Which one of the following does not exhibit dispersion

Options

A.
B.
C.
D.

Answer

To determine which of the given options does not exhibit dispersion, we need to understand the conditions under which dispersion occurs in optical systems, particularly in lenses and spherical surfaces.

### Step-by-Step Solution:

1. **Understanding Dispersion**: Dispersion occurs when different wavelengths of light are refracted by different amounts as they pass through a medium. This typically happens in materials with varying refractive indices for different wavelengths.

2. **Identify the Conditions for No Dispersion**: For a system to not exhibit dispersion, the following conditions must be met:
- The radii of curvature of the surfaces involved must be equal.
- The surfaces must have the same type of curvature (both concave or both convex).

3. **Analyzing the Options**:
- **Option 1**: If the radii are different, dispersion will occur.
- **Option 2**: If the radii are different, dispersion will occur.
- **Option 3**: If the radii are equal and both surfaces have the same curvature (both concave or both convex), there will be no dispersion.
- **Option 4**: If the radii are different, dispersion will occur.

4. **Conclusion**: Based on the analysis, the only option that does not exhibit dispersion is **Option 3**, where the radii are equal and of the same type.

### Final Answer:
The option that does not exhibit dispersion is **Option 3**.