The two lenses of a compound microscope are of focal lengths 2 cm and 5 cm. If an object is placed at a distance of 2.1 cm from the objetive of focal length 2 cm the final image forms at the least distance of distinct vision of a normal eye. Find the frnagnifying powerjof the microscope

Options

A. 20
B. 6
C. 120
D. 60

Explanation

To find the magnifying power of the compound microscope with given focal lengths and object distance, we can follow these steps:

### Step 1: Identify the given values
- Focal length of the objective lens (f₀) = 2 cm
- Focal length of the eyepiece lens (fₑ) = 5 cm
- Object distance from the objective lens (u₀) = -2.1 cm (negative as per sign convention)

### Step 2: Use the lens formula for the objective lens
The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
Where:
- \( v₀ \) = image distance from the objective lens
- \( u₀ \) = object distance from the objective lens
- \( f₀ \) = focal length of the objective lens

Substituting the values into the lens formula:
\[ \frac{1}{v₀} - \frac{1}{-2.1} = \frac{1}{2} \]
This simplifies to:
\[ \frac{1}{v₀} + \frac{1}{2.1} = \frac{1}{2} \]

### Step 3: Solve for \( v₀ \)
Rearranging gives:
\[ \frac{1}{v₀} = \frac{1}{2} - \frac{1}{2.1} \]
Finding a common denominator (which is 42):
\[ \frac{1}{v₀} = \frac{21 - 20}{42} = \frac{1}{42} \]
Thus,
\[ v₀ = 42 \text{ cm} \]

### Step 4: Calculate the magnifying power of the objective lens (M₀)
The magnifying power of the objective lens is given by:
\[ M₀ = \frac{v₀}{u₀} \]
Substituting the values:
\[ M₀ = \frac{42}{2.1} = 20 \]

### Step 5: Calculate the total magnification (M)
The total magnification of the compound microscope is given by:
\[ M = M₀ \left(1 + \frac{D}{fₑ}\right) \]
Where:
- \( D \) = least distance of distinct vision (approximately 25 cm for a normal eye)
- \( fₑ \) = focal length of the eyepiece lens = 5 cm

Substituting the values:
\[ M = 20 \left(1 + \frac{25}{5}\right) = 20 \left(1 + 5\right) = 20 \times 6 = 120 \]

### Final Answer
The magnifying power of the microscope is **120**.

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