The critical angle of light from medium A to medium B is `theta`. The speed of light in medium A is v. the speed of light in medium B is

Options

A. `v/(sin theta)`
B. `v/(cos theta)`
C. `v sin theta`
D. `v cos theta`

Answer

To find the speed of light in medium B (denoted as \( v_B \)) given the critical angle \( \theta \) and the speed of light in medium A (denoted as \( v_A \)), we can use Snell's law and the definition of the critical angle.

### Step-by-step Solution:

1. **Understanding the Critical Angle**:
The critical angle \( \theta \) is defined as the angle of incidence in the denser medium (medium A) at which light is refracted at an angle of 90 degrees in the less dense medium (medium B). This means that at the critical angle, the light ray travels along the boundary between the two media.

2. **Applying Snell's Law**:
Snell's law states that:
\[ n_A \sin(\theta_A) = n_B \sin(\theta_B) \]
Where \( n_A \) and \( n_B \) are the refractive indices of medium A and medium B, respectively, and \( \theta_A \) and \( \theta_B \) are the angles of incidence and refraction.

At the critical angle:
- \( \theta_A = \theta \) (the critical angle)
- \( \theta_B = 90^\circ \)

Therefore, we can write:
\[ n_A \sin(\theta) = n_B \sin(90^\circ) \]
Since \( \sin(90^\circ) = 1 \), this simplifies to:
\[ n_A \sin(\theta) = n_B \]

3. **Relating Refractive Index to Speed**:
The refractive index \( n \) of a medium is related to the speed of light in that medium by the equation:
\[ n = \frac{c}{v} \]
Where \( c \) is the speed of light in a vacuum and \( v \) is the speed of light in the medium.

Thus, we can express the refractive indices for both media:
\[ n_A = \frac{c}{v_A} \quad \text{and} \quad n_B = \frac{c}{v_B} \]

4. **Substituting into Snell's Law**:
Substituting these expressions into our earlier equation:
\[ \frac{c}{v_A} \sin(\theta) = \frac{c}{v_B} \]

5. **Simplifying the Equation**:
Cancel \( c \) from both sides:
\[ \frac{\sin(\theta)}{v_A} = \frac{1}{v_B} \]

6. **Finding \( v_B \)**:
Rearranging the equation to solve for \( v_B \):
\[ v_B = \frac{v_A}{\sin(\theta)} \]

### Final Answer:
The speed of light in medium B is:
\[ v_B = \frac{v_A}{\sin(\theta)} \]