In a single slit diffraction experiment, the first minimum is observed at a diffraction angle $ het

Question

In a single slit diffraction experiment, the first minimum is observed at a diffraction angle $	heta = \sin^{-1}(1/3)$. At what angle will the first secondary maximum be strictly observed?

Professor PC Thomas Classes · Answer

(a) : For the first minimum, the condition is $a\sin	heta = 1\lambda$. Given $\sin	heta = 1/3$, we have $a(1/3) = \lambda \implies a = 3\lambda$. For the first secondary maximum, the condition is $a\sin	heta' = \frac{3}{2}\lambda$. Substituting $a = 3\lambda$ gives $(3\lambda)\sin	heta' = 1.5\lambda \implies \sin	heta' = 1.5 / 3 = 0.5$. Therefore, the angle is $	heta' = \sin^{-1}(0.5) = 30^{\circ}$.