A slit of width a is illuminated by white light. For red light (λ= 6200 mathringA ), the first minima is obtained at a diffraction angle of 30° . Then the value of a is

Question

A slit of width a is illuminated by white light. For red light (λ= 6200 mathringA ), the first minima is obtained at a diffraction angle of 30° . Then the value of a is (A)  3250 mathringA  (B)  6.5× 10-4 mm  (C)  1.24 micron (D)  2.6× 10-4 cm

Tardigrade Admin · Accepted Answer

For first minima a sin θ1=λ ∴ a=(λ/ sin θ1)=(6200 × 10-10/ sin 30°) =1.24 × 10-6 m =1.24 μ

Q. A slit of width a is illuminated by white light. For red light $(λ = 6200 \overset{˚}{A}$ ), the first minima is obtained at a diffraction angle of $3 0^{\circ}$ . Then the value of $a$ is

$3250 \overset{˚}{A}$

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

$1.24$ micron

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

For first minima
$a sin θ_{1} = λ$
$∴ a = \frac{λ}{s i n θ _{1}} = \frac{6200 \times 1 0 ^{- 10}}{s i n 3 0 ^{\circ}}$
$= 1.24 \times 1 0^{- 6} m$
$= 1.24 μ$

Q. A slit of width a is illuminated by white light. For red light (λ=6200A˚ ), the first minima is obtained at a diffraction angle of 30∘ . Then the value of a is

3250A˚

6.5×10−4mm

1.24 micron

2.6×10−4cm