How does the shape of a lens affect focal lengths?

[jst81161]

Homework Statement

Why do two outer rays converge to a different focal point than the inner rays?

Homework Equations

The Attempt at a Solution

The distance to the focal point of the inner rays is shorter than the outer rays, the light has to bend a lot more for the outer rays

 

[Kurdt]

I don't think you've really hit the nail on the head. Think about the ideal shape of a lens and the actual shape of a lens.

 

[m2003]

to converge at the same point as the inner rays. This is due to the shape of the lens, which is designed to bend light in a specific way. The curvature of the lens determines how much the light will bend and at what angle it will converge. A lens with a steeper curvature will have a shorter focal length, causing the outer rays to converge at a different point than the inner rays. This is because the steeper curvature causes the light to bend more sharply, bringing the focal point closer to the lens. On the other hand, a lens with a flatter curvature will have a longer focal length, causing the outer rays to converge at a point farther away from the lens compared to the inner rays. This is because the flatter curvature causes the light to bend less, resulting in a longer focal length. Therefore, the shape of a lens directly affects the focal lengths of the inner and outer rays, causing them to converge at different points.