Optics Calculators: Thin Lenses, Mirrors & Snell’s Law

Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

Geometrical Optics: theory, method, and sources

This optics & photonics workspace publishes 3 governing equations, 2 stated assumptions, 1 documented boundary, and 3 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

A foundational ray-optics workbench organized around boundaries, imaging components, and multi-element systems.

Every graph or coordinate diagram displays units explicitly.

Calculators and topics covered

refraction
lenses
mirrors
prisms
ray optics
Snell law
critical angle
thin lens equation
lensmaker
two lens system
prism deviation

Core equations

n_{1}\; \sin \; \theta _{1} = n_{2}\; \sin \; \theta _{2}

\frac{1}{f} = \frac{1}{d_{o}} \frac{+ 1}{d_{i}}

\Phi = \left(n_{r} - 1\right) \left[\frac{1}{R_{1}} \frac{- 1}{R_{2}} \frac{+ \left(\left(n_{r} - 1\right) d\right)}{n_{r} R_{1} R_{2}}\right]

Method and assumptions

Assumptions

Paraxial thin-lens and mirror equations are used except for the thick lensmaker calculation.
Materials are homogeneous and isotropic.

Limitations and design boundaries

Aberrations, polarization, coatings, diffraction, and wavelength-dependent dispersion are outside these modules.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy

Hecht, OpticsRefraction, thin and thick lens imaging, and prism dispersion.
Jenkins and White, Fundamentals of OpticsSign conventions for image formation and multi-element systems.
Born and Wolf, Principles of OpticsLensmaker relation including the thickness term, and total internal reflection.