A compound microscope is made using a lens of focal `10 mm` as objective and another lens of focal length `15 mm` as eye piece. An object is held `1.1 cm` from the objective and final image is obtained at `oo`. Calculate distance between objective and eye piece.

Answer

To solve the problem of finding the distance between the objective and the eyepiece of a compound microscope, we will follow these steps:

### Step 1: Identify the given data
- Focal length of the objective lens, \( F_O = 10 \, \text{mm} \)
- Focal length of the eyepiece lens, \( F_E = 15 \, \text{mm} \)
- Object distance from the objective lens, \( U_O = -1.1 \, \text{cm} = -11 \, \text{mm} \) (negative sign indicates that the object is on the same side as the incoming light)

### Step 2: Use the lens formula for the objective lens
The lens formula is given by:
\[ \frac{1}{F} = \frac{1}{V} - \frac{1}{U} \]
For the objective lens, we can rearrange this to find the image distance \( V_O \):
\[ \frac{1}{V_O} = \frac{1}{F_O} + \frac{1}{U_O} \]
Substituting the values:
\[ \frac{1}{V_O} = \frac{1}{10} + \frac{1}{-11} \]
Finding a common denominator (which is 110):
\[ \frac{1}{V_O} = \frac{11}{110} - \frac{10}{110} = \frac{1}{110} \]
Thus, we find:
\[ V_O = 110 \, \text{mm} \]

### Step 3: Calculate the distance between the objective and the eyepiece
The final image formed by the eyepiece is at infinity, which means the image formed by the objective lens must be at the focal point of the eyepiece. Therefore, the distance \( d \) between the objective and the eyepiece can be calculated as:
\[ d = V_O + F_E \]
Substituting the values we found:
\[ d = 110 \, \text{mm} + 15 \, \text{mm} = 125 \, \text{mm} \]

### Step 4: Convert the distance to centimeters
Since the question asks for the distance in centimeters:
\[ d = 125 \, \text{mm} = 12.5 \, \text{cm} \]

### Final Answer
The distance between the objective and the eyepiece is \( 12.5 \, \text{cm} \).

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