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Snell's Law Constraint

In one sentence: Constrain the direction of two line segments meeting at a boundary point to obey Snell's Law of refraction for a specified refractive index ratio, enabling accurate optical path sketches.

Overview

Workbench: Sketcher · Menu: Sketch → Sketcher constraints → Snell's Law Constraint
Toolbar: Sketcher Constraints · Shortcut: K, W

Snell's Law Constraint is a highly specialised tool for optics design. It enforces the relationship n₁ sin(θ₁) = n₂ sin(θ₂) at a boundary point between two line segments, where θ₁ and θ₂ are the angles each line makes with the normal to the boundary, and n₁, n₂ are the refractive indices of the two media.

This allows you to sketch the exact path of a light ray through a lens or prism directly in Sketcher.

Intuition

When light passes from air into glass, it bends toward the perpendicular (normal) to the glass surface — this bending is refraction. Snell's Law quantifies exactly how much: a steeper entry angle bends more, a higher refractive index bends more. This constraint encodes that physics directly in the sketch so your optical ray-path sketch is geometrically exact.

When to use it

  • You are designing an optical lens, prism, or waveguide and want to sketch exact ray paths through the geometry.
  • You need to verify that a designed optical element will refract a specific incoming ray to a specific exit angle.
  • You are documenting optical bench layouts with accurate ray paths.

When NOT to use it

  • For non-optical use — Snell's Law is physically meaningful only for optics; do not use it as a general two-angle constraint.
  • For reflection — this constraint models refraction only; for reflection (angle of incidence = angle of reflection) use two Angle constraints with equal values about the normal.

Step-by-step walkthrough

  1. Draw the boundary edge (the interface between two optical media) as a line in the sketch.

  2. Draw two ray lines — one on each side of the boundary — that meet at a point on the boundary. Add a Point on Object or Coincident to anchor the meeting point to the boundary.

  3. Select three elements in order: the incident ray, the refracted ray, and the boundary line.

  4. Press K, W or activate Snell's Law Constraint.

  5. A value dialog appears asking for n₂/n₁ — the ratio of refractive indices. For an air-to-glass interface with n_glass = 1.5 and n_air = 1.0, enter 1.5.

  6. Click OK. The refracted ray adjusts to the correct angle.

Parameters

Parameter Type Description
Refractive index ratio (n₂/n₁) Float The ratio of the second medium's index to the first medium's index. n₂/n₁ > 1 = light slows down (bends toward normal).

Common mistakes and pitfalls

Constraint cannot be solved — geometry is inconsistent

Cause: The incident angle is so large that refraction is impossible (total internal reflection). Snell's Law has no real solution for n₁ sin(θ₁) > n₂.
Fix: Reduce the incident angle or use a lower refractive index ratio.

Wrong order of selections

Cause: The constraint uses the selection order to determine which ray is incident and which is refracted.
Fix: Select the incident ray first (the ray in medium 1), then the refracted ray (medium 2), then the boundary.

Python API

Minimal example

import FreeCAD as App
import Sketcher

doc = App.activeDocument()
sketch = doc.getObject("Sketch")

# Assuming: incident ray at geo 0, refracted ray at geo 1, boundary at geo 2
# Refractive index ratio n2/n1 = 1.5 (air to glass)
sketch.addConstraint(Sketcher.Constraint("SnellsLaw", 0, 2, 1, 2, 2, 3, 1.5))
# TODO: verify exact argument order against FreeCAD source
doc.recompute()

See also