The first diffraction minimum due to a single slit diffraction is seen at θ=30° for a light of wavelength 5000 mathringA falling perpendicularly on the slit. The width of the slit is :-

Question

The first diffraction minimum due to a single slit diffraction is seen at θ=30° for a light of wavelength 5000 mathringA falling perpendicularly on the slit. The width of the slit is :- (A) 5 × 10-5 cm (B) 2.5 × 10-5 cm (C) 1.25 × 10-5 cm (D) 10 × 10-5 cm

Tardigrade Admin · Accepted Answer

sin θ=(Δ x / a )=( n λ/ a ) sin 30°=(1 × 5000 × 10-10/ a ) a =5 × 10-7 × 2 a =10-6 m a =10 × 10-5 cm

Q. The first diffraction minimum due to a single slit diffraction is seen at $θ = 3 0^{\circ}$ for a light of wavelength $5000 \overset{˚}{A}$ falling perpendicularly on the slit. The width of the slit is :-

$5 \times 1 0^{- 5} c m$

$2.5 \times 1 0^{- 5} c m$

$1.25 \times 1 0^{- 5} c m$

$10 \times 1 0^{- 5} c m$

$sin θ = \frac{Δ x}{a} = \frac{nλ}{a}$
$sin 3 0^{\circ} = \frac{1 \times 5000 \times 1 0 ^{- 10}}{a}$
$a = 5 \times 1 0^{- 7} \times 2$
$a = 1 0^{- 6} m$
$a = 10 \times 1 0^{- 5} c m$

Q. The first diffraction minimum due to a single slit diffraction is seen at θ=30∘ for a light of wavelength 5000A˚ falling perpendicularly on the slit. The width of the slit is :-

5×10−5cm

2.5×10−5cm

1.25×10−5cm

10×10−5cm