Reflection and Refraction by Wave Theory Easy Explanation

Reflection and refraction are usually taught with rays and angles, but wave theory explains why those laws are true. Using Huygens principle, a wavefront striking a surface generates secondary wavelets. The envelope of these wavelets gives the reflected or refracted wavefront, and the angle rules follow from simple geometry.

This matters because it connects ray optics to wave optics. It shows that the laws are not just experimental facts; they are consequences of wave speed and wavefront construction. The same reasoning explains total internal reflection, mirage and fibre optics qualitatively.

Key Concepts

The angle of incidence i is between incoming ray and normal. The angle of reflection r is between reflected ray and normal. The angle of refraction, call it rt to avoid confusion, is between refracted ray and normal. Wavefronts are perpendicular to rays. In time delta t, a wavefront point travels distance v delta t in the medium. For refraction, speeds v1 and v2 differ, so wavelet radii differ.

• Reflection: incident and reflected wavefronts are in same medium, same speed.
• Refraction: transmitted wavefront is in second medium with different speed.
• Frequency stays same across boundary; wavelength and speed change.

Formulas

Law of reflection: angle i equals angle r. Snells law: sin i divided by sin rt equals v1 divided by v2 equals n2 divided by n1, where n is refractive index equals c divided by v. So n1 sin i equals n2 sin rt. Assumptions: plane wavefront, homogeneous isotropic media, flat boundary. Limits: laws hold for specular reflection from smooth surface; rough surface gives diffuse reflection with local laws still valid at each point.

Worked Example

A plane wavefront in air hits glass at incidence 45 degrees. Speed in air is 3.0 times 10 to power 8 m per second, in glass 2.0 times 10 to power 8 m per second. Find refraction angle using wave theory ratio.

sin i divided by sin rt equals v1 divided by v2 equals 3.0 divided by 2.0 equals 1.5.

sin 45 equals 0.707. So sin rt equals 0.707 divided by 1.5 equals 0.471.

rt equals sin inverse of 0.471 equals about 28.1 degrees. The wavefront tilts closer to normal because wavelets in glass are smaller, exactly as Huygens construction predicts.

Common Misconceptions

• Frequency changes during refraction: Wrong. Frequency is fixed by source; speed and wavelength adjust so f equals v divided by lambda remains constant.
• Reflection law fails for curved mirrors in wave theory: Wrong. Locally the surface is like a tangent plane; geometry gives focusing properties.
• Wave theory cannot explain straight shadows: Wrong. With wavelength much smaller than obstacles, diffraction is negligible and wavefronts give ray-like propagation.

Real-World Applications

Anti-reflection coatings on lenses use wave interference derived from these boundary interactions. Fibre optics use total internal reflection, a consequence of Snells law when angle exceeds critical angle. Seismic reflection surveys use similar wavefront rules for sound waves in earth layers. Architects use reflection geometry for concert hall acoustics to direct sound wavefronts to listeners.

Using Huygens wavelets, equal wavelet radii give angle of incidence equals angle of reflection, and different radii give Snells law. Wave theory therefore proves the ray laws from one basic construction.