Q136 / 180 · COMEDK 2025 (10 May Shift 1) · Physics
Two light rays A and B travel from a medium into air at angles of incidence 15 degrees and 42 degrees respectively. In the medium, light travels 3 cm in 0.2 ns . Will there be total internal reflection? If so, which ray?
- AYes, Both A and B
- Correct answerBYes, B
- CNo
- DYes, A
Solution
The speed of light in the medium is $v = \dfrac{d}{t} = \dfrac{3 \times 10^{-2} \text{ m}}{0.2 \times 10^{-9} \text{ s}} = 1.5 \times 10^{8} \text{ m/s}$.
The refractive index of the medium is $n = \dfrac{c}{v} = \dfrac{3 \times 10^{8}}{1.5 \times 10^{8}} = 2$.
The critical angle $\theta_{c}$ is given by $\sin(\theta_{c}) = \dfrac{n_{air}}{n_{medium}} = \dfrac{1}{2}$.
Thus, $\theta_{c} = 30^{\circ}$.
Total internal reflection occurs when the angle of incidence $i > \theta_{c}$.
For ray A, $i_{A} = 15^{\circ} < 30^{\circ}$, so no total internal reflection occurs.
For ray B, $i_{B} = 42^{\circ} > 30^{\circ}$, so total internal reflection occurs for ray B.
Answer: Yes, B
The refractive index of the medium is $n = \dfrac{c}{v} = \dfrac{3 \times 10^{8}}{1.5 \times 10^{8}} = 2$.
The critical angle $\theta_{c}$ is given by $\sin(\theta_{c}) = \dfrac{n_{air}}{n_{medium}} = \dfrac{1}{2}$.
Thus, $\theta_{c} = 30^{\circ}$.
Total internal reflection occurs when the angle of incidence $i > \theta_{c}$.
For ray A, $i_{A} = 15^{\circ} < 30^{\circ}$, so no total internal reflection occurs.
For ray B, $i_{B} = 42^{\circ} > 30^{\circ}$, so total internal reflection occurs for ray B.
Answer: Yes, B
Hence, the correct answer is option: 'B'.