When light strikes a curved surface, such as a convex or concave lens, it undergoes a process called reflection. The reflection of light at a curved surface follows the same principles as the reflection at a flat surface, but the curved shape introduces some interesting optical effects.

To understand the reflection of light at a curved surface, let’s consider a convex lens. A convex lens is thicker in the middle and thinner at the edges. When a beam of light approaches a convex lens, it encounters the curved surface. At this point, the light ray changes direction due to the change in the refractive index at the interface between the lens and the surrounding medium.

The key principle governing the reflection of light at a curved surface is known as Snell’s law. Snell’s law states that the angle of incidence (the angle between the incident ray and the normal to the surface) and the angle of refraction (the angle between the refracted ray and the normal to the surface) are related by the equation:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:

• n₁ is the refractive index of the medium from which the light is coming (e.g., air)
• θ₁ is the angle of incidence
• n₂ is the refractive index of the medium into which the light is entering (e.g., the lens material)
• θ₂ is the angle of refraction

When light passes from a less dense medium (lower refractive index) to a denser medium (higher refractive index), such as from air to glass, it bends towards the normal. Conversely, when light passes from a denser medium to a less dense medium, it bends away from the normal.

In the case of a convex lens, the curved surface causes the light rays to converge or focus at a point called the focal point. This is due to the varying curvature of the lens, which causes different regions of the lens to bend the light rays by different amounts. The focal point is where the refracted rays converge after passing through the lens.

For a concave lens, which is thinner in the middle and thicker at the edges, the curved surface causes the light rays to diverge or spread out. The refracted rays appear to originate from a virtual focal point located on the same side as the incident light. This is known as a virtual image.

In summary, when light interacts with a curved surface, such as a convex or concave lens, it undergoes reflection according to Snell’s law. The specific curvature of the surface determines how the light rays bend, leading to interesting optical phenomena like convergence or divergence of the rays and the formation of real or virtual images.