A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 mathring A and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is :

Question

A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 mathring A and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is : (A) 3 mm (B) 9 mm (C) 4.5 mm (D) 1.5 mm

Tardigrade Admin · Accepted Answer

a=0.1 mm =10-4 λ=6000 × 10-10=6 × 10-7 D =0.5 m for 3 text rd dark a sin θ=3 λ sin θ=(3 λ/a)=(x/D) x=(3 λ D/a) =(3 × 6 × 10-7 × 0.5/10-4) =9 mm

Q. A single slit of width $0.1 mm$ is illuminated by a parallel beam of light of wavelength $6000 \overset{˚}{A}$ and diffraction bands are observed on a screen $0.5 m$ from the slit. The distance of the third dark band from the central bright band is :

3 mm

9 mm

4.5 mm

1.5 mm

$a = 0.1 mm = 1 0^{- 4}$
$λ = 6000 \times 1 0^{- 10} = 6 \times 1 0^{- 7}$
$D = 0.5 m$
for $3^{rd}$ dark a $sin θ = 3 λ$
$sin θ = \frac{3 λ}{a} = \frac{x}{D}$
$x = \frac{3 λ D}{a}$
$= \frac{3 \times 6 \times 1 0 ^{- 7} \times 0.5}{1 0 ^{- 4}}$
$= 9 mm$

Q. A single slit of width 0.1mm is illuminated by a parallel beam of light of wavelength 6000A˚ and diffraction bands are observed on a screen 0.5m from the slit. The distance of the third dark band from the central bright band is :