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JEE Main 2018 · Physics · Waves and Sound · medium

Two slits, each of width 0.1 mm, have their centres 0.6 mm apart and are illuminated normally by monochromatic light. The number of bright…

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Two slits, each of width 0.1 mm0.1\ \mathrm{mm}, have their centres 0.6 mm0.6\ \mathrm{mm} apart and are illuminated normally by monochromatic light. The number of bright interference fringes visible within the central maximum of the single-slit diffraction envelope is
  1. A. 1212
  2. B. 55
  3. C. 1111
  4. D. 66
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Answer: (C) 1111

Interference maxima occur at dsin⁡θ=nλd\sin\theta=n\lambda, while the first diffraction minimum is at asin⁡θ=λa\sin\theta=\lambda. Equating, the minimum falls at order n=da=0.60.1=6n=\dfrac da=\dfrac{0.6}{0.1}=6. The order n=±6n=\pm6 fringes coincide with the diffraction zeros and are missing, so the central diffraction maximum contains orders n=−5,…,0,…,+5n=-5,\dots,0,\dots,+5, which is 2×5+1=112\times5+1=11 fringes. Counting 2×6=122\times6=12 wrongly includes the missing orders.
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