirror M which is L+a.

 

[ModerateMouse]

Sorry, I don't think that I get it.

What exactly is reflected in M?
Isn't the reflection from P reflected in M?

 

[tartrate]

Sorry, I don't think that I get it.

What exactly is reflected in M?
Isn't the reflection from P reflected in M?

Bold and underlined explains the answer choice.

To simplify, we know image distance is equal to object distance for plane mirrors. Here, we can treat the object as P, and P's distance from M is L+a, so that answers, "what distance behind the second mirror will the light source appear to be to an observer?" What is in quotes really just refers to the image distance.

Another way to look at is, think of a single plane mirror system. We treat the object distance as light being "emitted" from the object and hitting the surface of the mirror, but in reality the object is like a mirror in itself, receiving light from your lamp or the sun, and reflecting that light into the mirror. So in our case here, P in effect is doing the same thing.

 

[lixxx669]

If light from a light source is reflected in one mirror (P), and then this reflection is reflected in another (M), at what distance behind the second mirror will the light source appear to be to an observer?

My reasoning:

1)to someone looking at mirror P, the object appears a distance a behind it.
2)this image is then reflected in M, and now appears L+a+a behind this mirror

TPR says that "seen trough the eyepiece, the light source will appear to be located at a distance of L+a behind Mirror M."

(mirror P is 'partially silvered', so light coming up is reflected but light returning from M passes through to the eyepiece)

Here is a link to a website using my method for locating images in a 2 mirror system.

The graph is a little bit confusing, what's the distance between M and P? L or L+a??