Wave Optics

JEE Main level, single correct, medium

63 of 191

Question 63 of 191

The ratio of intensities at two points PP and QQ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are π3\dfrac{\pi }{3} and π2\dfrac{\pi }{2}, respectively are

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Answer: (D) 3:23:2

The formula to calculate the intensity of the interference pattern in Young's double slit experiment can be written as
I=4I0cos⁡2(ϕ2)...(1)I=4{I}_{0}{\cos }^{2}\left(\dfrac{\phi }{2}\right)...\left(1\right)
Hence, the ratio of the required intensities can be calculated as follows-
I1I2=4I0cos⁡2(π6)4I0cos⁡2(π4)=3412=32\begin{matrix}\dfrac{{I}_{1}}{{I}_{2}} & = & \dfrac{4{I}_{0}{\cos }^{2}\left(\dfrac{\pi }{6}\right)}{4{I}_{0}{\cos }^{2}\left(\dfrac{\pi }{4}\right)} \\ & = & \dfrac{\dfrac{3}{4}}{\dfrac{1}{2}} \\ & = & \dfrac{3}{2}\end{matrix}

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