Statement I: In Young's double-slit experiment, the two slits are at distance d apart. Interference pattern is observed on a screen at distance D from the slits. At a point on the screen which is directly opposite to one of the slits, a dark fringe is observed. Then, the wavelength of wave is proportional to the squar of distance between two slits.
Statement II: For a dark fringe, intensity is zero

Options

A. Statement I is True, statement II is True, Statement II is a correct explanation for Statement I.
B. Statement I is Ture, Statement II is Ture, Statement II is NOT a correct explanation for Statement I.
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Answer

b

Explanation

When dark fringe is obtained at the point oppoite to one of the slits, then
`S_(1) P = D`
`S_(2) P = sqrt(D^(2) + d^(2))`
`= D (1 + (d^(2))/(2D^(2)))^(1//2)D =(1+ (d^(2))/(2D))`
Path difference `= S_(2) P - S_(1) P`
`d(1 + (d^(2))/(2D^(2))) - D = (d^(2))/(2 D) = (lambda)/(2)`
or `lambda = (d^(2))/(D) implies lambda prop d^(2)`
Now, intensity of a dark fringe is zero.