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

• A. $V_{A} = V_{B} = V_{C} = 0$
• B. $V_{A} = V_{B} = V_{C}$
• C. $V_{A} > V_{B} > V_{C}$
• D. $V_{A} < V_{B} < V_{C}$

Hint:

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.

Answer 1

The Correct Option is C

Step 1: Snell's law idea.
For the same incidence angle, $\mu = \dfrac{\sin i}{\sin r}$. A smaller refraction angle $r$ means a bigger $\mu$.

Step 2: Speed and refractive index.
Light slows down in a denser medium: $\mu = \dfrac{c}{v}$. So a bigger $\mu$ means a smaller speed $v$.

Step 3: Link speed to refraction angle.
Putting these together, with $i$ fixed, $v \propto \sin r$. More bending (small $r$) means slower light.

Step 4: Compare the angles.
Given $r_{A}=35^{\circ}$, $r_{B}=25^{\circ}$, $r_{C}=15^{\circ}$. So $r_{A} > r_{B} > r_{C}$.

Step 5: Turn that into speeds.
Since $v \propto \sin r$ and the sines follow the same order, $V_{A} > V_{B} > V_{C}$.

Step 6: Pick the option.
The correct order is $V_{A} > V_{B} > V_{C}$, which is option 3.
\[ \boxed{V_{A} > V_{B} > V_{C}} \]