Category
Optics & Photonics
Optics and photonics formulas and calculators for geometric and wave optics used to design lenses, sensors, and optical instruments. Includes refraction, diffraction, interference, and lens system equations.
31Formulas
2Subcategories
Updated Oct 2026
Geometric Optics
Etendue (Optical Throughput)
E = A * Ω
Wave Optics
Optical Gain in Decibels
G (dB) = 10 * log10(Pout/Pin)
Wave Optics
Fiber Optic Attenuation
α (dB/km) = (10/L) * log10(Pin/Pout)
Geometric Optics
Fiber Optic Numerical Aperture
NA = sqrt(n_core² - n_cladding²)
Wave Optics
Gaussian Beam Waist Evolution
w(z) = w0 * sqrt(1 + (z/zR)²)
Wave Optics
Laser Beam Divergence
θ = λ / (π*w0)
Wave Optics
Photon Momentum
p = h/λ
Wave Optics
Photon Energy
E = h*c/λ
Wave Optics
Fresnel Number
F = a² / (λ*L)
Wave Optics
Coherence Length
Lc = λ² / Δλ
Wave Optics
Thin Film Interference (Constructive)
2*n*t = m*λ
Wave Optics
Optical Path Length
OPL = n * d
Wave Optics
Diffraction Limit (Rayleigh Criterion)
θ_min = 1.22 * λ / D
Wave Optics
Double-Slit Interference Fringe Spacing
Δy = λ*L / d
Geometric Optics
Combined Focal Length of Two Thin Lenses in Contact
1/f_combined = 1/f1 + 1/f2
Geometric Optics
Angular Magnification (Simple Magnifier)
M = 25cm / f
Geometric Optics
Depth of Field (Simplified)
DOF ≈ 2*N*c*s² / f²
Geometric Optics
Numerical Aperture
NA = n * sin(θ)
Geometric Optics
f-number (Focal Ratio) of a Lens
N = f / D
Geometric Optics
Brewster's Angle
θB = arctan(n2/n1)
Geometric Optics
Lensmaker's Equation
1/f = (n-1) * (1/R1 - 1/R2)
Geometric Optics
Magnification (Lens or Mirror)
m = -d_i / d_o
Geometric Optics
Mirror Equation (Spherical Mirror)
1/f = 1/d_o + 1/d_i
Wave Optics
Malus's Law (Polarization)
I = I0 * cos(theta)^2
Wave Optics
Single-Slit Diffraction Minima
a * sin(theta) = m * lambda
Geometric Optics
Critical Angle (Total Internal Reflection)
theta_c = arcsin(n2 / n1)
Geometric Optics
Index of Refraction
n = c / v
Wave Optics
Young's Double-Slit Equation
y = mλL / d
Wave Optics
Diffraction Grating Equation
d sinθ = mλ
Geometric Optics
Thin Lens Equation
1/f = 1/d_o + 1/d_i
Geometric Optics
Snell's Law
n₁sinθ₁ = n₂sinθ₂