Risley Prism Beam Deviation Calculator

Calculate the prism apex angle from the measured displacement of a laser spot on a screen, using the prism-to-screen distance and refractive index. The calculator also compares the exact geometric result with the thin-prism approximation.

Input parameters

Measurement

Prism → screen distance

Distance from the prism to the screen.

Spot displacement on screen

Use a negative value to indicate the opposite direction.

Prism material

Refractive index n

Example: BK7 ≈ 1.5168 at 587.6 nm.

Calculated values

Prism apex angle A

–

degrees

Beam deviation |δ|

–

degrees

Beam deviation |δ|

–

mrad

Thin-prism apex angle

–

degrees

Enter the input data and press Calculate.

Exact vs approximation: –

Simplified geometry used by the calculator: incident beam normal to the first prism surface.

Calculation model

Beam deviation from screen displacement

δ = atan(Δx / L)

Exact prism relation

δ = asin(n · sin A) − A

Thin-prism approximation

A ≈ δ / (n − 1)

Assumption: the incident laser beam is normal to the first prism surface. The calculator therefore infers the prism apex angle corresponding to the measured angular deviation. The calculation treats the prism as homogeneous and uses a single refractive-index value.

Using the calculator

Measure the distance from the prism to the screen and the lateral displacement of the laser spot. Enter the refractive index of the prism glass at the wavelength of interest, then press Calculate.

The sign of the displacement identifies the beam-deflection direction.
The apex angle is reported as a positive magnitude.
The exact calculation is compared with the thin-prism approximation.
This page calculates a single prism under the stated normal-incidence geometry; a separate calculator is used for a pair of Risley prisms.

Lambda Physics also offers optical prisms and other optical components in the General Stock catalog.