Question

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?

• A. No
• B. Yes, A
• C. Yes, B
• D. Yes, Both A and B

Hint:

Total internal reflection occurs only when angle of incidence is greater than critical angle and light travels from denser to rarer medium.

Answer 1

The Correct Option is C

Step 1: Find speed of light in the medium.
\[ v = \frac{\text{distance}}{\text{time}} = \frac{3 \, \text{cm}}{0.2 \, \text{ns}} \] \[ v = \frac{3 \times 10^{-2}}{0.2 \times 10^{-9}} = 1.5 \times 10^8 \, \text{m/s} \]

Step 2: Calculate refractive index of the medium.
\[ n = \frac{c}{v} = \frac{3 \times 10^8}{1.5 \times 10^8} = 2 \]

Step 3: Find critical angle.
\[ \sin c = \frac{1}{n} = \frac{1}{2} \] \[ c = 30^\circ \]

Step 4: Compare angle of incidence for ray A.
Ray A has angle \(15^\circ\), which is less than critical angle.
\[ 15^\circ<30^\circ \] So, no total internal reflection for ray A.

Step 5: Compare angle of incidence for ray B.
Ray B has angle \(42^\circ\), which is greater than critical angle.
\[ 42^\circ>30^\circ \] So, total internal reflection occurs for ray B. Only ray B undergoes total internal reflection.

Step 6: Final conclusion.
\[ \boxed{\text{Option (C)}} \]