The two coherent sources produce interference | vedclass

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(B) Let the intensities of the two coherent sources be $I_1$ and $I_2$. The ratio of intensities is given as $b = \frac{I_1}{I_2}$.We know that $I_{

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$\frac{1+b}{2\sqrt{b}}$

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(B) Let the intensities of the two coherent sources be $I_1$ and $I_2$. The ratio of intensities is given as $b = \frac{I_1}{I_2}$.We know that $I_{	ext{max}} = (\sqrt{I_1} + \sqrt{I_2})^2$ and $I_{	ext{min}} = (\sqrt{I_1} - \sqrt{I_2})^2$.The required ratio is $R = \frac{I_{	ext{max}} + I_{	ext{min}}}{I_{	ext{max}} - I_{	ext{min}}}$.Substituting the expressions for $I_{	ext{max}}$ and $I_{	ext{min}}$:$R = \frac{(\sqrt{I_1} + \sqrt{I_2})^2 + (\sqrt{I_1} - \sqrt{I_2})^2}{(\sqrt{I_1} + \sqrt{I_2})^2 - (\sqrt{I_1} - \sqrt{I_2})^2}$.Expanding the terms:$R = \frac{(I_1 + I_2 + 2\sqrt{I_1I_2}) + (I_1 + I_2 - 2\sqrt{I_1I_2})}{(I_1 + I_2 + 2\sqrt{I_1I_2}) - (I_1 + I_2 - 2\sqrt{I_1I_2})} = \frac{2(I_1 + I_2)}{4\sqrt{I_1I_2}} = \frac{I_1 + I_2}{2\sqrt{I_1I_2}}$.Dividing numerator and denominator by $I_2$:$R = \frac{\frac{I_1}{I_2} + 1}{2\sqrt{\frac{I_1}{I_2}}} = \frac{b + 1}{2\sqrt{b}}$.

The two coherent sources produce interference with intensity ratio $b$. In the interference pattern, the ratio $\frac{I_{\text{max}} + I_{\text{min}}}{I_{\text{max}} - I_{\text{min}}}$ will be

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