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 find the magnifying power of the microscope, we can use the formula:

\[ M = \frac{V_0}{U_0} \times \frac{D}{F_e} \]

where:
- \( M \) is the magnifying power,
- \( V_0 \) is the image distance from the objective lens,
- \( U_0 \) is the object distance from the objective lens,
- \( D \) is the least distance of distinct vision (typically taken as \( 25 \, \text{cm} \)),
- \( F_e \) is the focal length of the eyepiece.

### Step 1: Determine the object distance and focal length of the objective lens
Given:
- Focal length of the objective lens \( F_o = 1.2 \, \text{cm} \)
- Object distance \( U_0 = -1.25 \, \text{cm} \) (negative as per sign convention)

### Step 2: Calculate the image distance \( V_0 \) using the lens formula
Using the lens formula:
\[ \frac{1}{F_o} = \frac{1}{V_0} - \frac{1}{U_0} \]

Substituting the known values:
\[ \frac{1}{1.2} = \frac{1}{V_0} - \frac{1}{-1.25} \]

This simplifies to:
\[ \frac{1}{1.2} = \frac{1}{V_0} + \frac{1}{1.25} \]

### Step 3: Find a common denominator and solve for \( V_0 \)
The common denominator for \( 1.2 \) and \( 1.25 \) is \( 1.2 \times 1.25 \):
\[ \frac{1.25 + 1.2}{1.2 \times 1.25} = \frac{1}{V_0} \]

Calculating the left side:
\[ \frac{2.45}{1.5} = \frac{1}{V_0} \]

Thus,
\[ V_0 = \frac{1.5}{2.45} \approx 0.612 \, \text{cm} \]

### Step 4: Use the calculated \( V_0 \) to find the magnifying power
Now substituting \( V_0 \), \( U_0 \), \( D \), and \( F_e \) into the magnifying power formula:
- \( D = 25 \, \text{cm} \)
- \( F_e = 3 \, \text{cm} \)

\[ M = \frac{V_0}{U_0} \times \frac{D}{F_e} \]
\[ M = \frac{30}{-1.25} \times \frac{25}{3} \]

Calculating \( M \):
\[ M = \frac{30 \times 25}{-1.25 \times 3} \]
\[ M = \frac{750}{-3.75} = -200 \]

Since magnifying power is usually taken as a positive value, we conclude:
\[ M = 200 \]

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

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