The Mystery of 99% Reflecting Mirrors: A Physics Perspective

[naes213]

My professor today told us to think about the following situation:
If there is a 99% reflecting mirror, then if a beam of light shines on the mirror 99% of the light is reflected and 1% is transmitted. Now he says that if a second 99% reflecting mirror is placed behind the original mirror, 100% of the light is transmitted. This sounds impossible to me. The first mirror still reflects 99% of the light incident on it regardless of the presence or absence of the second mirror. My only guess is that the 1% transmitted through the first mirror reflects back and forth between the mirrors and then 1% of that is reflected, giving the apparent result that light "appears" when a second mirror is placed behind the first. If this is not the case then wouldn't conservation of energy be violated by the "appearance" of light? Thanks.

 

[mgb_phys]

You have this system in the rear view mirror of your car.
If you flick the switch down (dipped mode) then you only have the reflection from the front of the glass (eg 6-8%) when you flick the switch back to the normal position it places a 'real' eg 90% mirror behind the glass to give you a better reflection.

In practice the 1% wasted light in your mirror is probably absorbed rather than transmitted.

 

[Phrak]

This can be 'sorta' true in some conditions. For a reflecting surface the photon field penetrates some distance through the surface. In fact the field decays exponentially, so there is always some small amplitude at any given distance.

Take the example of a beam internal to a block of glass, reflecting off the glass-air interface at some angle so that we get total internal reflection. Bringing another piece of glass within a few wavelenths of the reflecting surface of the first block will allow some of the penetrating field to intercept the second block.

Bring the second block within a quater wavelength and the most of the light will pass through. This is called tunneling in quantum mechanics.

Bring two perfectly flat surfaces together and there is no interface left so you get the full 100%, but then you really don't have two mirrors anymore. Which is why I said 'sorta' true.

 

[naes213]

Hmmm... ok so i guess the situation can't be stated as simply as my professor would like us to think. Phrak, your description of the two pieces of glass brings to mind a discussion of evanescent waves (with the same professor). So then its not really 100% (the sort of true part) because the evanescent wave decays exponentially the further you get from the boundary of the first mirror or first piece of glass?

 

[Phrak]

Hmmm... ok so i guess the situation can't be stated as simply as my professor would like us to think. Phrak, your description of the two pieces of glass brings to mind a discussion of evanescent waves (with the same professor). So then its not really 100% (the sort of true part) because the evanescent wave decays exponentially the further you get from the boundary of the first mirror or first piece of glass?

The transmission amplitude approches 100% as the gap approches zero distance. Zero distance means, ideally, that you have one piece of glass, not two pieces with two 'mirrors'.

 

[naes213]

Ok, thanks for the replies.