Snell's Law Calculator

What is Snell's Law of Refraction?

Snell's law, also known as the law of refraction, describes how light bends when it travels from one transparent medium to another. It describes the relationship between the angle of incidence and the angle of refraction relative to the surface normal. Refraction occurs because the velocity of light changes across different materials. For related wave and optics tools, explore our Wavelength Calculator.

Snell's Law Formula

The relationship is mathematically expressed as:

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

Where:

• $n_1$ = Refractive index of the incident medium
• $\theta_1$ = Angle of incidence (measured from the normal)
• $n_2$ = Refractive index of the refracted medium
• $\theta_2$ = Angle of refraction (measured from the normal)

Critical Angle and Total Internal Reflection

When light travels from a denser medium (higher refractive index) to a less dense medium (lower refractive index, $n_1 > n_2$), the light bends away from the normal. As the angle of incidence increases, the refracted angle eventually reaches $90^\circ$. The incident angle at this threshold is called the critical angle ($\theta_c$):

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

If the incident angle $\theta_1$ exceeds the critical angle $\theta_c$, the light cannot cross the boundary and is instead reflected back entirely into the first medium. This phenomenon is called total internal reflection (TIR).

Typical Refractive Indices

Common materials have characteristic refractive indices ($n$):

• Vacuum: $1.0$ (by definition)
• Air: $1.0003$
• Ice: $1.31$
• Water: $1.333$
• Ethanol: $1.36$
• Crown Glass: $1.52$
• Flint Glass: $1.62$
• Diamond: $2.42$