The maximum intensity of fringes in Young's experiment is I. If one of the slit is closed, then the intensity at that place becomes `I_o`. Which of the following relation is true?

Options

A. `I=I_0`
B. `I=2I_0`
C. `I=4I_0`
D. There is no relation between I and `I_0`

Answer

C

Explanation

Suppose slit width.s are equal, so they produces waves of equal intensity say I.. Resultant intensity at any point `I_R = 4I. cos^(2) phi` where `phi` is the phase difference between the waves at the point of observation.
For maximum intensity
`phi = 0^@implies I_(max) = 4I. = I (i)`
If one of slit is closed, Resultant intensity at the same point will be I. only i.e. `I. = I_0 .... (ii)`
Comparing equation (i) and (ii) we get `I = 4I_0`