[\dfrac{2\sqrt{n}}{(n + 1...] The interference pattern is obtained with two coherent light sources of intensity ratio n. In the in

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The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio $\dfrac{I_{max} – I_{min}}{I_{max} + I_{min}}$ will be

$\dfrac{2\sqrt{n}}{(n + 1)^2}$

$\dfrac{\sqrt{n}}{(n + 1)}$

$\dfrac{2\sqrt{n}}{(n + 1)}$

$\dfrac{\sqrt{n}}{(n + 1)^2}$

Explanation:

$I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2 = (\sqrt{nI_1} + \sqrt{I})^2 = (\sqrt{n} + 1)^2I$

$I_{min} = (\sqrt{n} – 1)^2I$

$\dfrac{I_{max} – I_{min}}{I_{max} + I_{min}}$ = $\dfrac{(\sqrt{n} + 1)^2I – (\sqrt{n} – 1)^2I}{(\sqrt{n} + 1)^2I + (\sqrt{n} – 1)^2I}$

$= \dfrac{n + 1 + 2\sqrt{n} – n – 1 + 2\sqrt{n}}{(n + 1 + 2\sqrt{n}) + (n + 1 – 2\sqrt{n})} = \dfrac{4\sqrt{n}}{2(n + 1)} = \dfrac{2\sqrt{n}}{(n + 1)}$

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