Wedge, Window & Tilt Calculator

The three questions every optical bench asks eventually: how much does a wedge steer the beam, how far does a tilted window shift it, and how much astigmatism does that window add to a converging beam? Exact two-surface refraction — not just the small-angle formulas — with the approximations shown alongside.

Element

Mode

Refractive index n

–

Thickness t

Wedge angle α

deg

Incidence / tilt θ

deg

Glass preset

Results

What this means

Geometry

Field guide: which formula when?

Wedge: thin-wedge deviation δ ≈ (n−1)α is excellent below ~2° wedge and near-normal incidence; this tool always shows the exact two-surface Snell result so you can see when the approximation drifts. Tilted window: lateral displacement d = t·sinθ·(1 − cosθ/(n·cosθ′)) is exact; the beam exits parallel to itself. Window in a converging beam: the classic longitudinal shift Δz = t(n−1)/n at normal incidence, plus tilt-induced astigmatism ≈ t·θ²(n²−1)/n³ separating tangential and sagittal foci — the reason beamsplitter plates in imaging paths get compensated or used at low f-number only.