A slit of width a is illuminated by white light. The first minimum for red light (λ = 6500 mathringA ) will fall at θ = 30° when a will be

Question

A slit of width a is illuminated by white light. The first minimum for red light (λ = 6500 mathringA ) will fall at θ = 30° when a will be (A) 3200 mathringA  (B) 6.5 × 10-4 mm (C) 1.3 micron (D) 2.6 × 10-4 cm

Tardigrade Admin · Accepted Answer

For first minimum, a sinθ = 1λ a = (λ/sin θ) = (6.5 × 10-7/sin 30°) = 13 × 10-7 = 1.3 micron

Q. A slit of width a is illuminated by white light. The first minimum for red light $(λ = 6500 \overset{˚}{A})$ will fall at $θ = 3 0^{\circ}$ when $a$ will be

$3200 \overset{˚}{A}$

$6.5 \times 1 0^{- 4} mm$

$1.3$ micron

$2.6 \times 1 0^{- 4} c m$

For first minimum, $a s in θ = 1 λ$
$a = \frac{λ}{s in θ} = \frac{6.5 \times 1 0 ^{- 7}}{s in 3 0 ^{\circ}}$
$= 13 \times 1 0^{- 7}$
$= 1.3$ micron

Q. A slit of width a is illuminated by white light. The first minimum for red light (λ=6500A˚) will fall at θ=30∘ when a will be

3200A˚

6.5×10−4mm

1.3 micron

2.6×10−4cm