How this calculation works
A prism rotates a ray through two refracting surfaces. At minimum deviation the path is symmetric, allowing refractive index to be recovered from the prism apex angle and the measured minimum deflection. This calculation is an inverse optical measurement, distinct from predicting refraction at one flat interface. The minimum-deviation condition is essential to the equation, not an optional label for any observed prism angle.
nprism/nmedium = sin[(A+δmin)/2]/sin(A/2)A worked example
A sixty-degree prism with forty-degree minimum deviation in air gives relative index sin(50°)/sin(30°). The resulting refractive index is about 1.53209. The corresponding symmetric incidence angle is fifty degrees and each internal refraction angle is thirty degrees. Increasing minimum deviation at unchanged apex increases the inferred index.
Good to know
This page assumes the measurement has actually found the minimum-deviation configuration. A single arbitrary ray deflection cannot be inserted and interpreted as the material index. Dispersion, face-angle calibration, instrument resolution and angular uncertainty are excluded. A measured index therefore needs an experimental uncertainty assessment before comparison with a glass catalogue or material specification.
Reference: OpenStax — refraction (opens in a new tab) ↗
What this calculation answers
A prism rotates a ray through two refracting surfaces. At minimum deviation the path is symmetric, allowing refractive index to be recovered from the prism apex angle and the measured minimum deflection.
This calculation is an inverse optical measurement, distinct from predicting refraction at one flat interface. The minimum-deviation condition is essential to the equation, not an optional label for any observed prism angle.
The Snell refraction critical angle and Brewster angle calculator treats one interface. This prism inversion additionally requires the symmetric minimum-deviation path through two faces.
Use the right input conventions
Enter the physical apex angle between the prism faces and the smallest measured deviation for the chosen wavelength. Both use degrees. The surrounding index must apply at both entrance and exit.
Apex plus minimum deviation must remain below 180 degrees. The supported relation assumes a prism index at least as large as the surrounding medium index; it does not model arbitrary low-index cavities or non-symmetric paths.
Interpret the result
The derived index is absolute relative to vacuum after multiplication by the entered surrounding index. The relative-index output helps distinguish the geometrical measurement from that surrounding-medium adjustment.
The symmetric incidence angle is half the sum of apex and deviation, while the internal angle at each face is half the apex. Those intermediate angles provide a direct check against a ray sketch or experimental notebook.
Work through the example
A sixty-degree prism with forty-degree minimum deviation in air gives relative index sin(50°)/sin(30°). The resulting refractive index is about 1.53209.
The corresponding symmetric incidence angle is fifty degrees and each internal refraction angle is thirty degrees. Increasing minimum deviation at unchanged apex increases the inferred index.
Where the model stops
This page assumes the measurement has actually found the minimum-deviation configuration. A single arbitrary ray deflection cannot be inserted and interpreted as the material index.
Dispersion, face-angle calibration, instrument resolution and angular uncertainty are excluded. A measured index therefore needs an experimental uncertainty assessment before comparison with a glass catalogue or material specification.
A few questions, answered
Can I use a deviation measured at any prism rotation?
No. The symmetric minimum-deviation position is required for this inverse relation.
What changes in the comparison?
Increase the measured minimum deviation while holding apex angle fixed.