If the focal length of objective lens is increased then magnifying power of

Options

A. Microscope will increase but that of telescope decrease
B. Microscope and telescope both will increase
C. Microscope and telescope both will decrease
D. Microscope will decreases but that of telescope will increase

Answer

To solve the question regarding the effect of increasing the focal length of the objective lens on the magnifying power of a microscope and telescope, we can analyze the formulas for magnifying power for both instruments.

### Step-by-Step Solution:

1. **Understand the Magnifying Power of a Microscope**:
The magnifying power (M) of a microscope is given by the formula:
\[ M = \frac{L}{F_O} \cdot \frac{D}{F_E} \]
where:
- \(L\) = Length of the tube
- \(F_O\) = Focal length of the objective lens
- \(D\) = Minimum distance of distinct vision (usually taken as 25 cm)
- \(F_E\) = Focal length of the eyepiece

2. **Effect of Increasing Focal Length of Objective Lens**:
If the focal length of the objective lens \(F_O\) is increased, the magnifying power \(M\) becomes:
\[ M \propto \frac{1}{F_O} \]
This means that as \(F_O\) increases, the magnifying power \(M\) decreases.

3. **Understand the Magnifying Power of a Telescope**:
The magnifying power (M) of a telescope is given by the formula:
\[ M = \frac{F_O}{F_E} \]
where:
- \(F_O\) = Focal length of the objective lens
- \(F_E\) = Focal length of the eyepiece

4. **Effect of Increasing Focal Length of Objective Lens**:
For the telescope, if the focal length of the objective lens \(F_O\) is increased, the magnifying power \(M\) becomes:
\[ M \propto F_O \]
This indicates that as \(F_O\) increases, the magnifying power \(M\) also increases.

5. **Conclusion**:
- For a microscope, increasing the focal length of the objective lens decreases the magnifying power.
- For a telescope, increasing the focal length of the objective lens increases the magnifying power.

### Final Answer:
If the focal length of the objective lens is increased, then the magnifying power of the microscope decreases, while the magnifying power of the telescope increases.