Interference fringes are produced on a screen by using two light … - Vidyadip

MCQ

Interference fringes are produced on a screen by using two light sources of intensities $I$ and $9 I$. The phase difference between the beams is $\frac{\pi}{2}$ at point $P$ and $\pi$ at point $Q$ on the screen. The difference between the resultant intensities at point $P$ and $Q$ is

A
$2 I$
B
$4 I$
✓
$6 I$
D
81

✓

Answer

Correct option: C.

$6 I$

(c) : Resultant intensity, $I_t=I_1+I_2+2 \sqrt{I_1 I_2} \cos \phi$
Here, $I_1=I, I_2=9 I, \phi_P=\frac{\pi}{2}, \phi_Q=\pi$
$
\begin{aligned}
\therefore \quad & I_p=I+9 I+2 \sqrt{I \times 9 I} \cos \frac{\pi}{2} \\
& =10 I+2 \times 3 I \times 0=10 I \\
I_Q= & I+9 I+2 \sqrt{I \times 9 I} \cos \pi \\
= & 10 I+2 \times 3 I(-1) \\
= & 10 I-6 I=4 I
\end{aligned}
$
Hence, $I_p-I_Q=10 I-4 I=6 I$

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