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The interference pattern is obtained with two coherent light sources of intensity ratio $\mathrm{4:1}$ . And the ratio $\mathrm{\frac{I_{max}+I_{min}}{I_{max}-I_{min}}}$ is $\mathrm{\frac{5}{x}}$ . Then, the value of $\mathrm{x}$ will be equal to :
Option: 1
$3$

Option: 2
$4$

Option: 3
$2$

Option: 4
$1$

Answers (1)

best_answer

$\mathrm{\frac{I_{1}}{I_{2}}=\frac{4}{1}} \\$

$\mathrm{I_{\text {max }}=\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}} \\$

$\mathrm{I_{\text {min }}=\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}}$

$\mathrm{I_{\text {max }}+I_{\text {min }} =2\left(I_{1}+I_{2}\right)} \\$

$\mathrm{I_{\text {max }}-I_{\text {min }} =4 \sqrt{I_{1}} \sqrt{I_{2}}} \\$

$\mathrm{\frac{I_{\text {max }}+I_{\text {min }}}{I_{\text {max }}-I_{\text {min }}}}\\$ $\mathrm{=\frac{2\left(I_{1}+I_{2}\right)}{4 \sqrt{I_{1}} \sqrt{I_{2}}}} \\$

$\mathrm{=\frac{2(5)}{4(2)}=\frac{5}{4}} \\$

$\mathrm{\therefore x =4}$

Hence the correct answer is option 2.

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seema garhwal

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