We wish to make a microscope with the help of two positive lenses both with a focal length of 20 mm each and the object is positioned 25 mm from the objective lens. How far apart the lenses should be so that the final image is formed at infinity?

Options

A. 20mm
B. 100mm
C. 120mm
D. 80mm

Explanation

To find the distance between the two lenses in a microscope setup, we can follow these steps:

### Step 1: Identify the Given Values
- Focal length of both lenses (objective and eyepiece), \( f = 20 \, \text{mm} \)
- Object distance from the objective lens, \( u_0 = -25 \, \text{mm} \) (negative because the object is on the same side as the incoming light)

### Step 2: Use the Lens Formula
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Rearranging gives:
\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]
Substituting the known values:
\[ \frac{1}{v_0} = \frac{1}{20} + \frac{1}{-25} \]

### Step 3: Calculate the Image Distance for the Objective Lens
Calculating the right-hand side:
\[ \frac{1}{v_0} = \frac{1}{20} - \frac{1}{25} \]
Finding a common denominator (100):
\[ \frac{1}{v_0} = \frac{5}{100} - \frac{4}{100} = \frac{1}{100} \]
Thus:
\[ v_0 = 100 \, \text{mm} \]

### Step 4: Determine the Separation Between the Lenses
The separation \( x \) between the two lenses is the sum of the image distance from the objective lens and the focal length of the eyepiece lens:
\[ x = v_0 + f \]
Substituting the values:
\[ x = 100 \, \text{mm} + 20 \, \text{mm} = 120 \, \text{mm} \]

### Final Answer
The distance between the two lenses should be \( 120 \, \text{mm} \).

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