33. In a diffraction pattern due to a single slit of width ’ a ’, the first minimum is observed at an angle 30° when light of wavelength 5000Å is incident on the slit. The first secondary maximum is observed at an angle of :

33. In a diffraction pattern due to a single slit of width ’ a ’, the first minimum is observed at an angle 30° when light of wavelength 5000Å is incident on the slit. The first secondary maximum is observed at an angle of :

(a) \(\sin^{-1} \left(\frac{1}{4}\right)\)

(b) \(\sin^{-1} \left(\frac{2}{3}\right)\)

(c) \(\sin^{-1} \left(\frac{1}{2}\right)\)

(d) \(\sin^{-1} \left(\frac{3}{4}\right)\)

Answer :  (d) \(\sin^{-1} \left(\frac{3}{4}\right)\)

\(\sin \theta_1 = \frac{\lambda}{a}\)

\(\sin 30^\circ = \frac{5000 \mathring{A}}{a} = \frac{1}{2}\)

\(\frac{3\lambda}{2a} = \sin \theta_2\)

\(\frac{3}{2} \frac{5000 \mathring{A}}{a} = \sin \theta_2\)

\(\sin \theta_2 = \frac{3}{4}\)