Wave Optics

JEE Main level, single correct, medium

35 of 191

Question 35 of 191

In the Young's double slit experiment the intensity produced by each one of the individual slits is I0I_{0}. The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is 6000 A∘6000 \mathrm{~A}^{\circ}. The intensity of light on the screen in front of one of the slits is ____\_\_\_\_.

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Answer: (D) IoI_{\mathrm{o}}

In Young's double slit experiment:
d=2d = 2 mm, D=10D = 10 m, λ=6000\lambda = 6000 Å
The point in front of one slit is at y=d2y = \frac{d}{2} from the central axis.
I=4I0cos⁡2(πdyλD)I = 4I_0 \cos^2\left(\frac{\pi d y}{\lambda D}\right)
=4I0cos⁡2(π×2×10−3×1×10−36000×10−10×10)= 4I_0 \cos^2\left(\frac{\pi \times 2 \times 10^{-3} \times 1 \times 10^{-3}}{6000 \times 10^{-10} \times 10}\right)
=4I0cos⁡2(π3)=4I0×14=I0= 4I_0 \cos^2\left(\frac{\pi}{3}\right) = 4I_0 \times \frac{1}{4} = I_0

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