A slit of width a is illuminated by white light in single slit diffraction. The first minimum for red light λ =6500 Å will fall at θ =30o, when a is

Question

A slit of width a is illuminated by white light in single slit diffraction. The first minimum for red light λ =6500 Å will fall at θ =30o, when a is (A) 3250 Å (B) 6.5× 10- 4 cm (C) 1.3 μ m (D) 2.6× 10- 4 cm

Tardigrade Admin · Accepted Answer

sin θ =(λ /a) ⇒ sin 30o=(6500/a)â« ∴ (1/2)=(6500/a)â« ⇒ a=2× 6500 â« ⇒ a=2× 6500× 10- 10 m ∴ ⇒ a=1.3× 10- 6 m

Q. A slit of width $a$ is illuminated by white light in single slit diffraction. The first minimum for red light $λ = 6500 Å$ will fall at $θ = 3 0^{o},$ when $a$ is

$3250 Å$

$6.5 \times 1 0^{- 4} c m$

$1.3 μ m$

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

$s in θ = \frac{λ}{a}$
$\Rightarrow s in 3 0^{o} = \frac{6500}{a} Å$
$∴ \frac{1}{2} = \frac{6500}{a} Å$
$\Rightarrow a = 2 \times 6500 Å$
$\Rightarrow a = 2 \times 6500 \times 1 0^{- 10} m$
$∴ \Rightarrow a = 1.3 \times 1 0^{- 6} m$

Q. A slit of width a is illuminated by white light in single slit diffraction. The first minimum for red light λ=6500Å will fall at θ=30o, when a is

3250Å

6.5×10−4cm

1.3μm

2.6×10−4cm