Two light rays having the same wavelength in vacuum are in phase initially. Then the first ray travels a path L₁ through a medium of refractive index ₁ , while the second ray travels a path of length L₂ through a medium of refractive index ₂ . The two waves are then combined to observe interference. The phase difference between the two waves is

Step-by-step solution

The optical path between any two points is proportional to the time of travel. The distance traversed by light in a medium of refractive index in time t is given by where v is the velocity of light in the medium. The distance traversed by light in a vacuum in this time, =c t=c d v [ from equation (1)] This distance is the equivalent distance in vacuum and is called the optical path. Here, the optical path for first ray = ₁ L₁ The optical path for second ray = ₂ L₂ Path difference = ₁ L₁- ₂ L₂ Now, phase difference