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The interference pattern is obtained with two coherent light source of intensity ratio n. In the interference pattern, the ratio \frac{I_{max}-I_{min}}{I_{max+I_{min}}} will be 

Option: 1

\frac{\sqrt{n}}{n+1}


Option: 2

\frac{2\sqrt{n}}{n+1}


Option: 3

\frac{\sqrt{n}}{\left ( n+1 \right )^2}


Option: 4

\frac{2\sqrt{n}}{\left ( n+1 \right )^2}


Answers (1)

best_answer

Given :    I2?=nI1

Maximum intensity of interference       I_{max}= ( \sqrt{I_1}+\sqrt{I_2})^2

∴    $$I_{max} = (\sqrt{I_1} + \sqrt{nI_1})^2 = (1+\sqrt{n})^2 I_1 = (1+ n +2\sqrt{n } ) I_1$$

Minimum intensity of interference        I_{min}= ( \sqrt{I_1}-\sqrt{I_2})^2

∴    $$I_{min} = (\sqrt{I_1} - \sqrt{nI_1})^2 = (1-\sqrt{n})^2 I_1 = (1+ n - 2\sqrt{n})I_1$$

 

∴   $$\dfrac{I_{max} -I_{min}}{I_{max} + I_{min}} = \dfrac{2\sqrt{n} - (-2\sqrt{n})}{2(1+n) } = \dfrac{2\sqrt{n}}{1+n}$$

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