The magnifying power of a simple microscope is 6. The focal length of its lens in metres will be, if least distance of distinct vision is 25cm

Options

A. `0.05`
B. `0.06`
C. `0.25`
D. `0.12`

Answer

To find the focal length of a simple microscope given its magnifying power and the least distance of distinct vision, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Magnifying power (M) = 6
- Least distance of distinct vision (D) = 25 cm

2. **Recall the Formula for Magnifying Power:**
The formula for the magnifying power of a simple microscope is given by:
\[ M = 1 + \frac{D}{F} \]
where \( F \) is the focal length of the lens.

3. **Substitute the Known Values into the Formula:**
Substitute \( M = 6 \) and \( D = 25 \) cm into the formula:
\[ 6 = 1 + \frac{25}{F} \]

4. **Rearrange the Equation:**
First, subtract 1 from both sides:
\[ 6 - 1 = \frac{25}{F} \]
This simplifies to:
\[ 5 = \frac{25}{F} \]

5. **Solve for Focal Length (F):**
To find \( F \), rearrange the equation:
\[ F = \frac{25}{5} \]
Simplifying this gives:
\[ F = 5 \text{ cm} \]

6. **Convert Focal Length to Meters:**
Since the question asks for the focal length in meters, convert 5 cm to meters:
\[ F = \frac{5}{100} = 0.05 \text{ m} \]

### Final Answer:
The focal length of the lens is \( 0.05 \) meters.

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