The magnifing power of a compoundmicroscope increases when

Options

A. the focal length o fobjective lens is increased and that of eye lens is decreased
B. the focal length of eye lens is increased and that of objective lens in decreased
C. focal lengths of both objective and eye-piece are increased
D. focal lengths of both objective and eye-piece are decreased

Answer

To determine when the magnifying power of a compound microscope increases, we can analyze the formula for magnification and the factors that affect it.

### Step-by-Step Solution:

1. **Understanding the Magnification Formula**:
The magnifying power (M) of a compound microscope is given by the formula:
\[ M = -\frac{V_o}{U_o} \left(1 + \frac{D}{F_e}\right) \]
where:
- \( V_o \) is the image distance from the objective lens,
- \( U_o \) is the object distance from the objective lens,
- \( D \) is the near point distance (typically 25 cm for a normal human eye),
- \( F_e \) is the focal length of the eyepiece.

2. **Analyzing the Terms**:
- The term \(-\frac{V_o}{U_o}\) indicates that magnification increases if the object distance \( U_o \) decreases (as \( V_o \) is typically positive).
- The term \( \left(1 + \frac{D}{F_e}\right) \) shows that magnification increases if the focal length \( F_e \) of the eyepiece decreases.

3. **Conditions for Increased Magnification**:
- **Decrease in Object Distance**: If the object is placed closer to the objective lens (i.e., decreasing \( U_o \)), the magnification increases.
- **Decrease in Focal Length of Objective Lens**: A shorter focal length \( F_o \) of the objective lens will also increase magnification since it allows for a larger image to be formed.
- **Decrease in Focal Length of Eyepiece**: Similarly, a shorter focal length \( F_e \) of the eyepiece will increase the magnification.

4. **Conclusion**:
To increase the magnifying power of a compound microscope, one must:
- Decrease the focal lengths of both the objective lens and the eyepiece.
- Decrease the object distance \( U_o \).

### Final Answer:
The magnifying power of a compound microscope increases when the focal lengths of both the objective lens and the eyepiece are decreased, and when the object distance is minimized.

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