Total Internal Reflection Conditions – Rankers Physics

Refraction by Plane Surfaces: Practice Problem & Solution

Assertion (A): The refractive index of diamond is \(\sqrt{6}\), and that of liquid is \(\sqrt{3}\), . If the light travels from diamond to the liquid, it will totally reflected when the angle of incidence is \(30^\circ\). Reason (R): For total internal reflection, angle of incidence should be less than critical angle \(\theta_c = sin^{-1}(\frac{1}{\mu})\).
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

Short Solution (Best for NEET):

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

The critical angle \(\theta_c = sin^{-1}(\mu_{liquid}/\mu_{diamond}) = sin^{-1}(\sqrt{3}/\sqrt{6}) = sin^{-1}(1/\sqrt{2}) = 45^\circ\), . For TIR, the angle of incidence (i), must be greater than \(\theta_c), (i.e., (i > 45^\circ),\). Since \(i = 30^\circ\), is not greater than \(45^\circ\), A is false. Reason R is also false because TIR occurs when \(i > \theta_c\).

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