An object is seen thorugh a simple microscope of focal length 12 cm. Find the angular mgnification produced if the image is formed at the near point of the eye which is 25 cm away from it.

Options

A. 6.08
B. 3.08
C. 9.03
D. 5.09

Explanation

To find the angular magnification produced by a simple microscope when the image is formed at the near point of the eye, we can follow these steps:

### Step 1: Understand the parameters
- Focal length of the lens (f) = 12 cm
- Near point distance (D) = 25 cm

### Step 2: Use the formula for angular magnification
The angular magnification (M) of a simple microscope can be calculated using the formula:
\[ M = 1 + \frac{D}{f} \]
where:
- \( D \) is the distance of the near point of the eye (25 cm),
- \( f \) is the focal length of the lens (12 cm).

### Step 3: Substitute the values into the formula
Now we can substitute the values into the formula:
\[ M = 1 + \frac{25 \, \text{cm}}{12 \, \text{cm}} \]

### Step 4: Perform the calculation
Calculating the fraction:
\[ \frac{25}{12} \approx 2.0833 \]
Now, adding 1:
\[ M = 1 + 2.0833 \approx 3.0833 \]

### Step 5: Round off the result
The angular magnification can be rounded to two decimal places:
\[ M \approx 3.08 \]

### Final Answer
The angular magnification produced by the simple microscope is approximately **3.08**.

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