1/f = 1/v + 1/u
Mirror formula: 1/f = 1/v + 1/u. Spherical mirror, paraxial rays, New Cartesian signs. Use consistent length units.
Mirror formula
Use when — Spherical mirror, paraxial rays, New Cartesian signs. Use consistent length units.
m = h_i/h_o = -v/u
Mirror magnification: m = h_i/h_o = -v/u. Same sign convention.
Mirror magnification
Use when — Same sign convention.
n = c/v
Refractive index: n = c/v. Phase speed in medium for stated wavelength/frequency.
Refractive index
Use when — Phase speed in medium for stated wavelength/frequency.
n1 sin i = n2 sin r
Snell law: n1 sin i = n2 sin r. Angles from normal, isotropic media.
Snell law
Use when — Angles from normal, isotropic media.
n2/v - n1/u = (n2-n1)/R
Spherical refraction: n2/v - n1/u = (n2-n1)/R. Paraxial refraction at spherical interface with consistent Cartesian signs.
Spherical refraction
Use when — Paraxial refraction at spherical interface with consistent Cartesian signs.
1/v - 1/u = 1/f
Thin-lens formula: 1/v - 1/u = 1/f. Thin lens, paraxial rays, New Cartesian convention.
Thin-lens formula
Use when — Thin lens, paraxial rays, New Cartesian convention.
m = v/u
Lens magnification: m = v/u. Thin lens with same convention.
Lens magnification
Use when — Thin lens with same convention.
1/f = (n_l/n_m - 1)(1/R1 - 1/R2)
Lens maker: 1/f = (n_l/n_m - 1)(1/R1 - 1/R2). Thin lens in medium, paraxial surfaces. In air n_m approx 1.
Lens maker
Use when — Thin lens in medium, paraxial surfaces. In air n_m approx 1.
P = 1/f(m)
Lens power: P = 1/f(m). Thin lens; P in dioptre.
Lens power
Use when — Thin lens; P in dioptre.
P_eq = sum P_i
Thin lenses in contact: P_eq = sum P_i. Thin coaxial lenses in contact.
Thin lenses in contact
Use when — Thin coaxial lenses in contact.
sin i_c = n2/n1
Critical angle: sin i_c = n2/n1. n1 > n2, ray from denser medium 1 to rarer medium 2.
Critical angle
Use when — n1 > n2, ray from denser medium 1 to rarer medium 2.
delta = i + e - A
Prism deviation: delta = i + e - A. Geometric prism relation.
Prism deviation
Use when — Geometric prism relation.
n = sin[(A+delta_m)/2]/sin(A/2)
Prism at minimum deviation: n = sin[(A+delta_m)/2]/sin(A/2). Prism in air, symmetric minimum-deviation path.
Prism at minimum deviation
Use when — Prism in air, symmetric minimum-deviation path.
M = -f_o/f_e
Telescope normal adjustment: M = -f_o/f_e. Astronomical telescope, final image at infinity; sign shows inversion.
Telescope normal adjustment
Use when — Astronomical telescope, final image at infinity; sign shows inversion.
Compound microscope, normal adjustment: . M
Compound microscope, normal adjustment
Use when — M