A symmetrical biconvex lens of focal length f is cut into four identical pieces along its principal axis and to the perpendicular to principal axis. The focal length of one of four pieces is

Options

A. `f/4`
B. `f/2`
C. `2f`
D. `4f`

Explanation

To find the focal length of one of the four identical pieces of a symmetrical biconvex lens that has been cut along its principal axis and perpendicular to the principal axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Original Lens**:
- We start with a symmetrical biconvex lens with a focal length \( f \).

2. **Cutting the Lens**:
- The lens is cut into four identical pieces. This means we are making two cuts: one along the principal axis and one perpendicular to it.
- This results in four smaller biconvex lenses.

3. **Effect of Cutting on Focal Length**:
- When a lens is cut, the focal length of the resulting pieces changes. The focal length \( f \) of the original lens is inversely proportional to its diameter (aperture).
- When we cut the lens along the principal axis, we effectively reduce the diameter of the lens.

4. **Calculating the New Focal Length**:
- Each piece retains the curvature of the original lens but has a smaller effective diameter.
- If we consider that cutting the lens in half along the principal axis doubles the focal length, we can say that each piece will have a focal length of \( 2f \) after the first cut.
- Now, since we also cut the lens perpendicular to the principal axis, we further reduce the effective diameter of each piece.

5. **Final Focal Length Calculation**:
- After both cuts, the focal length of one of the four pieces can be calculated as:
\[ f' = 2f \]
- Thus, the focal length of one of the four pieces is \( 2f \).

### Final Answer:
The focal length of one of the four pieces is \( 2f \).