NEET Physics Question - Ray Optics

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 \(r_1 = A/2 = 30^{\circ}\).

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

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).

Rankers Physics

Prism Minimum Deviation Angle

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