Question

A slit of width \(e\) is illuminated by light of wavelength \(\lambda\). What should be the value of \(e\) to obtain the first maximum at an angle of diffraction \(\frac{\pi}{3}\)?

• A. \( \frac{2}{\sqrt{3}} \lambda \)
• B. \( \frac{\lambda}{\sqrt{3}} \)
• C. \( \sqrt{3} \lambda \)
• D. \( \frac{\sqrt{3}}{2} \lambda \)

Hint:

In single-slit diffraction, the angle of the first minimum and maximum are related to the slit width and wavelength.

Answer 1

The Correct Option is B

The first maximum in a single-slit diffraction pattern occurs when the angle \(\theta\) satisfies the condition: \[ a \sin \theta = m\lambda \quad (m = 1) \] For the first maximum, this becomes: \[ e \sin \left(\frac{\pi}{3}\right) = \lambda \] Using \(\sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}\), we get: \[ e \times \frac{\sqrt{3}}{2} = \lambda \quad \Rightarrow \quad e = \frac{\lambda}{\sqrt{3}} \]