The relationship between the angles of incidence and refraction is that they are connected through the refractive indices of the two media involved. When light passes from one medium into another, its speed changes, causing the light to bend.
If the light enters a denser medium (higher refractive index), it slows down and bends toward the normal line (an imaginary line perpendicular to the surface). If it enters a less dense medium (lower refractive index), it speeds up and bends away from the normal.
The greater the difference in refractive indices, the more the light bends. If the refractive indices of the two media are the same, the light does not bend at all—the angle of incidence equals the angle of refraction. This bending behavior helps explain many optical phenomena like lenses focusing light, apparent depth in water, and the separation of colors in prisms.