Question

In a diffraction pattern due to a single slit of width 'a', the first minimum is observed at an angle $30^{\circ}$ when light of wavelength $5000 \mathring A $ is incident on the slit. The first secondary maximum is observed at an angle of :

• A. $\sin^{-1} \left( \frac{2}{3} \right)$
• B. $\sin^{-1} \left( \frac{1}{2} \right)$
• C. $\sin^{-1} \left( \frac{3}{4} \right)$
• D. $\sin^{-1} \left( \frac{1}{4} \right)$

Answer 1

The Correct Option is C

First Minima and First Secondary Maxima 

For the first minima in diffraction, the equation is:

\(\sin 30^{\circ} = \frac{\lambda}{a} = \frac{1}{2}\)

To find the first secondary maxima, we use the following equation:

\(\sin \theta = \frac{3 \lambda}{2a} = \frac{3}{2} \times \frac{1}{2} \Rightarrow \theta = \sin^{-1} \left( \frac{3}{4} \right)\)

Conclusion:

The angle for the first secondary maxima is \( \theta = \sin^{-1} \left( \frac{3}{4} \right) \).