Understanding Snell’s Law

Snell’s Law is a fundamental principle in optics that describes how light (or other waves) changes direction when passing from one medium to another. This bending of light is called refraction and occurs because the speed of light is different in different materials.

The Formula

The relationship between the angles and the refractive indices of the two media is given by the formula:

Where:

• $n_1$: Refractive index of the first medium (where the light originates).
• $\theta_1$: Angle of incidence (the angle between the incoming ray and the normal to the boundary), measured in degrees.
• $n_2$: Refractive index of the second medium (where the light is refracted).
• $\theta_2$: Angle of refraction (the angle between the refracted ray and the normal), measured in degrees.

Total Internal Reflection (TIR)

A critical phenomenon occurs when light travels from a denser medium (higher $n$) to a less dense medium (lower $n$), i.e., when $n_1 > n_2$. In this case, if the angle of incidence ($\theta_1$) exceeds a specific value known as the critical angle ($\theta_c$), the light cannot pass through the boundary and is instead entirely reflected back into the first medium. This is called Total Internal Reflection (TIR).

The critical angle $\theta_c$ is calculated using the formula:

How to Use the Calculator

1. Enter $n_1$: Input the Refractive Index of the initial medium (e.g., $1.00$ for air, $1.52$ for glass). This value is unitless.
2. Enter $\theta_1$: Input the Angle of Incidence in degrees (must be between $0^\circ$ and $90^\circ$).
3. Enter $n_2$: Input the Refractive Index of the second medium (the medium the light enters).
4. Click ‘Calculate’: Press the “Calculate Angle of Refraction ($\theta_2$)” button.
5. View Results: The calculator will display the resulting angle of refraction ($\theta_2$) in degrees. If Total Internal Reflection occurs, a warning message will appear instead of a resulting angle.