Snell's Law

When light travels from one transparent medium into another, it changes direction. This bending of light at an interface is called refraction, and the relationship between the angles is described by Snell's Law.

The Law

$n_1 \sin\theta_1 = n_2 \sin\theta_2$

Where:

• $n_1$ is the refractive index of the first medium
• $n_2$ is the refractive index of the second medium
• $\theta_1$ is the angle of incidence (measured from the normal)
• $\theta_2$ is the angle of refraction (measured from the normal)

Refractive Index

The refractive index $n$ of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium:

$n = \frac{c}{v}$

Solving for the Refracted Angle

Rearranging Snell's Law to find $\theta_2$:

$\theta_2 = \arcsin\!\left(\frac{n_1 \sin\theta_1}{n_2}\right)$

Critical Angle and Total Internal Reflection

When light moves from a denser medium ($n_1 > n_2$) to a less dense medium, at a certain angle the refracted ray runs along the boundary. This is the critical angle $\theta_c$:

$\theta_c = \arcsin\!\left(\frac{n_2}{n_1}\right) \quad (n_1 > n_2)$

For angles of incidence greater than $\theta_c$, no light escapes — this is total internal reflection, the principle behind optical fibers and diamond sparkle.

Your Task

Implement the two functions below using math.asin, math.sin, math.degrees, and math.radians.