Wave Optics

JEE Main level, single correct, medium

146 of 191

Question 146 of 191

A single slit of width 0.1mm0.1mm is illuminated by a parallel beam of light of wavelength 6000Å6000Å and diffraction bands are observed on a screen 0.5m0.5m from the slit. The distance of the third dark band from the central bright band is:

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Answer: (A) 9mm9mm

a=0.1mm=10−4ma=0.1mm={10}^{-4}m

λ=6000×10−10=6×10−7m\lambda =6000\times {10}^{-10}=6\times {10}^{-7}m

D=0.5mD=0.5m

For 3rd{3}^{rd} dark

asin⁡⁡θ=3λa\sin ⁡\theta =3\lambda

sin⁡⁡θ=3λa=xD\sin ⁡\theta =\dfrac{3\lambda }{a}=\dfrac{x}{D}

x=3λDax=\dfrac{3\lambda D}{a}

=3×6×10−7×0.510−4=\dfrac{3\times 6\times {10}^{-7}\times 0.5}{{10}^{-4}}

=9mm=9mm

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