According to the longitudinal chromatic aberration formula, what happens to CA if Abbe value v is increased while keeping D constant?

According to the longitudinal chromatic aberration formula, what happens to CA if Abbe value v is increased while keeping D constant?

• A. CA decreases
• B. CA increases
• C. CA remains the same
• D. Cannot determine

Answer: (A)

The key idea is how dispersion affects chromatic blur. Longitudinal chromatic aberration comes from the way the lens’s refractive index changes with wavelength; blue and red light focus at different points. The Abbe number quantifies this dispersion: a higher Abbe value means a smaller difference between the indices for blue and red light, i.e., less dispersion. If you hold the lens’s power (or focal characteristics, represented here by D) constant and just increase the Abbe number, the wavelength-dependent focal shift shrinks. With less dispersion, the focal points for different colors align more closely, so the longitudinal chromatic aberration decreases. That’s why the correct outcome is a reduction in CA. A quick context: Abbe number is defined so that increasing V reduces the dispersion term (n_F − n_C), which is what drives LCA. Since D is unchanged, there’s no additional change in focusing strength—only the dispersion changes—leading to a smaller CA.

The key idea is how dispersion affects chromatic blur. Longitudinal chromatic aberration comes from the way the lens’s refractive index changes with wavelength; blue and red light focus at different points. The Abbe number quantifies this dispersion: a higher Abbe value means a smaller difference between the indices for blue and red light, i.e., less dispersion.

If you hold the lens’s power (or focal characteristics, represented here by D) constant and just increase the Abbe number, the wavelength-dependent focal shift shrinks. With less dispersion, the focal points for different colors align more closely, so the longitudinal chromatic aberration decreases. That’s why the correct outcome is a reduction in CA.

A quick context: Abbe number is defined so that increasing V reduces the dispersion term (n_F − n_C), which is what drives LCA. Since D is unchanged, there’s no additional change in focusing strength—only the dispersion changes—leading to a smaller CA.