Question

Depict refraction of a plane wave by a convex lens.

Hint:

A lens always introduces a phase delay proportional to its thickness. A thick center causes a lag in the middle, turning a flat plane wave into a concave, converging spherical wave.

Answer 1

Concept: When a plane wavefront passes through a convex lens, different parts of the wavefront travel through different thicknesses of glass. Light travels slower inside glass ($\mu > 1$) than in air. Let us break down the physical mechanism step-by-step:
• The center portion of an incident plane wavefront hits the thickest central part of the convex lens. Therefore, this central section travels through more glass and suffers the maximum time delay.
• The outer boundary edges of the plane wavefront pass through the thin peripheral edges of the convex lens. Hence, they travel mostly through air and a very thin layer of glass, suffering much less delay. As a direct result of this differential propagation delay across the lens body, the central region of the emerging wavefront lags behind the outer margins. The flat, uniform plane wavefront is transformed into a curved, inward-bending shape. This newly emerged wavefront forms a converging spherical wavefront, which gradually shrinks in radius as it travels, focusing down into a single point known as the principal focus ($F$) of the convex lens.