In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $\lambda=500 \mathrm{~nm}$ is incident on the slits. The total number of bright fringes that are observed in the angular range $-30^{\circ} \leq \theta \leq 30^{\circ}$ is:

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Wave Optics

In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength

λ = 500 nm

is incident on the slits. The total number of bright fringes that are observed in the angular range

- 3 0^{\circ} \leq θ \leq 3 0^{\circ}

is:

(A)640
(B)320
(C)321
(D)641✓ Correct

Answer: (D)

Solution

Bright fringes sit where

d sin θ = nλ

. The largest usable angle is

3 0^{\circ}

, so the highest order is

n = \frac{d s i n 3 0 ^{\circ}}{λ} = \frac{( 0.320 \times 1 0 ^{- 3} ) ( 0.5 )}{500 \times 1 0 ^{- 9}} = 320

. That order runs from

- 320

+ 320

, and including the central

n = 0

fringe the total count is

2 \times 320 + 1 = 641

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Single correct option

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