Wave Optics

JEE Main level, single correct, medium

22 of 191

Question 22 of 191

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16.16. The intensity of the waves are in the ratio:

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Answer: (A) 25:925:9

Imax=(I1+I2)2{I}_{max}={\left(\sqrt{{I}_{1}}+\sqrt{{I}_{2}}\right)}^{2}

Imin=(I1−I2)2{I}_{min}={\left(\sqrt{{I}_{1}}-\sqrt{{I}_{2}}\right)}^{2}

⇒ImaxImin=(I1+I2)2(I1−I2)2\Rightarrow \dfrac{{I}_{max}}{{I}_{min}}=\dfrac{{(\sqrt{{I}_{1}}+\sqrt{{I}_{2}})}^{2}}{{(\sqrt{{I}_{1}}-\sqrt{{I}_{2}})}^{2}}

⇒161=(I1+I2)2(I1−I2)2\Rightarrow \dfrac{16}{1}=\dfrac{{(\sqrt{{I}_{1}}+\sqrt{{I}_{2}})}^{2}}{{(\sqrt{{I}_{1}}-\sqrt{{I}_{2}})}^{2}}

⇒41=I1+I2I1−I2\Rightarrow \dfrac{4}{1}=\dfrac{\sqrt{{I}_{1}}+\sqrt{{I}_{2}}}{\sqrt{{I}_{1}}-\sqrt{{I}_{2}}}

⇒I1I2=259\Rightarrow \dfrac{{I}_{1}}{{I}_{2}}=\dfrac{25}{9}

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