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Physics Question on single slit diffraction

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

A

30∘30^{\circ}

B

45∘45^{\circ}

C

60∘60^{\circ}

D

15∘15^{\circ}

Answer

30∘30^{\circ}

Explanation

Solution

The distance of first diffraction minimum from the central principal maximum x=Dλdx=\frac{D \lambda}{d} xD=λd\frac{x}{D}=\frac{\lambda}{d} or d=λsin⁡θd=\frac{\lambda}{\sin \theta} ⇒sin⁡θ=λd=5000×10−81×10−4sin⁡θ\Rightarrow \sin \theta=\frac{\lambda}{d}=\frac{5000 \times 10^{-8}}{1 \times 10^{-4}} \sin \theta =0.5=sin⁡30θ=30∘=0.5=\sin 30 \theta=30^{\circ}