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. (Use any variable or symbol stated above as necessary.) n =

Answer 1

The fringe shifts occur because the wavelength of the light changes inside the gas-filled tube

If Initially the number of wavelengths in the cylinder is given by

m1 = 2L/

Now these wavelengths changes to

m2 = 2L/(/n)

n = refractive index of glass

So, number of bright fringes

N = m2 - m1

N = 2n*L/ - 2L/

N = (2L/)*(n - 1)

n - 1 = N*/(2L)

n = 1 + (N* / 2L)