Question

What is the width of a single slit if the first minimum is observed at an angle $2^{\circ }$ with a light of wavelength $6980\stackrel{{}^{\circ }}{A}$ ?

• A. $0.2mm$
• B. $2\times 10^{-2}mm$
• C. $2\times 10^{5}mm$
• D. $2mm$

Answer 1

Answer: (B)

The angular distance $\left(\theta \right)$ is given by
$\theta =\frac{\lambda }{d}$
Given, $\theta =2^{\circ }=\frac{\pi }{180}\times 2,\lambda =6980\stackrel{{}^{\circ }}{A}$
$=6980\times 10^{-10}m$
$\therefore d=\frac{\lambda }{\theta }=\frac{6980\times 10^{-10}\times 180}{3.14\times 2}$
$\Rightarrow d\approx 2\times 10^{-5}m$ $=2\times 10^{-2}mm$