Question

Two coherent light sources having intensity in the ratio $2 x$ produce an interference pattern.
The ratio $\frac{ I _{\max }- I _{\min }}{ I _{\max }+ I _{\min }}$ will be :

• A. $\frac{2 \sqrt{2 x }}{ x +1}$
• B. $\frac{\sqrt{2 x}}{2 x+1}$
• C. $\frac{\sqrt{2 x }}{ x +1}$
• D. $\frac{2 \sqrt{2 x }}{2 x +1}$

Answer 1

Answer: (D)

Given that, $\frac{I_{1}}{I_{2}}=2 x$
We know,
$I _{\max }=\left(\sqrt{ I _{1}}+\sqrt{ I _{2}}\right)^{2} \& I _{\min }=\left(\sqrt{ I _{1}}-\sqrt{ I _{2}}\right)^{2}$
$\therefore \frac{ I _{\max }- I _{\min }}{ I _{\max }+ I _{\min }}=\frac{2 \sqrt{ I _{1} I _{2}}}{ I _{1}+ I _{2}}=\frac{2 \sqrt{ I _{1} / I _{2}}}{\frac{ I _{1}}{ I _{2}}+1}=\frac{2 \sqrt{2 x }}{2 x +1}$