A parallel beam of wavelength λ=450 × 10-9 m passes through a long slit of width 2 × 10-4 m. The angular divergence for which most of light is diffracted is

Question

A parallel beam of wavelength λ=450 × 10-9 m passes through a long slit of width 2 × 10-4 m. The angular divergence for which most of light is diffracted is (A) 5.4 × 10-4 rad (B) 4.5 × 10-3 rad (C) 3.5 × 10-3 rad (D) 2.8 × 10-4 rad

Tardigrade Admin · Accepted Answer

Most of the light is diffracted between the two first order minima. ∴ Required angle =2 θ =2 sin θ=(2 λ/d)=(2 × 450 × 10-9/2 × 10-4) =450 × 10-5 text radian =4.5 × 10-3 text radian

Q. A parallel beam of wavelength $λ = 450 \times 1 0^{- 9} m$ passes through a long slit of width $2 \times 1 0^{- 4} m$ . The angular divergence for which most of light is diffracted is

$5.4 \times 1 0^{- 4} r a d$

$4.5 \times 1 0^{- 3} r a d$

$3.5 \times 1 0^{- 3} r a d$

$2.8 \times 1 0^{- 4} r a d$

Most of the light is diffracted between the two first order minima.
$∴$ Required angle $= 2 θ$
$= 2 sin θ = \frac{2 λ}{d} = \frac{2 \times 450 \times 1 0 ^{- 9}}{2 \times 1 0 ^{- 4}}$
$= 450 \times 1 0^{- 5} radian$
$= 4.5 \times 1 0^{- 3} radian$

Q. A parallel beam of wavelength λ=450×10−9m passes through a long slit of width 2×10−4m. The angular divergence for which most of light is diffracted is

5.4×10−4rad

4.5×10−3rad

3.5×10−3rad

2.8×10−4rad