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

`m=42\ fringes`

Step-by-step 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=(2t)/(\lambda_0)`

Therefore

`m=(2t)/(\lambda_0/n)-(2t)/(\lambda_0)`

`m=(2t)/(\lambda_0) n-1`

`m=(2(3.7*10^(-2)))/(400*10^(-9))*(1.00028-1)`

`m=51.8`

`m=42\ fringes`