The focal length of each part of a diverging lens after being cut into two equal parts.

When a diverging lens is cut into two equal parts, each part will still have the same focal length as the original lens. This is because the focal length of a lens is determined by its shape and curvature, which remains unchanged even after cutting.

Explanation:

1. Focal length of a lens:
The focal length of a lens is the distance between the lens and the point where parallel rays of light converge or appear to diverge from. It is a measure of the lens's ability to converge or diverge light.

2. Diverging lens:
A diverging lens is a type of lens that is thinnest in the middle and thicker at the edges. It causes incoming parallel rays of light to diverge or spread out.

3. Effect of cutting a lens:
When a lens is cut into two equal parts, each part retains the same shape and curvature as the original lens. The shape and curvature of a lens determine its ability to converge or diverge light. Therefore, cutting the lens does not change its focal length.

4. Conservation of focal length:
The focal length of a lens is determined by its shape and curvature, which are preserved when the lens is cut. The two resulting lens pieces will have the same shape and curvature as the original lens, and thus the focal length of each part will remain the same.

5. Practical considerations:
In practice, cutting a lens into two equal parts may introduce imperfections or irregularities that can affect its optical properties. However, assuming the cutting process is precise and does not introduce any significant changes to the shape or curvature of the lens, each part will have the same focal length as the original lens.

Conclusion:

When a diverging lens is cut into two equal parts, each part will have the same focal length as the original lens. This is because the focal length is determined by the shape and curvature of the lens, which remain unchanged after cutting.

Lens is converging when cut through vertically f' =2f