Reflection & Refraction
At a boundary, part of a wave may reflect while the transmitted part changes speed and direction. Frequency stays continuous across the boundary; wavelength adjusts with speed.
Why does a wave bend when it crosses into a new medium?
The boundary does not reset the source oscillation frequency. Instead, the propagation speed changes, which changes wavelength. Matching the wavefront across the interface forces a new direction.
For light, . Larger refractive index means smaller wave speed in the medium.
Aim a ray at the interface and change both media.
For a smooth boundary, the reflected ray leaves at the same angle to the normal as the incoming ray: θr = θ1.
Across the interface, the source frequency remains continuous. In this setup the speed ratio v₂/v₁ is 0.67, so the wavelength ratio matches it.
When a wave moves from higher index to lower index at a sufficiently large angle, Snell's law has no transmitted solution and all idealized ray energy reflects.
Entering a higher-index, slower medium bends the transmitted ray toward the normal.
Entering a lower-index, faster medium bends the transmitted ray away from the normal until total internal reflection becomes possible.
Refraction is not a mysterious force on a ray. It emerges because different portions of a wavefront enter the new medium at different times and speeds.