The length of an astronomical telescope is 40 cm. The focal lengths of its lenses will be

Options

A. 35 cm and -5 cm
B. `-35` cm and -5 cm
C. 35 cm and +5 cm
D. `-35` cm and +5 cm

Explanation

To solve the problem of finding the focal lengths of the lenses in an astronomical telescope with a total length of 40 cm, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Components of the Telescope**:
An astronomical telescope consists of two main lenses: the objective lens and the eyepiece lens. Both of these lenses are convex lenses.

2. **Define the Length of the Telescope**:
The total length (L) of the astronomical telescope is given as 40 cm. This length is the sum of the focal lengths of the objective lens (F₀) and the eyepiece lens (Fₑ):
\[ L = F₀ + Fₑ \]
Therefore, we have:
\[ F₀ + Fₑ = 40 \text{ cm} \]

3. **Assign Values to the Focal Lengths**:
Since both lenses are convex, their focal lengths will be positive. We can assign arbitrary values to F₀ and Fₑ that satisfy the equation. A common approach is to choose a focal length for one lens and calculate the other.

4. **Choose Focal Lengths**:
Let's assume:
\[ F₀ = 35 \text{ cm} \quad \text{(focal length of the objective lens)} \]
Then, substituting this value into the equation:
\[ 35 \text{ cm} + Fₑ = 40 \text{ cm} \]
Solving for Fₑ gives:
\[ Fₑ = 40 \text{ cm} - 35 \text{ cm} = 5 \text{ cm} \quad \text{(focal length of the eyepiece lens)} \]

5. **Final Focal Lengths**:
Thus, the focal lengths of the lenses in the astronomical telescope are:
- Focal length of the objective lens (F₀) = 35 cm
- Focal length of the eyepiece lens (Fₑ) = 5 cm

### Summary of the Solution:
- Focal length of the objective lens (F₀) = 35 cm
- Focal length of the eyepiece lens (Fₑ) = 5 cm