Wave Optics

JEE Main level, single correct, medium

132 of 191

Question 132 of 191

The diffraction pattern of a light of wavelength 400nm400nm diffracting from a slit of width 0.2mm0.2mm is focused on the focal plane of a convex lens of focal length 100cm100cm. The width of the 1st{1}^{\text{st}} secondary maxima will be :

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Answer: (A) 2mm2mm

Width of 1st{1}^{st} secondary maxima =λa⋅D=\dfrac{\lambda }{a}\cdot D
Here
a=0.2×10−3ma=0.2\times {10}^{-3}m
λ=400×10−9m\lambda =400\times {10}^{-9}m
D=100×10−2=1mD=100\times {10}^{-2}=1m
Therefore, width of 1st{1}^{st} secondary maxima
=400×10−90.2×10−3×1=\dfrac{400\times {10}^{-9}}{0.2\times {10}^{-3}}\times 1
=2×10−3m=2mm=2\times {10}^{-3}m =2mm

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