Question

Two beams of light having intensities I and 4 I interface to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{\pi }{2}$ at point A and $\pi$ at point B, Then the difference between the resultant intensities at A and B is

• A. 2 I
• B. 4 I
• C. 5 I
• D. 7I

Answer 1

The correct option is B 4 I

Resultant intensity at a point, $I_R=I_1+I_2+2\sqrt{I_1{I}_2}cos\varphi$

where $I_1$ and $I_2$ be the intensities of two sources and $\varphi$ be the phase differences of the sources at that point.

Here, $I_1=I$ and $I_2=4I$

At point $A$, $\varphi =\frac{\pi }{2}$

So,Resulant intensity at point $A$, $I_A=5I+2\sqrt{4I^2}cos\frac{\pi }{2}=5I$

At point $B$, $\varphi =\pi$

So,Resulant intensity at point $B$, $I_B=5I+2\sqrt{4I^2}cos\pi =5I-4I=I$

Hence, Required difference between the intensities at $A$ and $B=I_A-I_B=5I-I=4I$