The frequency of a wave plays a crucial role in its refraction, which is the bending of the wave as it transitions between different media.

Refraction is described by Snell’s Law, which states that the ratio of the sine of the angle of incidence ($\theta_1$) to the sine of the angle of refraction ($\theta_2$) is equal to the ratio of the velocities of the wave in the two media. Mathematically, this can be expressed as:

where $v_1$ and $v_2$ are the velocities of the wave in the first and second media, respectively. The velocity of a wave in a medium is influenced by the medium’s refractive index ($n$), which is also affected by the wave’s frequency.

When a wave with a higher frequency enters a new medium, it tends to slow down more than a wave with a lower frequency. This phenomenon occurs because the refractive index of a medium generally increases with frequency. Consequently, the wave bends more significantly, resulting in a smaller angle of refraction. This behavior explains why different colors of light—each corresponding to distinct frequencies—refract at various angles when passing through a prism. This effect is known as dispersion.

It is essential to recognize that the relationship between frequency and refractive index is not always linear. In some materials, the refractive index may decrease with increasing frequency, a phenomenon referred to as anomalous dispersion. This unusual behavior can happen under specific conditions, particularly near the absorption lines of certain materials.

In summary, a wave’s frequency significantly affects its refraction when it transitions from one medium to another, primarily due to changes in speed associated with the medium’s refractive index. Higher frequency waves tend to bend more sharply. However, in some materials, this relationship can exhibit complexity, leading to atypical bending patterns known as anomalous dispersion.