Which of the following entities related to spherical mirrors do not depend on whether rays are paraxial or not ?

Options

A. Pole
B. Principal axis
C. Radius of curvature
D. focal length

Explanation

To determine which entities related to spherical mirrors do not depend on whether rays are paraxial or not, we need to analyze each option carefully. Here’s a step-by-step solution:

### Step 1: Understand Paraxial Rays
Paraxial rays are those rays that are close to the principal axis of the mirror. They make small angles with the principal axis and are used in approximations for ray optics.

### Step 2: Identify the Options
We need to evaluate the following entities:
1. Pole
2. Principal Axis
3. Radius of Curvature
4. Focal Length

### Step 3: Analyze Each Entity
1. **Pole**:
- The pole is the midpoint of the mirror's surface. It is a fixed point and does not depend on the nature of the rays (whether they are paraxial or not).
- **Conclusion**: Does not depend on paraxial rays.

2. **Principal Axis**:
- The principal axis is defined as the line that passes through the center of curvature and the pole of the mirror. This is a geometric property and remains constant regardless of the rays' nature.
- **Conclusion**: Does not depend on paraxial rays.

3. **Radius of Curvature**:
- The radius of curvature is the radius of the sphere from which the mirror is made. It is a fixed property of the mirror and does not change with the type of rays.
- **Conclusion**: Does not depend on paraxial rays.

4. **Focal Length**:
- The focal length is defined based on the mirror's curvature and is affected by the nature of the rays. For non-paraxial rays, spherical aberration can occur, leading to variations in the effective focal length.
- **Conclusion**: Depends on paraxial rays.

### Step 4: Final Answer
The entities related to spherical mirrors that do not depend on whether rays are paraxial or not are:
- Pole
- Principal Axis
- Radius of Curvature

### Summary
- **Pole**: Not dependent on paraxial rays.
- **Principal Axis**: Not dependent on paraxial rays.
- **Radius of Curvature**: Not dependent on paraxial rays.
- **Focal Length**: Dependent on paraxial rays.