Refraction at a curved surface occurs when light passes from one medium to another medium with a different refractive index, and that interface between the two media is curved or has a non-uniform shape. The change in the direction of light as it travels through the curved surface is due to the variation in the refractive index.

When light encounters a curved surface, such as a convex or concave lens, several phenomena can occur:

1. Converging lenses (Convex): When light passes through a convex lens, which is thicker in the middle and thinner at the edges, it undergoes refraction. Parallel rays of light that strike the lens converge towards a focal point on the other side of the lens. This converging effect is used in optical systems to focus light, such as in magnifying glasses or camera lenses.
2. Diverging lenses (Concave): On the other hand, a concave lens, which is thinner in the middle and thicker at the edges, causes parallel rays of light to diverge or spread out. The refracted rays appear to originate from a focal point on the same side of the lens from which the light came. Concave lenses are used to correct certain vision problems, like myopia (nearsightedness).
3. Spherical Aberration: When light passes through a curved surface, especially one that is not perfectly shaped, it can result in spherical aberration. Spherical aberration causes different parts of the curved surface to focus light at slightly different points, leading to a blurred or distorted image. This effect can be minimized by using specially designed lenses or optical systems.
4. Astigmatism: Astigmatism is another effect that can occur due to the refraction at curved surfaces. It is caused by an irregularly shaped cornea or lens, resulting in different focal lengths in different meridians of the eye. This leads to distorted or blurry vision.

Understanding the principles of refraction at curved surfaces is crucial in fields such as optics, lens design, and ophthalmology. These principles allow for the creation of corrective lenses, telescopes, microscopes, and other optical devices that manipulate and control the path of light for various applications.