The length of an astronomical telescope for normal vision (relaxed eye) ( `f_(o)` = focal length of objective lens and `f_(e)` = focal length of eye lens) is

Options

A. `f_(0)xxf_(e)`
B. `f_(0)/f_(e)`
C. `f_(0)+f_(e)`
D. `f_(0)-f_(e)`

Answer

To find the length of an astronomical telescope for normal vision (relaxed eye), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Components of the Telescope**:
An astronomical telescope consists of two lenses: the objective lens and the eyepiece (or eye lens). The objective lens has a focal length denoted as \( f_o \), and the eyepiece has a focal length denoted as \( f_e \).

2. **Image Formation**:
When observing distant objects, light rays coming from the object are considered to be parallel. These rays first pass through the objective lens, which focuses them to form a real image. This image acts as the object for the eyepiece lens.

3. **Position of the Lenses**:
The length of the telescope is defined as the distance between the objective lens and the eyepiece lens. For a telescope designed for normal vision (where the eye is relaxed), the image formed by the objective lens is at the focal point of the eyepiece lens.

4. **Calculating the Length**:
In the case of relaxed vision, the distance between the two lenses (length of the telescope) is given by the sum of the focal lengths of the objective and eyepiece lenses:
\[ L = f_o + f_e \]

5. **Final Answer**:
Therefore, the length of the astronomical telescope for normal vision (relaxed eye) is:
\[ L = f_o + f_e \]