The velocity of light through media 'A' and 'B' are V and 2V, respectively. The value of sin C is ______ [where 'C' is the critical angle].

Options

A. `1/(2)`
B. `1/(3)`
C. 3
D. 2

Explanation

To find the value of sin C (where C is the critical angle) given the velocities of light in two media A and B, we can follow these steps:

### Step 1: Understand the relationship between velocity and refractive index
The refractive index (μ) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v). It can also be expressed as:
\[ \mu = \frac{v_b}{v_a} \]
where \( v_a \) is the velocity of light in medium A and \( v_b \) is the velocity of light in medium B.

### Step 2: Assign the given velocities
From the question, we know:
- Velocity in medium A, \( v_a = V \)
- Velocity in medium B, \( v_b = 2V \)

### Step 3: Calculate the refractive index
Using the velocities assigned:
\[ \mu = \frac{v_b}{v_a} = \frac{2V}{V} = 2 \]

### Step 4: Relate the refractive index to the critical angle
The critical angle (C) can be found using Snell's law, which states:
\[ \mu = \frac{1}{\sin C} \]
From our calculation, we have:
\[ 2 = \frac{1}{\sin C} \]

### Step 5: Solve for sin C
Rearranging the equation gives:
\[ \sin C = \frac{1}{2} \]

### Final Answer
Thus, the value of sin C is:
\[ \sin C = \frac{1}{2} \]

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