Q. The width of a single slit if the first minimum is observed at an angle $2{^\circ}$ with a light of wavelength $6980\mathring{\mathrm{A}}$
A) 0.2 mm
B) $2 \times 10^{- 5}\ mm$
C) $2 \times 10^{5}\ mm$
D) 2 mm
Explanation
(b) The angular distance $(\theta)$ is given by
$\theta = \frac{\lambda}{d}$
$\theta = 2{^\circ} = \frac{\pi}{180} \times 2,\ \lambda = 6980\ \mathring{\mathrm{A}}$
$= 6980 \times 10^{- 10}\ m$
$\Rightarrow d = \frac{\lambda}{\theta} = \frac{6980 \times 10^{- 10} \times 180}{3.14 \times 2}$
$= 1.89 \times 10^{- 5}\ mm$
$\Rightarrow d = 2 \times 10^{- 5}\ mm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.