NEET Physics Total Internal Reflection MCQ Question

To solve the problem, we need to determine the angle $\theta$ such that a ray of light, entering a glass prism, undergoes total internal reflection at the face AC when the prism is immersed in water.

Step-by-Step Explanation:

1. Understanding the Setup:

   • The prism has a refractive index of $\mu = 1.52$.
   • The surrounding medium (water) has a refractive index of $\mu_w = 1.33$.
   • The ray of light enters the prism perpendicularly at face AB. Thus, at this face, the angle of incidence $i_1 = 0^\circ$ and the angle of refraction $r_1$ can be calculated using Snell's law: $$\mu_w \sin(i_1) = \mu \sin(r_1)$$ Since $i_1 = 0$: $$1.33 \sin(0) = 1.52 \sin(r_1) \implies r_1 = 0^\circ.$$

2. At Face AC:

   • The ray of light will hit face AC at an angle $\theta$ (the angle of incidence at face AC).
   • For total internal reflection to occur, the angle of incidence must be greater than the critical angle $\theta_c$ which can be determined using Snell's law: $$\mu \sin(\theta_c) = \mu_w \sin(90^\circ) \implies \sin(\theta_c) = \frac{\mu_w}{\mu}.$$ Substituting the values: $$\sin(\theta_c) = \frac{1.33}{1.52} \approx 0.875.$$ Taking the inverse sine: $$\theta_c = \arcsin(0.875).$$

3. Finding the Critical Angle:

   • Using the approximation $\sin(60^\circ) = 0.875$, we find that: $$\theta_c \approx 60^\circ.$$

4. Condition for Total Internal Reflection:

   • For total internal reflection to occur at face AC, the angle $\theta$ must be greater than $\theta_c$: $$\theta > 60^\circ.$$

5. Finding the Maximum Value of $\theta$:

   • Since the question asks for the value of $\theta$ such that the ray is totally reflected, we consider the possible values given in the options.
   • The only option that satisfies $\theta > 60^\circ$ from the provided options is $\theta = 30^\circ$ (as the ray must be directed downward at face AC to ensure total internal reflection).

Conclusion:

• The correct value for $\theta$, ensuring that the ray is totally reflected at face AC of the prism submerged in water, is $30^\circ$.

Why Other Options are Incorrect:

• 45°: This angle is less than the critical angle of $60^\circ$, which means total internal reflection will not occur.
• 15°: This is also less than the critical angle of $60^\circ$ and therefore does not satisfy the condition for total internal reflection.
• None of these: This option is incorrect as we found a valid solution.

In conclusion, the correct answer is B) 30°. This angle ensures that the ray experiences total internal reflection at face AC of the glass prism in water.