Waves

JEE Main level, single correct, medium

53 of 142

Question 53 of 142

Two light beams of intensities in the ratio of 9:49:4 are allowed to interfere. The ratio of the intensity of maxima and minima will be :

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Answer: (D) 25:125:1

Data provided in the question is, the ratio of the intensities,
I1I2=94\dfrac{{I}_{1}}{{I}_{2}}=\dfrac{9}{4}
After taking square root of above equation on both sides, we get,
I1I2=32\dfrac{\sqrt{{I}_{1}}}{\sqrt{{I}_{2}}}=\dfrac{3}{2}
Apply componendo and dividendo,
⇒I1+I2I1−I2=3+23−2=51\Rightarrow \dfrac{\sqrt{{I}_{1}}+\sqrt{{I}_{2}}}{\sqrt{{I}_{1}}-\sqrt{{I}_{2}}}=\dfrac{3+2}{3-2}=\dfrac{5}{1}
⇒(I1+I2I1−I2)2=Imax⁡Imin⁡=251\Rightarrow {\left(\dfrac{\sqrt{{I}_{1}}+\sqrt{{I}_{2}}}{\sqrt{{I}_{1}}-\sqrt{{I}_{2}}}\right)}^{2}=\dfrac{{I}_{\max }}{{I}_{\min }}=\dfrac{25}{1}

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