If the red light is replaced by blue light illuminating the object in a microscope the resolving power of the microscope

Options

A. decreases
B. increases
C. gets halved
D. remain unchanged

Explanation

To solve the question regarding the effect of replacing red light with blue light on the resolving power of a microscope, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Resolving Power**:
The resolving power (R) of a microscope is defined by the formula:
\[ R = \frac{2 \mu \sin \theta}{\lambda} \]
where:
- \( \mu \) is the refractive index of the medium,
- \( \theta \) is the half-angle of the maximum cone of light that can enter or exit the lens,
- \( \lambda \) is the wavelength of the light used.

2. **Identifying Wavelengths**:
- The wavelength of red light is longer (approximately 620-750 nm) compared to that of blue light (approximately 450-495 nm).
- Therefore, when red light is replaced by blue light, the wavelength \( \lambda \) decreases.

3. **Analyzing the Effect on Resolving Power**:
- Since the resolving power is inversely proportional to the wavelength (\( \lambda \)), a decrease in wavelength will result in an increase in resolving power.
- Mathematically, if \( \lambda \) decreases, \( R \) increases.

4. **Conclusion**:
- Thus, when red light is replaced by blue light, the resolving power of the microscope increases.

### Final Answer:
The resolving power of the microscope **increases** when red light is replaced by blue light.

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