Four lenses A, B, C and D of power +100D, -50D, 20D and 5D. Which lenses will you use to design a compound microscope for best magnification ?

Options

A. A and C
B. B and D
C. C and D
D. A and B

Answer

To determine which lenses to use for designing a compound microscope with the best magnification, we need to analyze the powers of the given lenses and apply the relevant principles of optics.

### Step-by-Step Solution:

1. **Identify the Lenses and Their Powers**:
- Lens A: +100 D (Diopters)
- Lens B: -50 D
- Lens C: +20 D
- Lens D: +5 D

2. **Understand the Requirements for a Compound Microscope**:
- A compound microscope typically consists of two convex lenses: the objective lens and the eyepiece lens.
- The magnification of a compound microscope is given by the formula:
\[ M = M_O \times M_E \]
where \(M_O\) is the magnification produced by the objective lens and \(M_E\) is the magnification produced by the eyepiece lens.

3. **Determine Which Lenses Can Be Used**:
- Only convex lenses (positive power) can be used for magnification in a compound microscope.
- From the given lenses, the convex lenses are:
- Lens A: +100 D
- Lens C: +20 D
- Lens B (-50 D) is a concave lens and cannot be used for magnification.
- Lens D (+5 D) is also a convex lens but has a lower power compared to lenses A and C.

4. **Select the Lenses for Best Magnification**:
- To achieve the best magnification, we should select the lenses with the highest powers.
- Lens A (+100 D) has the highest power, followed by Lens C (+20 D).
- Therefore, the best combination for the compound microscope would be Lens A and Lens C.

5. **Conclusion**:
- The lenses to be used for designing a compound microscope for the best magnification are Lens A (+100 D) and Lens C (+20 D).

### Final Answer:
- **Use Lens A (+100 D) and Lens C (+20 D) for the best magnification in a compound microscope.**