Question

Depict refraction of a plane wave by a convex lens.

Hint:

To easily remember this, just think of a marching band walking into a muddy field that is thickest in the middle. The people on the dry edges will walk faster and naturally curve inward ahead of the people struggling through the deep mud in the center.

Answer 1

Concept:
• A wavefront physically tracks the speed of light.
• A convex lens is remarkably thicker strictly at its center and aggressively tapers to become thinner at its peripheral edges.
• Because the refractive index of solid glass is much higher than air, the wave travels noticeably slower through the glass.

Step 1: Describe the incident wavefront
Imagine a completely flat, perfectly vertical plane wavefront smoothly advancing through the air and making contact with the front face of a biconvex lens.
Because it is a flat plane wavefront, all portions of the wave (top, middle, bottom) strike the front surface of the lens at almost the exact same time.

Step 2: Analyze the optical path differences
As the entire wavefront begins to force its way through the dense glass structure, different portions experience vastly different physical thicknesses.
The absolute center portion of the wavefront is forced to travel through the thickest, densest chunk of glass. Since speed $v = \frac{c}{\mu}$, it is severely slowed down for the longest duration, causing a massive phase delay.
Conversely, the upper and lower outer edges of the wavefront travel through the very thin, tapered edges of the lens. They exit the glass relatively quickly, experiencing far less delay.

Step 3: Depict the final emerging wavefront
Because the peripheral edges strictly travel faster and exit sooner, they powerfully surge forward ahead of the delayed central portion.
This differential delay aggressively curves the previously flat wavefront.
The emerging wavefront completely transforms from a flat plane into a deeply curved, spherical shape.
Because the center is dragging behind, the spherical curvature actively collapses inward, perfectly converging all the wave energy toward a single central focal point precisely on the principal axis.