Optics & Light Calculators — Lenses, Mirrors & Refraction
Solve the thin lens equation, mirror equation, Snell's law refraction, magnification, and critical angle problems for converging and diverging optical systems.
Optics & Light Calculators
Critical Angle Calculator
Find the critical angle for total internal reflection with θc = arcsin(n₂/n₁) — plus fiber-optic numerical aperture, acceptance cone, and real material presets.
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Lens Equation Calculator
Solve the thin lens equation 1/f = 1/do + 1/di for image distance, object distance, or focal length. Get magnification, image type, and a live ray diagram.
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Magnification Calculator
Calculate magnification from heights or distances, plus angular magnification for magnifiers, telescopes, and microscopes. See the height ratio and full breakdown.
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Mirror Equation Calculator
Solve 1/f = 1/dₒ + 1/dᵢ for concave and convex mirrors. Enter focal length or radius to get image distance, magnification, and a live reflection diagram.
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Snell's Law Calculator
Solve n₁ sin θ₁ = n₂ sin θ₂ for the refraction angle, incident angle, or refractive index. Get the critical angle, light speed, and a live ray diagram.
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Thin Lens Calculator
Find focal length and lens power in diopters from surface radii with the lensmaker's equation, combine two-lens systems, and measure unknown lenses.
Use CalculatorUnderstanding Optics & Light
Optics is the study of light behavior, including reflection, refraction, and image formation. The thin lens equation (1/f = 1/d_o + 1/d_i) is the workhorse formula for solving lens and mirror problems. Place an object 20 cm from a converging lens with a 15 cm focal length, and the equation gives an image distance of 60 cm — a real, inverted image magnified 3 times.
Snell's law (n&sub1; sinθ&sub1; = n&sub2; sinθ&sub2;) governs how light bends at material boundaries. When light passes from water (n = 1.33) into diamond (n = 2.42) at 45°, it refracts to 22.8°. At steep enough angles, light in a denser medium undergoes total internal reflection — the principle behind fiber optics and the sparkle of a well-cut diamond, where the critical angle of 24.4° traps light inside.
Light is an electromagnetic wave, so optics builds on the foundations of wave physics — concepts like wavelength, frequency, interference, and diffraction all apply. At very small scales or high energies, classical optics gives way to modern physics, where light behaves as photons with energy E = hf, connecting optics to quantum mechanics and the photoelectric effect.