A ray of light travels from a medium of refractive index `mu` to air. Its angle of incidence in the medium is `i`, measured from the normal to the boundary , and its angle of deviation is `delta. delta` is plotted against `i`. Which of the following best represents the resulting curve ?

Options

A.
B.
C.
D.

Explanation

To solve the problem, we need to analyze the relationship between the angle of incidence \(i\) and the angle of deviation \(\delta\) when light travels from a medium with refractive index \(\mu\) to air.

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- The angle of incidence \(i\) is the angle between the incident ray and the normal to the surface at the boundary.
- The angle of deviation \(\delta\) is defined as the angle between the original path of the ray and the path after refraction.

2. **Applying Snell's Law**:
- According to Snell's Law, we have:
\[ \mu \sin(i) = \sin(r) \]
- Rearranging gives us:
\[ r = \sin^{-1}(\mu \sin(i)) \]

3. **Finding the Angle of Deviation**:
- The angle of deviation \(\delta\) can be expressed as:
\[ \delta = r - i \]
- Substituting for \(r\):
\[ \delta = \sin^{-1}(\mu \sin(i)) - i \]

4. **Considering Two Cases**:
- **Case 1**: When \(i < i_c\) (less than the critical angle).
- In this case, the light will refract into the air. The relationship will be non-linear due to the sine function.
- **Case 2**: When \(i \geq i_c\) (greater than or equal to the critical angle).
- Total Internal Reflection (TIR) occurs, and the angle of deviation can be expressed as:
\[ \delta = 180^\circ - 2i \]
- This relationship is linear.

5. **Graphical Representation**:
- For \(i < i_c\), the graph of \(\delta\) vs. \(i\) is non-linear.
- For \(i \geq i_c\), the graph of \(\delta\) vs. \(i\) is linear.

6. **Conclusion**:
- The resulting curve will show a non-linear relationship for angles of incidence less than the critical angle and a linear relationship for angles of incidence greater than or equal to the critical angle. Therefore, the graph will have a distinct change in slope at the critical angle.