It is desired to have a combination of two lenses placed very close to each other such that effective focal length of the combination for all the colours is same then

Options

A. Both must be biconvex lenses
B. Both must be biconcave lenses
C. At least one lens must be plano-concave lens
D. if one lens is a converging lens then the other must be a diverging lens

Answer

To solve the problem of finding a combination of two lenses that results in the same effective focal length for all colors, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to find a combination of two lenses such that the effective focal length (F) remains the same for all colors of light. This implies that the refractive indices of the materials for different colors should not affect the focal length.

2. **Lens Maker's Formula**:
The focal length (f) of a lens is given by the lens maker's formula:
\[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
where \( n \) is the refractive index of the lens material, and \( R_1 \) and \( R_2 \) are the radii of curvature of the lens surfaces.

3. **Refractive Index Variation**:
Different colors of light have different refractive indices (n) due to dispersion. This means that for each color, the focal length will be different if both lenses are made of the same material.

4. **Condition for Same Effective Focal Length**:
For the effective focal length to be the same for all colors, the variation in refractive index must not affect the overall focal length. This can be achieved if the two lenses have opposite effects on the light.

5. **Combining Lenses**:
If one lens is converging (biconvex) and the other is diverging (biconcave), their effects can cancel each other out. The effective focal length (F) of two lenses in contact is given by:
\[ \frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} \]
where \( f_1 \) is the focal length of the converging lens and \( f_2 \) is the focal length of the diverging lens.

6. **Achieving Infinite Focal Length**:
To achieve an effective focal length of infinity (which means the combination does not converge or diverge light), we need:
\[ \frac{1}{f_1} + \frac{1}{f_2} = 0 \]
This implies that \( f_1 \) and \( f_2 \) must be equal in magnitude but opposite in sign, which is possible if one lens is converging and the other is diverging.

7. **Conclusion**:
Therefore, the correct combination of lenses that results in the same effective focal length for all colors is one converging lens (biconvex) and one diverging lens (biconcave).

### Final Answer:
The correct option is D: One lens must be converging (biconvex) and the other must be diverging (biconcave).