How Does Finesse Influence the Performance of a Fabry-Perot Interferometer?

[ayesha203]

Design a Fabry perot interferometer, that provides a transmission of T =1 for light with λ1 = 499nm under orthogonal incidence and a transmission for λ2 = 500nm of T≤0.01 (without any further maxima in between). How big has to be the finesse?

Draw the transmission curve of several Fabry - Perot interferometer with this particular geometry (i.e. the same optical path length) for different finesse - values of F-1, 10 and 100 in the range from 498 nm to 501nm.

 

[BvU]

hello Ayesha,

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[ayesha203]

I have tried to solve the above question in the following way:

T = 1 for λ1 = 499nm

T ≤ 0.01 for λ2 = 500nm

for orthogonal incidence : Δs = 2nd, n = 1

Δs = m (λm)

m=1; n=1

d= λ1/2 = 249.5 nm

and i couldn't solve further...

Please help :)

 

[BvU]

It will be difficult to build such an instrument. 249.5 nm is too small, and a deviation of +0.5 nm would already let the 500 nm through with the same T. A hair is 50 μm !

You need an expression for the transmission of such a thing as a function of the wavelength. Nicely to be accommodated under 2): relevant equations...