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 lens 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. **Use the Magnifying Power Formula**:
The formula for the magnifying power (M) of a simple microscope is given by:
\[ M = 1 + \frac{D}{F} \]
where:
- \( M \) is the magnifying power,
- \( D \) is the least distance of distinct vision,
- \( F \) 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**:
To isolate \( \frac{25}{F} \), subtract 1 from both sides:
\[ 6 - 1 = \frac{25}{F} \]
\[ 5 = \frac{25}{F} \]

5. **Solve for Focal Length (F)**:
Rearranging gives:
\[ F = \frac{25}{5} \]
\[ F = 5 \text{ cm} \]

6. **Convert Focal Length to Meters**:
Since the answer is required in meters, convert centimeters to meters:
\[ F = 5 \text{ cm} = \frac{5}{100} \text{ m} = 0.05 \text{ m} \]

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

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