Question

Assertion: In young's double slit experiment the two slits are at distance d apart. Interference pattern is obse ved on a screen at distance D from the slits. At a point onthe screen when it is directly opposite to one ofthe slits, a dark fringe is observed. Then, the wavelength of wave is proportional to square of distance of two slits.
Reason: For a dark fringe intensity is zero.

• A. If both assertion and reason are true but the reason is the correct explanation of assertion
• B. If both assertion and reason are true but the reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both the assertion and reason are false
• E. If reason is true but assertion is false

Answer 1

The correct option is B If both assertion and reason are true but the reason is not the correct explanation of assertion

When dark fringe is obtained at the point opposite to one of the slits then
and $S_{2}P=\sqrt{D^2+d^2}=D{(1+\frac{d^2}{D^2})}^{1/2}$
$=D(1+\frac{d^2}{2D^2})$ (By binomial theorem)
Path difference = $S_{2}P-S_{1}P$
$=D(1+\frac{d^2}{2D^2})-D=\frac{d^2}{2D}=\frac{\lambda }{2}$
Now, intensity of a dark fringe is zero.