When light travels obliquely from one transparent medium into another (e.g., from air into water), its direction of propagation changes. This phenomenon is known as the refraction of light. Refraction occurs because light travels at different speeds in different media.
The refraction of light follows Snell's Law:

• Coplanarity: The refracted ray lies in the plane defined by the incident ray and the normal;
  
• Constant sine ratio: The ratio of the sine of the angle of refraction to the sine of the angle of incidence is independent of the angle of incidence and is determined solely by the properties of the two media.
  

Its mathematical expression is: $$n_1 \times \sin(\theta_1) = n_2 \times \sin(\theta_2)$$ where: $n_1$ and $n_2$ are the absolute refractive indices (often simply referred to as refractive indices) of the first and second media, respectively; $\theta_1$ is the angle of incidence; and $\theta_2$ is the angle of refraction.

Refractive index (n) is a physical quantity that describes the speed of light propagation in a medium. It is defined as the ratio of the speed of light in a vacuum © to the speed of light in the medium (v), i.e., n = c / v. The higher the refractive index of a medium, the slower light propagates through it.

The refractive index of a vacuum is 1, and the refractive index of a medium relative to a vacuum is called its absolute refractive index. When light travels obliquely from a medium with a higher speed of light (lower refractive index, known as an optically rarer medium) into a medium with a lower speed of light (higher refractive index, known as an optically denser medium), such as from air into water, the angle of refraction is smaller than the angle of incidence, and the refracted ray bends toward the normal. Conversely, when light travels obliquely from an optically denser medium into an optically rarer medium, such as from water into air, the angle of refraction is greater than the angle of incidence, and the refracted ray bends away from the normal.

Applications:
Image Formation by a Convex Lens
Light first enters the lens (higher refractive index) from air (lower refractive index), bending toward the normal during the first refraction; it then exits the lens back into air, bending away from the normal during the second refraction. These two deviations work together to converge the light rays onto the principal axis.

Image Formation by a Concave Lens
Because a concave lens is thinner in the center and thicker at the edges, parallel incident light rays diverge away from the principal axis after undergoing two refractions (following the law of refraction). The backward extensions of these diverging rays form a virtual image.

“Bending” of a Pen in Water
Phenomenon: Schematic diagram: As shown in the figure, a pencil is partially immersed in water. At the interface between air and water, the pencil appears “broken” or “displaced.” Additionally, the water appears shallower than its true depth. This phenomenon occurs because light refracts as it travels from water (refractive index of 1.33) into air (refractive index of 1), altering the propagation direction of the light rays from the submerged portion. This causes the human eye to misjudge its position, creating the visual illusion of bending.