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Q.

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

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a

2

b

1

c

3

d

4

answer is B.

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Detailed Solution

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$\begin{aligned} \frac{I_{1}}{I_{2}} = 4 \\ \frac{I_{max}}{I_{min}} = {[\frac{\sqrt{I_{1}} + \sqrt{I_{2}}}{\sqrt{I_{1}} - \sqrt{I_{2}}}]}^{2} \\ \frac{I_{max}}{I_{min}} = {[\frac{2 \sqrt{I_{2}} + \sqrt{I_{2}}}{2 \sqrt{I_{2}} - \sqrt{I_{2}}}]}^{2} \\ \frac{I_{max}}{I_{min}} = 9 \\ \frac{I_{max}}{I_{max}} + I_{min} = \frac{10}{\min} \\ \frac{5}{x} = \frac{10}{8} \\ x = 4 \end{aligned}$

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The interference pattern is obtained with two coherent light sources of intensity ratio 4: 1. And the ratio Imax+IminImax-Imin is 5x. Then, the value of x will be equal to :