Two light waves having the same wavelength `lambda` in vacuum are in phase initially. Then the first ray travels a path of length `L_(1)` through a medium of refractive index `mu_(1)`. Then second ray travels a path of length `L_(2)` throug a medium of refractive index `mu_(2)`. The two waves are then combined to observed interference effects. The phase difference between the two, when they interfere, is

Options

A. `(2pi)/(lambda) (L_1 - L_2)`
B. `(2pi)/(lambda) ((L_1)/(mu_1) - (L_2)/(mu_2))`
C. `(2pi)/(lambda) (mu_1L_1 - mu_2L_2)`
D. `(2pi)/(lambda) ((L_1)/(mu_2) - (L_2)/(mu_1))`

Answer

C

Explanation

Phase difference in terms of optical path difference can be written as follows:
`delta = (2pi)/(lambda) xx "Optical path difference"`
Optical path is refractive index multiplied with geometric path length. Hence we can write the following:
`delta = (2pi)/(lambda) (mu_1L_1 - mu_2L_2)`