Refraction

When light moves from a less dense medium (like air) to a more dense medium (like glass or water), it slows down and bends towards the normal ($r < i$).

Conversely, when light moves from a more dense medium to a less dense medium, it speeds up and bends away from the normal ($r > i$).

The degree of bending depends on the difference in optical density; a larger difference in density results in a more significant change in speed and a sharper bend.

This behavior is consistent across all wave types, including light, sound, and water waves, provided they are crossing a boundary between different media.

During refraction, the frequency of the wave remains constant because it is determined by the source and does not change when entering a new medium.

Since the speed ($v$) changes and the frequency ($f$) is constant, the wavelength ($\lambda$) must also change according to the wave equation $v = f \lambda$.

In a denser medium where the wave slows down, the wavelength decreases (the waves become more closely spaced).

Because the frequency remains the same, the color of light (which depends on frequency) does not change when it refracts, even though its speed and wavelength do.

Always draw the normal first: Before sketching any rays, draw a dashed line at $90^{\circ}$ to the boundary to ensure your angles are measured correctly.

Measure from the normal: A common mistake is measuring the angle between the ray and the surface; ensure you always measure the angle between the ray and the normal line.

Check the bending direction: Use the 'FAST' mnemonic (Fast to Slow, Towards normal; Slow to Fast, Away from normal) to verify if your refracted ray is on the correct side of the original path.

Label your rays: Clearly distinguish between the incident ray, the refracted ray, and the emergent ray (the ray that exits the second medium back into the first).