If the length of objective lens in increased, then magnifying power of

Options

A. microscpoe sili increase but that of telescope decrease
B. microscope and telescope both will increase
C. microscope and telescope both will decrease
D. microscope will decrease but that of telescope will increase

Answer

To solve the question regarding the effect of increasing the length of the objective lens on the magnifying power of a microscope and telescope, we can follow these steps:

### Step 1: Understand the Magnifying Power Formulas
The magnifying power (M) of optical instruments can be expressed using specific formulas:
- For a microscope:
\[ M_m = \frac{L}{f_o} \cdot \frac{D}{f_e} \]
where \(L\) is the length of the microscope tube, \(f_o\) is the focal length of the objective lens, \(D\) is the near point distance (usually taken as 25 cm), and \(f_e\) is the focal length of the eyepiece.

- For a telescope:
\[ M_t = \frac{f_o}{f_a} \]
where \(f_o\) is the focal length of the objective lens and \(f_a\) is the focal length of the eyepiece.

### Step 2: Analyze the Effect on Microscope
From the microscope formula, we see that the magnifying power is inversely proportional to the focal length of the objective lens (\(f_o\)). Therefore:
- If the length of the objective lens increases, it typically means that the focal length \(f_o\) is also increasing.
- As \(f_o\) increases, the magnifying power \(M_m\) of the microscope will decrease.

### Step 3: Analyze the Effect on Telescope
From the telescope formula, we see that the magnifying power is directly proportional to the focal length of the objective lens (\(f_o\)). Therefore:
- If the focal length \(f_o\) increases, the magnifying power \(M_t\) of the telescope will increase.

### Step 4: Conclusion
- For the microscope, increasing the length of the objective lens decreases the magnifying power.
- For the telescope, increasing the length of the objective lens increases the magnifying power.

Thus, the final conclusion is:
- The magnifying power of the microscope decreases, while the magnifying power of the telescope increases.

### Final Answer
- The magnifying power of the microscope decreases, and the magnifying power of the telescope increases.

---