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One leg of a Michelson interferometer contains an evacuated cylinder of length L, having glass plates on each end. A gas is slowly leaked into the cylinder until a pressure of 1 atm is reached. If N bright fringes pass on the screen when light of wavelength λ is used, provide an expression for the index of refraction of the gas?
Hint: The fringe shifts occur because the wavelength of the light changes inside the gas-filled tube.

Respuesta :

Answer:

Explanation:

Due to  change in the refractive index of the medium , wavelength changes. If λ  be wave length in vacuum ,  wave-length in refractive index μ

will become  λ / μ

Initially no of wavelengths in length L were  L / λ

Finally no of wavelengths in length L were L / λ / μ = Lμ / λ

Given

Lμ / λ  -  L / λ  = N

L / λ ( μ -1 ) = N

μ = ( Nλ / L + 1 )

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