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`
On introducing a transparent slab `(mu)` the central fringe shifts to the point originally occupied by the fifth bright fringe. The thickness of the slab is

Options

A. `(5 lambda)/(mu - 1)`
B. `(4 lambda)/(mu - 1)`
C. `(mu -1)/(4 lambda)`
D. `(mu -1)/(5 lambda)`

Answer

a

Explanation

Position of nth bright fringe `= Y = D // d(Delta x)`, where `Delta x` is the path difference.
When a slab of refractive index `'mu'` and thickness 't' is introduced, the new position will be
`Y' = (D)/(d) [Delta x + (mu - 1) t]`
`:.` Shift `= (D)/(d) (mu - 1) t`
Shift is given by `5 lambda // d`.
`:. (5 lambda D)/(d) = (D)/(d) (mu - 1) t`
`implies t = (5 lambda)/(mu - 1)`
choice (c ) and (d) are wrong dimensioally. Choice (b) is wrong numerically. So, choice (a) is correct.