Wave Optics

JEE Main level, numerical answer, medium

92 of 191

Question 92 of 191

A Young's double-slit experiment is performed using monochromatic light of wavelength λ\lambda. The intensity of light at a point on the screen, where the path difference is λ\lambda, is KK units. The intensity of light at a point where the path difference is λ6\dfrac{\lambda }{6} is given by nK12\dfrac{nK}{12}, where nn is an integer. The value of nn is

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Answer: 9

I=I0cos⁡2ϕ2I={I}_{0}{\cos }^{2}\dfrac{\phi }{2}=kcos2(πλ×λ6)={kcos}^{2}\left(\dfrac{\pi }{\lambda }\times \dfrac{\lambda }{6}\right)
=kcos⁡2(π6)=k{\cos }^{2}\left(\dfrac{\pi }{6}\right)
=3k4=9k12=\dfrac{3k}{4}=\dfrac{9k}{12}
n=9n=9

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