The focal length of the objective lens of a telescope is 50
cm If the magnification of the telescope is 25, then the
focal length of the eye-piece is

Options

A. a 12.5 cm
B. b 5 m
C. c 2 m
D. d 10 cm

Explanation

To find the focal length of the eyepiece in a telescope, we can use the formula for the magnification of a telescope, which is given by:

\[ M = \frac{f_o}{f_e} \]

where:
- \( M \) is the magnification of the telescope,
- \( f_o \) is the focal length of the objective lens,
- \( f_e \) is the focal length of the eyepiece.

Given:
- The focal length of the objective lens \( f_o = 50 \) cm,
- The magnification \( M = 25 \).

We need to find the focal length of the eyepiece \( f_e \).

### Step 1: Rearranging the magnification formula
From the magnification formula, we can rearrange it to find \( f_e \):

\[ f_e = \frac{f_o}{M} \]

### Step 2: Substitute the known values
Now, substituting the known values into the equation:

\[ f_e = \frac{50 \, \text{cm}}{25} \]

### Step 3: Calculate \( f_e \)
Now perform the division:

\[ f_e = 2 \, \text{cm} \]

### Step 4: Final answer
Thus, the focal length of the eyepiece is:

\[ f_e = 2 \, \text{cm} \]

### Summary of the solution:
1. Use the magnification formula \( M = \frac{f_o}{f_e} \).
2. Rearrange to find \( f_e = \frac{f_o}{M} \).
3. Substitute \( f_o = 50 \, \text{cm} \) and \( M = 25 \).
4. Calculate \( f_e = 2 \, \text{cm} \).