Fabry-Perot Interferometer: Energy Conservation

[smithg86]

Homework Statement

This is regarding a Fabry-Perot Interferometer with identical mirrors:

If you shine a beam of light on a 99% reflecting mirror, 1% goes through and the other 99% is reflected. But if a second mirror is placed behind the first one, where there is only 1% of the light present, somehow 100% of the light appears. Explain this, also explain how energy is conserved.

Homework Equations

I_t = I_0 * {T^2 / (1-R^2)} * { 1 / (1 + F * sin^2(\Delta/2))}

F = finesse = 4R / (1-R)^2

I_t = transmitted intensity
I_0 = original intensity

T = transmittance
R = reflectance

\Delta = \delta + \delta_r
\delta = phase difference per round trip between mirrors
\delta_r = phase difference due to reflection = 0 or pi

The Attempt at a Solution

I understand mathematically why it's true. If you set \Delta to an integer multiple of pi, then sin \Delta = 0 and then

I_t/I_0 = {T^2 / (1-R^2)} * { 1 / (1 + F*(0)) }

I_t/I_0 = T^2 / (1 - R^2) = 1

so I_t = I_0, so 100% of the light appears.

I really don't know how to explain this physically. Help?

 

[Gokul43201]

Can you write down the question EXACTLY as it was given to you?

I can't seem to make much sense of it. First of all, the interferometer set-up I'm familiar with has the mirrors facing each other, not one behind the other. Secondly, in this geometry, I expect that only about half the incident power is transmitted through in the forward direction, the rest is transmitted backwards.

What does the question mean by "100% of the light appears"? Appears where?

I may be completely off here, so it would help if someone else takes a look.

 

[MeChaState]

"I really don't know how to explain this physically. Help?"

Has anyone an answer to this question?

That is the question of my life too.