The focal length of a lens depends on

Options

A. colour of light
B. radius of curvature of the lens
C. material of the lens
D. all the above

Answer

To determine the factors on which the focal length of a lens depends, we can analyze the relevant aspects step by step.

### Step-by-Step Solution:

1. **Understanding Focal Length**: The focal length of a lens is the distance from the lens at which parallel rays of light converge (or appear to diverge from) after passing through the lens. It is a crucial property that affects how the lens will focus light.

2. **Lens Maker's Formula**: The focal length (f) of a lens can be derived from the lens maker's formula:
\[ \frac{1}{f} = \left(\frac{n_2}{n_1} - 1\right) \left(\frac{1}{R_1} - \frac{1}{R_2}\right) \]
where:
- \( n_1 \) is the refractive index of the medium from which light is coming,
- \( n_2 \) is the refractive index of the lens material,
- \( R_1 \) and \( R_2 \) are the radii of curvature of the two surfaces of the lens.

3. **Factors Affecting Focal Length**:
- **Radius of Curvature**: The focal length is directly influenced by the radii of curvature \( R_1 \) and \( R_2 \). A larger radius of curvature results in a longer focal length.
- **Refractive Index**: The refractive index of the lens material (which varies with the material) also plays a significant role. Different materials (like glass, plastic, etc.) have different refractive indices, which affects the focal length.
- **Color of Light**: The refractive index of materials can change with the wavelength of light (color). For example, blue light has a shorter wavelength than red light, and thus, it may be refracted differently, leading to variations in the focal length for different colors.

4. **Conclusion**: Based on the analysis, the focal length of a lens depends on:
- The radius of curvature of the lens surfaces.
- The material of the lens (which affects the refractive index).
- The color of light (due to the dependence of refractive index on wavelength).

Thus, the correct answer is that the focal length of a lens depends on all of the above factors.

### Final Answer:
The focal length of a lens depends on:
1. Radius of curvature of the lens.
2. Material of the lens.
3. Color of light.
Therefore, the answer is **all of the above**.

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