Optical Geometry Calculator

Five geometry relationships recur throughout optical alignment and layout work. Angle conversion translates between degrees, radians, milliradians, microradians, arcminutes, and arcseconds — the six units that appear across positioning datasheets, beam divergence specs, and vibration isolation requirements. Beam displacement computes how far a reflected beam moves at a target when a mirror tilts by a small angle α, noting when the paraxial approximation (displacement ≈ 2αL) deviates from the exact tangent expression. Parallel plate displacement applies Snell's law to find the lateral offset introduced when a beam passes obliquely through a flat window or beamsplitter substrate. Solid angle converts an aperture diameter and distance into steradians, f-number, and numerical aperture. Error propagation converts an angular pointing error into a linear position error at a given distance.