A scientist is observing a bacteria through a compound microscope.For better analysis and to improve its resolving power he should.(Select the best option)

Options

A. Decrease the focal length of the eye piece.
B. Increase the wave length of the light
C. Decrease the diameter of the objective lens
D. Increase the refractive index of the medium between the object and objective lens

Answer

To solve the problem of improving the resolving power of a compound microscope while observing bacteria, we need to understand the relationship between resolving power and various factors involved.

### Step-by-Step Solution:

1. **Understanding Resolving Power**:
The resolving power (RP) of a microscope is defined by the formula:
\[ RP = \frac{2 \mu \sin \theta}{\lambda} \]
where:
- \( \mu \) = refractive index of the medium,
- \( \theta \) = half of the angular aperture of the lens,
- \( \lambda \) = wavelength of light used.

2. **Analyzing the Formula**:
From the formula, we can deduce:
- The resolving power is directly proportional to the refractive index (\( \mu \)).
- The resolving power is inversely proportional to the wavelength (\( \lambda \)).
This means that to increase the resolving power, we can either increase the refractive index or decrease the wavelength of light used.

3. **Evaluating the Options**:
Now, let's evaluate the provided options:
- **Option 1**: Decrease the focal length of the objective lens.
- This does not directly affect resolving power. **(Incorrect)**
- **Option 2**: Increase the wavelength of light.
- Increasing the wavelength will decrease the resolving power. **(Incorrect)**
- **Option 3**: Decrease the diameter of the objective lens.
- The diameter of the lens does not directly affect resolving power in this context. **(Incorrect)**
- **Option 4**: Increase the refractive index of the medium between the objective and the specimen.
- Increasing the refractive index will increase the resolving power. **(Correct)**

4. **Conclusion**:
Based on the analysis, the best option to improve the resolving power of the microscope is to **increase the refractive index of the medium between the objective and the specimen**.

### Final Answer:
**Option 4: Increase the refractive index of the medium between the objective and the specimen.**

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