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-C`
B. `pi-2C`
C. `2C`
D. `pi/2+C`

Explanation

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 critical angle \( C \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Situation**:
- We have a ray of light traveling from an optically denser medium to a rarer medium. The critical angle between these two media is given as \( C \).

2. **Defining Deviation**:
- The deviation \( \delta \) of a ray of light is defined as the angle between the incident ray and the refracted ray. Mathematically, it can be expressed as:
\[ \delta = \theta - \phi \]
where \( \theta \) is the angle of incidence and \( \phi \) is the angle of refraction.

3. **Condition for Maximum Deviation**:
- The maximum deviation occurs when the angle of refraction \( \phi \) approaches \( 90^\circ \). This is because as the angle of refraction increases, the deviation will also increase.

4. **Applying the Critical Angle**:
- The critical angle \( C \) is defined as the angle of incidence at which the angle of refraction is \( 90^\circ \). Thus, when the angle of incidence \( \theta \) is equal to the critical angle \( C \), we can express the relationship as:
\[ \phi = 90^\circ \text{ when } \theta = C \]

5. **Calculating Maximum Deviation**:
- Substituting \( \phi = 90^\circ \) into the deviation formula gives:
\[ \delta = \theta - \phi = C - 90^\circ \]
- Since we are looking for the maximum deviation, we consider the scenario where the ray undergoes total internal reflection (TIR) when \( \theta \) is just greater than \( C \).

6. **Final Expression for Maximum Deviation**:
- In the case of total internal reflection, the deviation can be expressed as:
\[ \delta = 180^\circ - 2\theta \]
- To maximize \( \delta \), we set \( \theta \) to its minimum value, which is \( C \):
\[ \delta_{max} = 180^\circ - 2C \]

7. **Conclusion**:
- Therefore, the maximum possible deviation of the ray when traveling from an optically denser medium to a rarer medium is:
\[ \delta_{max} = 180^\circ - 2C \]