Diffraction: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Diffraction. Understanding the underlying formula is key to arriving at the correct answer below:

For the first minimum, $a\sin\theta_1 = \lambda \Rightarrow a\sin(30^\circ) = \lambda \Rightarrow a/2 = \lambda \Rightarrow a = 2\lambda$. For the first secondary maximum, $a\sin\theta_2 = \frac{3\lambda}{2} \Rightarrow (2\lambda)\sin\theta_2 = \frac{3\lambda}{2} \Rightarrow \sin\theta_2 = \frac{3}{4}$, so $\theta_2 = \sin^{-1}(\frac{3}{4})$.