Snell's Law — Core Principles

Core Principles

Snell's Law, or the law of refraction, describes how light bends when it passes from one transparent medium to another. This bending occurs because light changes its speed in different media. The optical density of a medium is quantified by its refractive index ($n$), defined as the ratio of the speed of light in vacuum ($c$) to its speed in the medium ($v$), i.

e., $n = c/v$. Snell's Law states that for a given pair of media, the product of the refractive index and the sine of the angle of incidence (or refraction) in that medium is constant: $n_1 \sin \theta_1 = n_2 \sin \theta_2$.

Here, $\theta_1$ is the angle of incidence in medium 1 (refractive index $n_1$), and $\theta_2$ is the angle of refraction in medium 2 (refractive index $n_2$). Angles are always measured with respect to the normal (perpendicular line) to the interface.

If light enters an optically denser medium ($n_2 > n_1$), it bends towards the normal ($\theta_2 < \theta_1$). If it enters an optically rarer medium ($n_2 < n_1$), it bends away from the normal ($\theta_2 > \theta_1$).

This law is fundamental to understanding lenses, prisms, and phenomena like apparent depth and total internal reflection.

Important Differences

vs Law of Reflection

Aspect	This Topic	Law of Reflection
Phenomenon	Refraction (Snell's Law)	Reflection (Law of Reflection)
Light Path	Light passes from one medium to another, changing direction.	Light bounces back into the same medium.
Speed of Light	Changes (unless $n_1 = n_2$ or $\theta_1 = 0^circ$).	Remains constant.
Wavelength	Changes ($v = f\lambda$, $f$ constant).	Remains constant.
Frequency	Remains constant.	Remains constant.
Angles Relationship	$n_1 \sin \theta_1 = n_2 \sin \theta_2$	Angle of incidence = Angle of reflection ($\theta_i = \theta_r$)
Media Involved	Two different transparent media.	One medium and an interface (e.g., mirror).

While both Snell's Law (refraction) and the Law of Reflection describe how light interacts with interfaces, they represent distinct phenomena. Refraction involves light passing *through* a boundary into a new medium, leading to a change in its speed and wavelength, and a bending of its path (unless normal incidence). Reflection, conversely, involves light bouncing *off* a boundary and returning to its original medium, with its speed and wavelength remaining unchanged. The angle relationships are also fundamentally different: Snell's Law relates angles via refractive indices, while reflection dictates that the angle of incidence equals the angle of reflection.