Question

A Michelson interferometer operating at a 500 nm wavelength has a 3.73-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

The number of bright-dark fringe is 42

Solution:

As per the question:

Wavelength of light,
`\lambda = 500\ nm = 500* 10^(- 9)\ m`

Length of the glass cell, x = 3.73 cm = 0.0373 m

Refractive index,
`\mu = 1.00028`

Now,

To calculate the bright-dark fringe shifts, we use the formula given below:

`d_(m) = (2x)/(\lambda )* (\mu - 1)`

Now, substituting the appropriate values in the above formula:

`d_(m) = (2* 0.0373)/(500* 10^(- 9))* (1.00028 - 1)`

`d_(m) = 41.77` ≈ 42