Question

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

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

Answer 1

The Correct Option is A

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