Question

A Michelson interferometer operating at a 600 nm wavelength has a 3.59-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 shifts is 35

Solution:

As per the question:

Wavelength of the light,
`\lambda = 600\ nm`

Refractive index of air,
`\mu_(a) = 1.0028`

Length, d = 3.59 cm

Now,

The no. of bright-dark fringe shifts can be calculated by the given formula:

`m = (\mu - 1)(2d)/(\lambda)`

Thus

`m = (\mu_(a) - 1)(2d)/(\lambda)`

`m = (1.00028 - 1)(2* 3.59* 10^(- 2))/(600* 10^(- 9))`

m = 33.5 ≈ 34