A simple microscope has a focal length of `5 cm` . The magnification at the least distince of distinct vision is-

Options

A. `1`
B. `5`
C. `4`
D. `6`

Explanation

To find the magnification of a simple microscope with a focal length of 5 cm at the least distance of distinct vision (which is conventionally taken as 25 cm), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Lens Formula**:
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where:
- \( f \) = focal length of the lens,
- \( v \) = image distance,
- \( u \) = object distance.

2. **Identify the Values**:
- Focal length \( f = 5 \, \text{cm} \)
- Least distance of distinct vision \( D = 25 \, \text{cm} \) (this is the image distance \( v \) when the image is formed at the least distance of distinct vision).

3. **Set the Image Distance**:
Since the image is formed on the same side as the object (for a simple microscope), we take \( v = -25 \, \text{cm} \) (the negative sign indicates that the image is virtual).

4. **Use the Lens Formula**:
Substitute the known values into the lens formula:
\[ \frac{1}{5} = \frac{1}{-25} - \frac{1}{u} \]

5. **Rearranging the Lens Formula**:
Rearranging gives:
\[ \frac{1}{u} = \frac{1}{-25} - \frac{1}{5} \]
To combine these fractions, find a common denominator (which is 25):
\[ \frac{1}{u} = -\frac{1}{25} - \frac{5}{25} = -\frac{6}{25} \]
Therefore:
\[ u = -\frac{25}{6} \, \text{cm} \]

6. **Calculate Magnification**:
The magnification \( M \) is given by:
\[ M = \frac{v}{u} \]
Substituting the values:
\[ M = \frac{-25}{-\frac{25}{6}} = 6 \]

7. **Final Answer**:
The magnification at the least distance of distinct vision is:
\[ M = 6 \]