Two coherent light sources having intensity

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 :

  1. $\frac{2 \sqrt{2 x}}{x+1}$

  2. $\frac{\sqrt{2 x}}{2 x+1}$

  3. $\frac{\sqrt{2 x}}{x+1}$

  4. $\frac{2 \sqrt{2 x}}{2 x+1}$


Correct Option: , 4

Solution:

Given that, $\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=2 \mathrm{x}$

We know,

$I_{\max }=\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2} \& I_{\min }=\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}$

$\therefore \frac{\mathrm{I}_{\max }-\mathrm{I}_{\min }}{\mathrm{I}_{\max }+\mathrm{I}_{\min }}=\frac{2 \sqrt{\mathrm{I}_{1} \mathrm{I}_{2}}}{\mathrm{I}_{1}+\mathrm{I}_{2}}=\frac{2 \sqrt{\mathrm{I}_{1} / \mathrm{I}_{2}}}{\frac{\mathrm{I}_{\mathrm{J}}}{\mathrm{I}_{2}}+1}=\frac{2 \sqrt{2 \mathrm{x}}}{2 \mathrm{x}+1}$

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