A ray of light travels from an optically denser to rarer medium. The critical angle of the two media is C. The maximum possible deviation of the ray will be

Options

A. `((pi)/(2)-C)`
B. 2C
C. `pi-2C`
D. `pi-C`

Answer

To solve the problem of finding the maximum possible deviation of a ray of light traveling from an optically denser medium to a rarer medium with a given critical angle \( C \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- A ray of light is traveling from an optically denser medium (medium 1) to a rarer medium (medium 2).
- The critical angle \( C \) is defined as the angle of incidence in the denser medium at which the angle of refraction in the rarer medium is \( 90^\circ \).

2. **Defining Angles**:
- Let \( \theta \) be the angle of incidence in the denser medium.
- The angle of refraction \( \phi \) in the rarer medium can be expressed using Snell's law, but for maximum deviation, we will consider the critical angle.

3. **Maximum Deviation Condition**:
- The maximum deviation occurs when the ray grazes the surface of the rarer medium. This happens when the angle of refraction \( \phi \) reaches \( 90^\circ \).
- Therefore, at maximum deviation, \( \phi = 90^\circ \).

4. **Calculating Deviation**:
- The deviation \( \delta \) is given by:
\[ \delta = \phi - \theta \]
- Substituting \( \phi = 90^\circ \):
\[ \delta = 90^\circ - \theta \]

5. **Condition for Total Internal Reflection (TIR)**:
- For TIR to occur, the angle of incidence \( \theta \) must be greater than the critical angle \( C \).
- The maximum deviation occurs when \( \theta \) is equal to the critical angle \( C \).

6. **Finding Maximum Deviation**:
- The maximum deviation \( \delta_{\text{max}} \) can be calculated as:
\[ \delta_{\text{max}} = 180^\circ - 2\theta \]
- Substituting \( \theta = C \):
\[ \delta_{\text{max}} = 180^\circ - 2C \]

### Final Result:
The maximum possible deviation of the ray of light when it travels from an optically denser medium to a rarer medium with a critical angle \( C \) is:
\[ \delta_{\text{max}} = 180^\circ - 2C \]