Question

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.

Answer 1

Step-by-step 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 )