# Achromatic Thin-Lens Doublet Calculator

nD = 1.6477
VD = 33.82
nD = 1.5168
VD = 64.167
Calculation Results:
R1: -116.2374
R2: 116.2374
R3: -41.5933

### How the Achromatic Thin-Lens Doublet calculator works:

This calculator assumes that both lenses are thin lenses to perform calculations, and provides a good starting point for a thick achromatic doublet re-optimization. The thicknesses rendered in the achromat shown are for illustration purposes only.

This calculator works in unitless quantities. The nominal powers and focal lengths are for d (587.56nm) light.

The total power for a thin lens doublet is: φ = φ₁ + φ₂

And assuming we have linear dispersion the system must also satisfy: φ₁/V₁ + φ₂/V₂ = 0

Solving for φ₁ and φ₂ we get:

φ₁ = φ ⋅ V₁/(V₁ - V₂)

φ₂ = - φ ⋅ V₂/(V₁ - V₂)

Finally to calculate our radii of curvature we assume that the first lens has equal but opposite signed radii of curvature, using the thin lens formula we can also calculate the powers for each individual lens as follows:

φ₁ = (n₁ - 1) ⋅ (1/R₁ - 1/R₂)

φ₂ = (n₂ - 1) ⋅ (1/R₂ - 1/R₃)

Assuming R₁ = -R₂

φ₁ = (n₁ - 1) ⋅ (1/R₁ + 1/R₁) = (n₁ - 1) ⋅ 2/R₁

R₁ = [ (n₁ - 1) ⋅ 2 ] / φ₁

R₃ = 1/[ 1/R₂ - φ₂ / (n₂ - 1) ]