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

Answer 1

Answer: (B)

$a=0.1 \,mm =10^{-4}$
$\lambda=6000 \times 10^{-10}=6 \times 10^{-7}$
$D =0.5\, m$
for $3^{\text {rd }}$ dark a $\sin \theta=3 \lambda$
$\sin \theta=\frac{3 \lambda}{a}=\frac{x}{D}$
$x=\frac{3 \lambda D}{a}$
$=\frac{3 \times 6 \times 10^{-7} \times 0.5}{10^{-4}}$
$=9\, mm$