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

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The discussion focuses on designing a Fabry-Perot interferometer that achieves a transmission of T = 1 for light at 499 nm and T ≤ 0.01 at 500 nm under orthogonal incidence. The challenge lies in determining the necessary finesse to meet these transmission specifications while maintaining the same optical path length. Participants emphasize the importance of providing a clear problem statement and initial attempts to facilitate effective assistance. The calculations indicate that achieving a thickness of 249.5 nm is impractical due to the sensitivity of the transmission to slight wavelength variations. Overall, the conversation highlights the complexities involved in designing high-finesse optical instruments.
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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.
 
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hello Ayesha,

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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 :)
 
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...
 
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