What is the formula for longitudinal chromatic aberration?

What is the formula for longitudinal chromatic aberration?

• A. CA = D/v (D = power of lens; v = Abbe value)
• B. CA = (dD)/v (d = distance from OC; v = Abbe value)
• C. CA = D×v
• D. CA = v/D

Answer: (A)

Longitudinal chromatic aberration comes from the fact that lenses bend blue light more than red light, so light of different wavelengths focuses at different distances along the optical axis. In ophthalmic optics, the amount of this axial focus shift for a given lens is estimated by dividing the lens power by the material’s Abbe number. So the formula is CA ≈ D / v, where D is the dioptric power of the lens and v is the Abbe value of the lens material. Higher Abbe numbers mean less dispersion, which lowers LCA; higher lens power increases LCA, which is captured by the division by v. Why the other forms don’t fit: multiplying power by the Abbe number would imply that dispersion effects grow with higher Abbe numbers, which is opposite of what is observed. Using a derivative with respect to distance isn’t the standard way to quantify LCA in a simple lens model. Inverting the ratio as v/D would suggest that LCA increases as power decreases and as Abbe number increases, which contradicts the relationship that LCA grows with power and shrinks with higher dispersion resistance (higher Abbe number).

Longitudinal chromatic aberration comes from the fact that lenses bend blue light more than red light, so light of different wavelengths focuses at different distances along the optical axis. In ophthalmic optics, the amount of this axial focus shift for a given lens is estimated by dividing the lens power by the material’s Abbe number. So the formula is CA ≈ D / v, where D is the dioptric power of the lens and v is the Abbe value of the lens material. Higher Abbe numbers mean less dispersion, which lowers LCA; higher lens power increases LCA, which is captured by the division by v.

Why the other forms don’t fit: multiplying power by the Abbe number would imply that dispersion effects grow with higher Abbe numbers, which is opposite of what is observed. Using a derivative with respect to distance isn’t the standard way to quantify LCA in a simple lens model. Inverting the ratio as v/D would suggest that LCA increases as power decreases and as Abbe number increases, which contradicts the relationship that LCA grows with power and shrinks with higher dispersion resistance (higher Abbe number).