In Young's double-slit experiment, let A and B be the two slit. A thin film of thickness t and refractive index `mu` is placed in front of A. Let `beta = ` fringe width. Then the central maxima will shift

Options

A. toward A
B. toward B
C. by `t(mu - 1) (beta)/(lambda)`
D. by `mu t (beta)/(lambda)`

Answer

a.,c

Explanation

For a certain point P on the screen at a distance x from the center of the screen, paht difference `Delta = (x d)/(D)`
Path differnce introduced due to sheet `= (mu - 1)t`.
For central maximum at P,
`(x d)/(D) = (mu - 1)`
or `x = t(mu - 1) (D)/(d)`
Now, `beta = (D lambda)/(d)`
`:. (D)/(d) = (beta)/(lambda)`
Hence, `x = t(mu - 1) (beta)/(lambda)`