JEE PYQ: Wave Optics Question 7
Question 7 - 2021 (25 Feb Shift 1)
Two coherent light sources having intensity in the ratio $2x$ produce an interference pattern. The ratio $\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$ will be :
(1) $\frac{2\sqrt{2x}}{x+1}$
(2) $\frac{\sqrt{2x}}{2x+1}$
(3) $\frac{2\sqrt{2x}}{2x+1}$
(4) $\frac{\sqrt{2x}}{x+1}$
Show Answer
Answer: (3)
Solution
Let $I_1 = 2x$, $I_2 = 1$
$I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^2$
$I_{\min} = (\sqrt{I_1} - \sqrt{I_2})^2$
$\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}} = \frac{(\sqrt{2x} + 1)^2 - (\sqrt{2x} - 1)^2}{(\sqrt{2x} + 1)^2 + (\sqrt{2x} - 1)^2}$
$= \frac{4\sqrt{2x}}{2(2x + 1)} = \frac{2\sqrt{2x}}{2x + 1}$
BETA
