In an astronomical telescope the focal lengths of objective and eyepiece should respectively be

Options

A. large and small
B. small and large
C. equal
D. too small are too large

Answer

To determine the focal lengths of the objective and eyepiece in an astronomical telescope, we need to understand the basic principles of how the telescope operates, particularly in normal adjustment.

### Step-by-Step Solution:

1. **Understanding the Configuration**:
An astronomical telescope consists of two lenses: the objective lens and the eyepiece lens. The objective lens is responsible for gathering light and forming a real image of a distant object, while the eyepiece lens magnifies this image for viewing.

2. **Normal Adjustment**:
In normal adjustment, the telescope is set up so that the final image is at infinity. This means that the image formed by the objective lens is at the focal point of the eyepiece lens.

3. **Focal Length of the Objective**:
The objective lens must have a large focal length (f_o) to capture light from distant objects effectively. A larger focal length allows the objective to create a clear and well-defined image of the object at infinity.

4. **Focal Length of the Eyepiece**:
The eyepiece lens, on the other hand, should have a small focal length (f_e). A shorter focal length in the eyepiece allows for greater magnification of the image produced by the objective lens.

5. **Conclusion**:
Therefore, in an astronomical telescope, the focal lengths should be:
- Focal length of the objective (f_o): **Large**
- Focal length of the eyepiece (f_e): **Small**

### Final Answer:
- Focal length of the objective: **Large**
- Focal length of the eyepiece: **Small**