Resolving power of a microscope is given by

Options

A. `(2musintheta)/(lamda^(2))`
B. `(musintheta)/(lamda)`
C. `(2musintheta)/(lamda)`
D. `(2mucostheta)/(lamda)`

Explanation

To find the resolving power of a microscope, we can use the formula:

**Resolving Power (R) = (2 * μ * sin(θ)) / λ**

Where:
- **μ** is the refractive index of the medium between the objective lens and the specimen.
- **θ** is the half-angle of the maximum cone of light that can enter the objective lens.
- **λ** is the wavelength of the light used for imaging.

### Step-by-Step Solution:

1. **Understand the Concept of Resolving Power**:
- Resolving power refers to the ability of a microscope to distinguish between two closely spaced objects. A higher resolving power means better clarity and detail in the image.

2. **Identify the Formula**:
- The resolving power of a microscope can be expressed using the formula:
\[ R = \frac{2 \mu \sin \theta}{\lambda} \]

3. **Define the Variables**:
- **μ (Refractive Index)**: This is a measure of how much the speed of light is reduced inside a medium compared to a vacuum.
- **θ (Half-Angle)**: This angle is formed between the optical axis and the line from the lens to the edge of the aperture. It determines how much light can enter the lens.
- **λ (Wavelength)**: This is the wavelength of the light used to illuminate the specimen.

4. **Analyze the Options**:
- Given the formula, we can analyze the options provided in the question to find which one matches the formula for resolving power.

5. **Select the Correct Option**:
- After analyzing, we find that the correct option that matches the formula \( R = \frac{2 \mu \sin \theta}{\lambda} \) is option C.

### Final Answer:
The resolving power of a microscope is given by \( R = \frac{2 \mu \sin \theta}{\lambda} \), and the correct option is C.