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 $6980 \, \overset{^\circ }{A}$ ?

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

Answer 1

Answer: (B)

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