Why can light bend when it enters another material?

A straw in a glass of water can look bent at the surface even though it is straight. The straw has not changed shape. Light from its submerged part changes direction on the way to your eyes. Your visual system follows the arriving directions back as though the light had traveled straight, so the underwater part appears in a different place.

The turning happens at the boundary between materials. Light travels at different speeds in air, water, and glass. When a wave reaches a boundary at a slant, one part of its front enters the new material before the rest. If that part slows first, neighboring parts keep advancing faster for a little longer. The wavefront turns, and the direction in which the wave travels turns with it. This change of direction is called refraction.

An imaginary line perpendicular to the boundary, called the normal, gives a reference for measuring the turn. The incoming and outgoing angles are measured from that line, not from the surface itself. For light entering glass from air, the lower speed in glass makes the ray bend toward the normal. Going the other way, a transmitted ray bends away from the normal.

The size of the turn depends on how much the speed changes. Refractive index is a number that compares light's speed in vacuum with its speed in a material. Air's index is very close to 1. For the chosen light, take this glass's index as 1.50: light travels through it at about two-thirds of its speed in vacuum. An incoming angle of 30° then becomes about 19.47° in the glass. The smaller angle means the ray is closer to the normal. These angles are a worked example for this glass, not a fixed rule for every transparent material.

The wave does not change its frequency at this ordinary, stationary boundary. Instead, slower travel puts successive wavefronts closer together, shortening the wavelength. There is also an important exception to the turning: a ray arriving straight along the normal slows without bending. Its wavefront reaches the boundary all at once, so neither side gets a head start.

Different colors can travel at slightly different speeds in a material, and some light can also reflect at the surface. Those effects add detail to a real glass of water. The essential idea already explains why clear materials can reshape a view. A curved lens changes its surface direction from place to place, using many small turns of light to bring an image into focus.