The focal length of the objective and eye lenses of a microscope are 1.6 cm and 2.5 cm respectively. The distance between the two lenses is 21.7 cm. If the final image is formed at infinity. What is the linear magnification ?

Options

A. a.11
B. b.110
C. c.`1.1`
D. d.44

Explanation

To find the linear magnification of the microscope, we can follow these steps:

### Step 1: Identify the given values
- Focal length of the objective lens (\(f_o\)) = 1.6 cm
- Focal length of the eyepiece lens (\(f_e\)) = 2.5 cm
- Distance between the two lenses (\(d\)) = 21.7 cm

### Step 2: Determine the distance \(l\) from the objective lens to the final image
Since the final image is formed at infinity, we can use the formula:
\[ l = d - f_o \]
Substituting the values:
\[ l = 21.7 \, \text{cm} - 1.6 \, \text{cm} = 20.1 \, \text{cm} \]

### Step 3: Use the magnification formula
The linear magnification \(M\) of the microscope when the final image is at infinity is given by:
\[ M = \frac{l \cdot d}{f_e \cdot f_o} \]
Substituting the known values:
\[ M = \frac{20.1 \, \text{cm} \cdot 21.7 \, \text{cm}}{2.5 \, \text{cm} \cdot 1.6 \, \text{cm}} \]

### Step 4: Calculate the magnification
Calculating the numerator:
\[ 20.1 \cdot 21.7 = 436.17 \, \text{cm}^2 \]
Calculating the denominator:
\[ 2.5 \cdot 1.6 = 4.0 \, \text{cm}^2 \]
Now substituting these values into the magnification formula:
\[ M = \frac{436.17}{4.0} = 109.04 \]

### Step 5: Round the magnification
Rounding \(109.04\) gives us approximately:
\[ M \approx 110 \]

### Final Answer
The linear magnification of the microscope is approximately **110**.

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