💡 Prism & dispersion
Angle of deviation δ = i + e − A. At minimum deviation i = e, δ_m = 2i − A and n = sin((A+δ_m)/2)/sin(A/2). Angular dispersion δ_v − δ_r = (n_v − n_r)A. Dispersive power ω = (n_v − n_r)/(n−1). Achromatic combination: ω₁/f₁ + ω₂/f₂ = 0.
Prism calculators
Deviation, minimum deviation, n, dispersion, ω, achromatic
Angle of incidence i (°)
Angle of emergence e (°)
Prism angle A (°)
δ = i + e − A
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Angle of incidence i (°) = e at min deviation
Prism angle A (°)
δ_m = 2i − A
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Prism angle A (°)
Minimum deviation δ_m (°)
n = sin((A+δ_m)/2)/sin(A/2)
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n_v (violet)
n_r (red)
Prism angle A (°)
δ_v − δ_r = (n_v − n_r)A
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n_v (violet)
n_r (red)
Mean n (optional; default (n_v+n_r)/2)
ω = (n_v − n_r)/(n − 1)
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Solve for
ω₁
f₁ (cm)
ω₂
f₂ (cm)
ω₁/f₁ + ω₂/f₂ = 0
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🔺 Prism diagram
🧮Step-by-Step Solution▼ Show
| Concept | Formula | Notes |
|---|---|---|
| Angle of deviation | δ = i + e − A | i = incidence, e = emergence, A = prism angle |
| Minimum deviation | δ_m = 2i − A | At minimum deviation i = e |
| Refractive index (min deviation) | n = sin((A+δ_m)/2) / sin(A/2) | — |
| Angular dispersion | δ_v − δ_r = (n_v − n_r) A | — |
| Dispersive power | ω = (n_v − n_r) / (n − 1) | n = mean refractive index |
| Achromatic combination | ω₁/f₁ + ω₂/f₂ = 0 | Usually f₁ = −f₂ (convex + concave) |
About prism and dispersion
Angle of deviation δ = i + e − A. For a given prism, deviation is minimum when i = e; then δ_m = 2i − A and the refractive index is n = sin((A+δ_m)/2)/sin(A/2). Different wavelengths have different n, causing dispersion: angular dispersion δ_v − δ_r = (n_v − n_r)A. Dispersive power ω = (n_v − n_r)/(n−1). Two prisms (or lenses) can be combined so that ω₁/f₁ + ω₂/f₂ = 0 for an achromatic combination (no net dispersion).