Question

A Michelson interferometer operating at a 600nm wavelength has a 2.02-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

19

Step-by-step explanation:

Given that:

wavelength = 600 nm

Distance (d) = 2.02 cm = 2.02 × 10⁻² m

refraction index of air (n) = 1.00028

Pressure = 1.00 atm

∴

The number of bright-dark-bright fringe shifts can be determined by using the formula:

`\Delta m = (2d)/(\lambda) (n -1 ) \\ \\ \Delta m = (2*2.02 * 10^(-2))/(600* 10^(-9)) (1.00028 -1 ) \\ \\ \Delta m = 67333.33 * 10^(-5)(1.00028 -1) \\ \\ \Delta m = 67333.33 * 10^(-5)(2.8* 10^(-4)) \\ \\ \Delta m = 18.853 \\ \\ \mathbf{\Delta m = 19}`