A telescope has magnification 5 and length of tube 60cm then the focal length of eye piece is–

Options

A. 10cm
B. 40cm
C. 30cm
D. 20cm

Answer

To find the focal length of the eyepiece (Fe) of a telescope given its magnification (M) and the length of the tube (L), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between magnification and focal lengths**:
The magnification (M) of a telescope is given by the formula:
\[ M = \frac{f_o}{f_e} \]
where \( f_o \) is the focal length of the objective lens and \( f_e \) is the focal length of the eyepiece.

2. **Substitute the given magnification**:
From the problem, we know that the magnification \( M = 5 \). Therefore, we can write:
\[ 5 = \frac{f_o}{f_e} \]
This implies:
\[ f_o = 5f_e \]

3. **Use the length of the tube**:
The length of the telescope tube (L) is the sum of the focal lengths of the objective and the eyepiece:
\[ L = f_o + f_e \]
Given that the length of the tube \( L = 60 \) cm, we can write:
\[ 60 = f_o + f_e \]

4. **Substitute \( f_o \) in terms of \( f_e \)**:
Now, substitute \( f_o = 5f_e \) into the equation for the length of the tube:
\[ 60 = 5f_e + f_e \]
This simplifies to:
\[ 60 = 6f_e \]

5. **Solve for \( f_e \)**:
To find \( f_e \), divide both sides of the equation by 6:
\[ f_e = \frac{60}{6} = 10 \text{ cm} \]

### Final Answer:
The focal length of the eyepiece \( f_e \) is **10 cm**.

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