For a telescope, the focal lengths of two lenses are 30 cm and 10 cm. One acts as objective and the other as eye-piece. The length of the telescope is

Options

A. 40 cm
B. 3 cm
C. 200 cm
D. 30 cm

Answer

To find the length of the telescope, we need to consider the two lenses involved: the objective lens and the eyepiece lens. The focal lengths of these lenses are given as follows:

- Focal length of the objective lens (f₁) = 30 cm
- Focal length of the eyepiece lens (f₂) = 10 cm

The length of the telescope is the sum of the distances from the objective lens to the eyepiece lens. This distance is equal to the focal length of the objective lens plus the focal length of the eyepiece lens.

### Step-by-Step Solution:

1. **Identify the Focal Lengths**:
- Objective lens focal length (f₁) = 30 cm
- Eyepiece lens focal length (f₂) = 10 cm

2. **Calculate the Length of the Telescope**:
- The length of the telescope (L) is given by the formula:
\[ L = f₁ + f₂ \]
- Substitute the values:
\[ L = 30 \, \text{cm} + 10 \, \text{cm} \]
- Perform the addition:
\[ L = 40 \, \text{cm} \]

3. **Conclusion**:
- The length of the telescope is 40 cm.

### Final Answer:
The length of the telescope is **40 cm**.

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