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  • The interference pattern is obtained with two coherent light sources of intensity ratio 4. In the interference pattern the ratio <img alt="\frac{I \max -I \min }{I \max +I \min }" src="https:/

The interference pattern is obtained with two coherent light sources of intensity ratio 4. In the interference pattern the ratio \frac{I \max -I \min }{I \max +I \min }    will be ?

Option: 1

\frac{4}5{}


Option: 2

\frac{3}{5 }


Option: 3

\frac{6}{5}


Option: 4

None of the above


Answers (1)

best_answer

\begin{aligned} & \frac{I_1}{I_2}=4 \\ & \frac{I_{\max }^{}}{I \min }=\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)^2=\left(\frac{\sqrt{\frac{I_1}{I_2}}+1}{\sqrt{\frac{I_1}{I_2}}-1}\right)^2 \\ & =\left(\frac{\sqrt{4}+1}{\sqrt{4}-1}\right)^2 \end{aligned}

\frac{I \max -I \min }{I \max +I \min }=\frac{\frac{I \max }{I \min }-1}{\frac{I \max }{I \min }+1}

\begin{aligned} & =\frac{\left(\frac{\sqrt{4}+1}{\sqrt{4}-1}\right)^2-1}{\left(\frac{\sqrt{4}+1}{\sqrt{n}-1}\right)^2+1}=\frac{8}{10}=\frac{4}{5} \\ & \\ & \frac{I \text { max }-I \text { min }}{I_{\text {max }}+I_{\text {min }}}=\frac{4}{5} \end{aligned}

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vishal kumar

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