Question

A Michelson interferometer operating at a 400 nm wavelength has a 3.70-cm-long glass cell in one arm. To begin, the air is pumped out of the cell and mirror M2 is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at 1.00 atm pressure is 1.00028.
How many bright-dark-bright fringe shifts are observed as the cell fills with air?

Answer 1

Answer:

$m=42\ fringes$

Explanation:

From the question we are told that:

Wavelength $\lambda=400nm$

Length of cell arm $h=3.70cm$

Refraction of air at  at 1.00 atm pressure $n=1.00028.$

Generally the equation for Number of shifts is mathematically given by

$m=N-N_o$

Since

$N_0=\frac{2t}{\lambda_0}$

Therefore

$m=\frac{2t}{\lambda_0/n}-\frac{2t}{\lambda_0}$

$m=\frac{2t}{\lambda_0} n-1$

$m=\frac{2(3.7*10^{-2})}{400*10^{-9}}*(1.00028-1)$

$m=51.8$

$m=42\ fringes$