The focal length of the objective of a microscope is-

Options

A. Greater than the focal length of eye piece
B. Lesser than the focal length of the eye piece
C. Equal to the focal length of the eye piece
D. Any of (A) (B) and (C)

Answer

To solve the question regarding the focal length of the objective of a microscope, we need to understand the relationship between the focal lengths of the objective and the eyepiece in a compound microscope.

### Step-by-Step Solution:

1. **Understanding Microscope Components**:
- A compound microscope consists of two main lenses: the objective lens and the eyepiece (ocular) lens.
- The objective lens is responsible for forming a real image of the object, while the eyepiece magnifies this image for the viewer.

2. **Focal Lengths of Lenses**:
- The focal length of the objective lens (denoted as \( F_O \)) is typically shorter than that of the eyepiece lens (denoted as \( F_E \)).
- This is because the objective lens needs to create a magnified image of an object that is placed very close to it.

3. **Magnification Consideration**:
- The magnification \( M \) of a microscope is given by the formula:
\[ M = \frac{L}{F_O} \times \frac{D}{F_E} \]
- Here, \( L \) is the distance from the objective to the eyepiece, and \( D \) is the near point distance of the eye.
- For effective magnification, the object must be placed close to the objective lens, which requires a smaller focal length for the objective lens.

4. **Comparison of Focal Lengths**:
- Since the object is placed very close to the objective lens, the focal length \( F_O \) must be less than \( F_E \) to achieve a higher magnification.
- Therefore, we can conclude that:
\[ F_O < F_E \]

5. **Final Conclusion**:
- The focal length of the objective lens of a microscope is less than the focal length of the eyepiece lens.

### Answer:
The focal length of the objective of a microscope is less than the focal length of the eyepiece.