Question:
For the same angle of incidence, the angles of refraction of light ray in different media A, B, C are $35^{\circ}$, $25^{\circ}$, $15^{\circ}$. If $V_{A}, V_{B}, V_{C}$ are velocities of light in A, B, C media respectively, then
For the same angle of incidence, the angles of refraction of light ray in different media A, B, C are $35^{\circ}$, $25^{\circ}$, $15^{\circ}$. If $V_{A}, V_{B}, V_{C}$ are velocities of light in A, B, C media respectively, then
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A larger angle of refraction ($r$) means the medium bends light less, meaning it is optically rarer and light travels faster through it! Larger $r \implies$ larger velocity.
Updated On: Jun 3, 2026
- $V_{A} = V_{B} = V_{C} = 0$
- $V_{A} = V_{B} = V_{C}$
- $V_{A} > V_{B} > V_{C}$
- $V_{A} < V_{B} < V_{C}$
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The Correct Option is C
Solution and Explanation
Step 1: Concept
According to Snell's Law, the refractive index of a medium is related to the angle of incidence ($i$) and angle of refraction ($r$) by $\mu = \frac{\sin i}{\sin r}$. Also, the velocity of light in a medium is inversely proportional to its refractive index ($\mu = \frac{c}{v}$).
Step 2: Meaning
Combining these relations reveals that the velocity of light in a medium is directly related to the sine of its refraction angle for a constant incidence angle: $v \propto \sin r$.
Step 3: Analysis
Since the angle of incidence $i$ is constant across all media, a smaller angle of refraction $r$ results in a smaller value of $\sin r$, leading to a higher refractive index $\mu$ and a lower propagation velocity $v$. Given the angles of refraction are $r_A = 35^{\circ}$, $r_B = 25^{\circ}$, and $r_C = 15^{\circ}$, we have the ordering: $r_A > r_B > r_C \implies \sin r_A > \sin r_B > \sin r_C$. This translates directly into the velocity relationship: $V_{A} > V_{B} > V_{C}$.
Step 4: Conclusion
Hence, the correct order of the velocities of light across these media is $V_{A} > V_{B} > V_{C}$.
Final Answer: (C)
According to Snell's Law, the refractive index of a medium is related to the angle of incidence ($i$) and angle of refraction ($r$) by $\mu = \frac{\sin i}{\sin r}$. Also, the velocity of light in a medium is inversely proportional to its refractive index ($\mu = \frac{c}{v}$).
Step 2: Meaning
Combining these relations reveals that the velocity of light in a medium is directly related to the sine of its refraction angle for a constant incidence angle: $v \propto \sin r$.
Step 3: Analysis
Since the angle of incidence $i$ is constant across all media, a smaller angle of refraction $r$ results in a smaller value of $\sin r$, leading to a higher refractive index $\mu$ and a lower propagation velocity $v$. Given the angles of refraction are $r_A = 35^{\circ}$, $r_B = 25^{\circ}$, and $r_C = 15^{\circ}$, we have the ordering: $r_A > r_B > r_C \implies \sin r_A > \sin r_B > \sin r_C$. This translates directly into the velocity relationship: $V_{A} > V_{B} > V_{C}$.
Step 4: Conclusion
Hence, the correct order of the velocities of light across these media is $V_{A} > V_{B} > V_{C}$.
Final Answer: (C)
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