\[n=\frac{\sin(\theta_1)}{\sin(\theta_2)}\]
Variables
nrefractive index
theta1[θ₁]angle of incidence (rad)
theta2[θ₂]angle of refraction (rad)
Description
What is this formula?
The refractive index formula relates the angle of incidence and the angle of refraction when light passes from one medium to another. It is derived from Snell's Law and describes how much the light ray bends at the interface between two materials.
When to use it
Use this formula when analyzing light propagation through transparent materials such as glass, water, plastics, lenses, optical fibers, and crystals.
Example
A light ray enters glass from air.
Data:
θ1 = 45°
θ2 = 28°
Formula:
n = sin(θ1) / sin(θ2)
Substitution:
n = sin(45°) / sin(28°)
Result:
n ≈ 1.50
The glass has a refractive index of approximately 1.50.
Applications
Optical lens design, fiber optics, microscopy, photography, laser systems, prism calculations, optical coatings, and material characterization.