Ray Transfer Matrix Analysis - Table of Ray Transfer Matrices

Table of Ray Transfer Matrices

for simple optical components

Element Matrix Remarks
Propagation in free space or in a medium of constant refractive index d = distance
Refraction at a flat interface n1 = initial refractive index

n2 = final refractive index.
Refraction at a curved interface R = radius of curvature, R > 0 for convex (centre of curvature after interface)

n1 = initial refractive index
n2 = final refractive index.
Reflection from a flat mirror
Reflection from a curved mirror R = radius of curvature, R > 0 for concave
Thin lens f = focal length of lens where f > 0 for convex/positive (converging) lens.

Only valid if the focal length is much greater than the thickness of the lens.
Thick lens n1 = refractive index outside of the lens.

n2 = refractive index of the lens itself (inside the lens).
R1 = Radius of curvature of First surface.
R2 = Radius of curvature of Second surface.
t = thickness of lens (not taking into account thickness of curved parts. If total thickness is desired, total thickness would equal t + both curved thickness parts.
Single right angle prism k = (cos/cos) is the beam expansion factor, where is the angle of incidence, is the angle of refraction, d = prism path length, n = refractive index of the prism material. This matrix applies for orthogonal beam exit.

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