When a light wave passes from a rarer medium to a denser medium, there will be a phase change of `pi` radians. This difference brings change in the conditions for constructive and destructive interference. This phenomena also reasons the fromation of interference pattern in thin films like, oily layer, soap film, etc., but has no reason on the shifting of fringes from the central portion outward. The shift is dependent on the refractive index of the material as per the relation, `Delta y = (mu - 1) t`
The condition for constructive interference in Lloyd's single mirror experiment is the path difference which is equal to

Options

A. `N lambda`
B. `(2 N - 1)(lambda)/(2)`
C. `(N - 1)(lambda)/(2)`
D. `(lambda)/(2(2 N - 1))`

Answer

b

Explanation

In Lloyds' single mirror experiment, the interference is between the light reflected by the mirror and the direct ligth from the source.
The reflected light undergoes a phase difference of `pi` radians or path difference of `lambda // 2`
So, path difference `+ (lambda)/(2) = N lambda` for bright fringe. Hence,
Path difference `= (2N - 1) (lambda)/(2)`
So, choice (b) is correct and rest are wrong.