Refraction by Prism: Practice Problem & Solution
Assertion (A): A prism of refracting angle \(60^{\circ}\) is made of a material of refractive index \(\sqrt{2}\) for a certain wavelength. As light of this wavelength passes through the prism, the prism, angle of minimum deviation is \(30^{\circ}\). Reason (R): At minimum deviation, angle of refraction of the first face is \(r_1 = A/2 = 30^{\circ}\).
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Refraction by Prism. Understanding the underlying formula is key to arriving at the correct answer below:
For a prism at minimum deviation, the angle of refraction at the first face is \(r_1 = A/2\), where \(A\) is the prism angle. Given \(A = 60^{\circ}\), \(r_1 = 30^{\circ}\). This makes Reason (R) true. Using the prism formula \(n = \frac{sin((A + \delta_m)/2)}{sin(A/2)}\), with \(n=\sqrt{2}\) and \(A=60^{\circ}\), we find \(\delta_m = 30^{\circ}\). Thus, Assertion (A) is also true. Reason (R) provides a key condition used in calculating the minimum deviation, hence it is the correct explanation for (A).
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