A slit of width e is illuminated by light of wavelength λ. What should be the value of e to obtain the first maximum at an angle of diffraction of \( \displaystyle\frac{\pi}{3} \)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \sqrt{3}\,\lambda \)
In single-slit diffraction the secondary maxima lie roughly midway between the minima, at \( e\sin\theta = \left(n + \frac{1}{2}\right)\lambda \). The central maximum is \( n = 0 \) at \( \theta = 0 \), so the first (secondary) maximum is \( n = 1 \):
\( \displaystyle e\sin\theta = \frac{3\lambda}{2} \)
With \( \theta = \frac{\pi}{3} \), \( \sin\theta = \frac{\sqrt{3}}{2} \).
\( \displaystyle e = \frac{3\lambda}{2}\times\frac{2}{\sqrt{3}} = \frac{3\lambda}{\sqrt{3}} = \sqrt{3}\,\lambda \)