JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Wave Optics

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If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is

3 0^{\circ}

in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is _______

μ m

Answer: 6

Solution

Single-slit minima satisfy

a sin θ = nλ

. The second minimum on one side and the third on the other together subtend

θ_{2} + θ_{3} = 3 0^{\circ}

, and for small angles

\frac{2 λ}{a} + \frac{3 λ}{a} = \frac{5 λ}{a} = \frac{π}{6}

. Solving,

a = \frac{5 λ \times 6}{π} = \frac{30 \times 628 \times 1 0 ^{- 9}}{π} \approx 6 \times 1 0^{- 6}

m, a slit width of 6

μ

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Integer answer

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