Question

The first diffraction minimum due to single slit diffraction is $\theta ,$ for a light of wave length $5000\, ?$ . If the width of the slit is $1\times {{10}^{-4}}cm,$ then the value of $\theta$ is:

• A. $30{}^\circ$
• B. $45{}^\circ$
• C. $60{}^\circ$
• D. $15{}^\circ$

Answer 1

Answer: (A)

$30{}^\circ$

Answer 2

The distance of first diffraction minimum from the central principal maximum. $x =\frac{D \lambda}{d}$ $\frac{x}{D} =\frac{\lambda}{d}$ or $d =\frac{\lambda}{\sin \theta}$ $\Rightarrow \sin \theta =\frac{\lambda}{d}=\frac{5000 \times 10^{-8}}{1 \times 10^{-4}}$ $\sin \theta =0.5=\sin 30$ $\theta =30^{\circ}$