Huygens’ Principle can be used to derive Snell’s Law by analyzing how a wavefront changes direction when it passes from one medium to another with a different speed of light.
According to Huygens’ Principle, every point on a wavefront acts as a source of secondary wavelets. When light moves from one medium to another (like air to glass), the speed of these wavelets changes depending on the medium’s optical density.
Imagine a wavefront striking the interface at an angle. The point that first touches the boundary begins producing wavelets in the second medium immediately. However, the other end of the wavefront, still in the first medium, continues to move at the original speed. Because the wavelets in the second medium spread more slowly or quickly (depending on whether the medium is denser or rarer), the new wavefront becomes tilted — it changes direction.
This change in direction corresponds to refraction. The angles involved and the relative speeds of the wave in the two media can be shown to lead directly to Snell’s Law, which states that the ratio of the sine of the angles of incidence and refraction equals the ratio of wave speeds (or inversely, the refractive indices) of the two media. Thus, Huygens’ Principle provides a wave-based explanation of Snell’s Law.