NEET Questions Solved

NEET - 2016

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

(a) $\frac{\sqrt{n}}{n+1}$             (b) $\frac{2\sqrt{n}}{n+1}$

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

(b) It is given that $\frac{{l}_{2}}{{l}_{1}}=n⇒{l}_{2}=n{l}_{1}$

Ratio of intensites is given by

$\frac{{l}_{max}-{l}_{min}}{{l}_{max}+{l}_{min}}=\frac{{\left(\sqrt{{l}_{2}}+\sqrt{{l}_{1}}\right)}^{2}_{\left(\sqrt{{l}_{2}}-\sqrt{{l}_{1}}\right)}^{2}}{{\left(\sqrt{{l}_{1}}+\sqrt{{l}_{2}}\right)}^{2}+{\left(\sqrt{{l}_{2}}-\sqrt{{l}_{1}}\right)}^{2}}$

$=\frac{{\left(\sqrt{\frac{{l}_{2}}{{l}_{1}}}+1\right)}^{2}-{\left(\sqrt{\frac{{l}_{2}}{{l}_{1}}-1}\right)}^{2}}{{\left(\sqrt{\frac{{l}_{2}}{{l}_{1}}}+1\right)}^{2}+{\left(\sqrt{\frac{{l}_{2}}{{l}_{1}}-1}\right)}^{2}}$

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

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