Question

Assertion :STATEMENT-1 : For the situation shown in the figure two monochromatic identical coherent light sources produce interference pattern on the screen. The intensity of minima nearest to $S_1$ is not exactly zero. Reason: STATEMENT-2 : Minimum intensity is zero when interfering waves have same intensity at the location of super position.

• A. Statement-1 is True, Statement-2 is True.Statement-2 is a correct explanation for Statement-1.
• B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
• C. Statement-1 is True, Statement-2 is False
• D. Statement-1 is False, Statement-2 is True

Answer 1

The correct option is A Statement-1 is True, Statement-2 is True.Statement-2 is a correct explanation for Statement-1.

The intensity due to superposition of two waves is given by
$I=I_1+I_2+2\sqrt{I_1{I}_2}cos\varphi$
where $\varphi$ is phase difference between interfering waves:
the minimum value will be $Imin=I_1+I_2+2\sqrt{I_1{I}_2}$ when $cos\varphi =-1$
$I_{min}=(\sqrt{I_1}-\sqrt{I_2}{)}^2$
Hence, minimum intensity is zero when the intensity of both interfering waves are equal.