Select the correct option

Options

A. The aperture and focal length of the objective lens of microscope is smaller than eye-piece lens
B. The aperture and focal length of the objective lens of telescope is large than eye-piece lens
C. The magnifying powers of astronomical telescope and terrestrial telescope are same
D. All of these

Answer

To solve the question, we need to analyze the statements given in the options regarding the optical instruments, specifically microscopes and telescopes.

### Step-by-Step Solution:

1. **Understanding the Focal Length of Lenses**:
- In a microscope, the objective lens has a shorter focal length compared to the eyepiece lens. This is because the objective lens is designed to create a magnified image of a small object.
- In a telescope, the objective lens has a longer focal length than the eyepiece lens. This is because telescopes are used to view distant objects like stars and planets.

2. **Evaluating Option 1**:
- The statement claims that the focal length of the objective lens of a microscope is smaller than that of the eyepiece. This is **correct**.

3. **Evaluating Option 2**:
- The statement claims that the aperture and focal length of the objective lens is larger than the eyepiece lens in a telescope. This is also **correct** as telescopes require larger apertures to gather more light from distant objects.

4. **Evaluating Option 3**:
- The statement discusses the magnifying power of astronomical and terrestrial telescopes. The magnifying power for both types of telescopes is indeed calculated using similar formulas, but they are not the same. Thus, this statement is **incorrect**.

5. **Evaluating Option 4**:
- The statement claims that astronomical and terrestrial telescopes have the same magnifying power. This is **incorrect** as they have different configurations and applications, leading to different magnifying powers.

### Conclusion:
Based on the evaluations, the correct options are 1 and 2. However, since the question asks for the correct option, and the video transcript suggests option 4 as the correct answer, it appears to be a misunderstanding in the evaluation of the statements.

### Final Answer:
The correct answer is **Option 1 and Option 2 are correct**.