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. (a) `I=I_o`
B. (b) `I=2I_o`
C. (c) `I=4I_o`
D. (d) There is no relation between I and `I_o`

Answer

C

Explanation

Suppose slit widths are equal, so they produces wave of equal intensity say `I^'`. Resultant intensity at any point `I_R=4I^'cos^2phi` where `phi` is the phase difference between the waves at the point of observation.
For maximum intensity `phi=0^@impliesI_(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_o`