Orange light of wavelength $6000 \times 10^{-10} \mathrm{~m}$ illuminates a single slit of width $0.6 \times 10^{-4} \mathrm{~m}$. the maximum possible number of diffraction minima produced on both sides of the central maximum is ____

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Wave Optics

Orange light of wavelength

6000 \times 1 0^{- 10} m

illuminates a single slit of width

0.6 \times 1 0^{- 4} m

. the maximum possible number of diffraction minima produced on both sides of the central maximum is ____

Answer: 200

Solution

For a single slit the minima satisfy

d sin θ = nλ

. The largest diffraction angle corresponds to

sin θ = 1

, so the highest order possible is

n_{m a x} = \frac{d}{λ} = \frac{0.6 \times 1 0 ^{- 4}}{6000 \times 1 0 ^{- 10}} = 100

. With up to

100

minima on each side of the central maximum, the greatest number produced on both sides together is

2 \times 100 = 200

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Integer answer

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