If the focal length of objective and eye lens are `1.2 cm` and `3 cm` respectively and the object is put `1.25cm` away from the objective lens and the final image is formed at infinity. The magnifying power of the microscope is

Options

A. `150`
B. `200`
C. `250`
D. `400`

Explanation

To solve the problem, we need to find the magnifying power of the microscope given the focal lengths of the objective and eye lens, the object distance from the objective lens, and the information that the final image is formed at infinity.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Focal length of the objective lens, \( F_o = 1.2 \, \text{cm} \)
- Focal length of the eye lens, \( F_e = 3 \, \text{cm} \)
- Object distance from the objective lens, \( U_o = -1.25 \, \text{cm} \) (negative as per sign convention)
- Least distance of distinct vision (D) = \( 25 \, \text{cm} \)

2. **Use the Lens Formula for the Objective Lens:**
The lens formula is given by:
\[ \frac{1}{F} = \frac{1}{V} - \frac{1}{U} \]
Rearranging gives:
\[ \frac{1}{V_o} = \frac{1}{F_o} + \frac{1}{U_o} \]
Plugging in the values:
\[ \frac{1}{V_o} = \frac{1}{1.2} - \frac{1}{1.25} \]

3. **Calculate \( V_o \):**
First, calculate \( \frac{1}{1.2} \) and \( \frac{1}{1.25} \):
\[ \frac{1}{1.2} = 0.8333 \quad \text{and} \quad \frac{1}{1.25} = 0.8 \]
Thus,
\[ \frac{1}{V_o} = 0.8333 - 0.8 = 0.0333 \]
Therefore,
\[ V_o = \frac{1}{0.0333} \approx 30 \, \text{cm} \]

4. **Calculate the Magnifying Power (M):**
The formula for the magnifying power of the microscope is:
\[ M = \frac{V_o}{U_o} \cdot \frac{D}{F_e} \]
Substituting the known values:
\[ M = \frac{30}{-1.25} \cdot \frac{25}{3} \]

5. **Calculate Each Part:**
First calculate \( \frac{30}{-1.25} \):
\[ \frac{30}{-1.25} = -24 \]
Now calculate \( \frac{25}{3} \):
\[ \frac{25}{3} \approx 8.33 \]
Now, multiply these results:
\[ M = -24 \cdot 8.33 \approx -200 \]

6. **Final Result:**
The magnifying power of the microscope is:
\[ M \approx 200 \]

### Summary:
The magnifying power of the microscope is \( 200 \).