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

Options

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

Explanation

To solve the problem step by step, we will use the relationships between the magnification of a telescope, the focal lengths of the objective and eyepiece, and the length of the telescope tube.

### Step 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,
- \( f_e \) is the focal length of the eyepiece lens.

Given that the magnification \( M = 5 \), we can write:
\[ 5 = \frac{f_o}{f_e} \]
This implies:
\[ f_o = 5 f_e \]

### Step 2: Use the length of the telescope
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 \( L = 60 \, \text{cm} \), we can write:
\[ 60 = f_o + f_e \]

### Step 3: Substitute the expression for \( f_o \)
Now, substitute \( f_o = 5 f_e \) into the length equation:
\[ 60 = 5 f_e + f_e \]
This simplifies to:
\[ 60 = 6 f_e \]

### Step 4: Solve for \( f_e \)
Now, we can solve for \( f_e \):
\[ f_e = \frac{60}{6} = 10 \, \text{cm} \]

### Conclusion
The focal length of the eyepiece is:
\[ f_e = 10 \, \text{cm} \]