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Q.A slit of width 0.15 cm is illuminated by light of wavelength 5×10⁻⁵ cm and a diffraction pattern is obtained on a screen 2.1 m away. Calculate the width of the central maximum.

Mizoram MbseMizoram Board of School Education HSSLC 2023Subjective· 2mImportance★★★★★
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The linear width of the central maximum in single-slit diffraction is 2λD/a2\lambda D/a, where aa is the slit width and DD the slit-to-screen distance.

Why: The first minima on either side of the central maximum occur at sin⁡θ=λ/a\sin\theta=\lambda/a; for small angles, the half-width on the screen is λD/a\lambda D/a, so the full width of the central maximum is twice that.

Steps:

  1. Convert units: a=0.15 cm=1.5×10−3 ma=0.15\,cm=1.5\times10^{-3}\,m, λ=5×10−5 cm=5×10−7 m\lambda=5\times10^{-5}\,cm=5\times10^{-7}\,m, D=2.1 mD=2.1\,m …

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