Prism Deviation Calculator
Determine how much a glass prism bends a light ray using its apex angle, refractive index, and incident angle. Use this when studying optics, designing spectrometers, or verifying Snell's law experiments.
About this calculator
When light enters a prism, it refracts at both surfaces according to Snell's law. The total deviation δ is the sum of deviations at each surface: δ = i₁ + i₂ − A, where i₁ is the angle of incidence, i₂ is the exit angle, and A is the apex angle. At minimum deviation, the ray travels parallel to the base and i₁ = i₂, giving D_min = 2·arcsin(n·sin(A/2)) − A. The refractive index n can then be extracted as n = sin((A + D_min)/2) / sin(A/2). Critical angle, beyond which total internal reflection occurs, is θ_c = arcsin(1/n). These relationships are foundational in spectroscopy and optical instrument design.
How to use
Example: A glass prism has apex angle A = 60°, refractive index n = 1.5, and incident angle i₁ = 45°. Step 1: Convert to radians. Step 2: r₁ = arcsin(sin(45°)/1.5) = arcsin(0.4714) ≈ 28.13°. Step 3: r₂ = A − r₁ = 60° − 28.13° = 31.87°. Step 4: i₂ = arcsin(1.5 × sin(31.87°)) = arcsin(0.7906) ≈ 52.1°. Step 5: δ = 45° + 52.1° − 60° = 37.1°. The light ray is deviated by approximately 37.1°.
Frequently asked questions
What is minimum deviation in a prism and why does it matter?
Minimum deviation occurs when light passes symmetrically through the prism, meaning the ray inside is parallel to the base. At this condition i₁ = i₂ and r₁ = r₂ = A/2. It matters because the refractive index formula n = sin((A + D_min)/2) / sin(A/2) is most accurate and easy to use at minimum deviation. Spectroscopists use this condition to precisely measure n for different wavelengths.
How does the refractive index affect the deviation angle of a prism?
A higher refractive index causes greater bending at each surface, so the total deviation angle increases. This is why dense glass or flint glass prisms spread colours more than crown glass prisms. The relationship is captured in Snell's law n₁ sin θ₁ = n₂ sin θ₂ applied at both prism faces. Different wavelengths of light have slightly different refractive indices in the same material, producing dispersion (the rainbow effect).
When does total internal reflection occur inside a prism?
Total internal reflection happens when a ray inside the prism hits a surface at an angle greater than the critical angle θ_c = arcsin(1/n). For glass with n = 1.5, θ_c ≈ 41.8°. If the refracted angle r₂ at the second surface exceeds this value, no light exits and it reflects internally. Prism periscopes and retroreflectors intentionally exploit this effect to redirect beams without any silvered coating.