gen-define-spherical-aberration-and-give-one-short-worked-exampl-c3ba

Define spherical aberration and give one short worked example.

# Spherical Aberration **Definition:** Spherical aberration is an optical defect that occurs when light rays passing through different zones of a spherical lens or mirror fail to converge at a single focal point. Rays near the edge (marginal rays) focus closer to the lens than rays near the center (paraxial rays), causing a blurred image. ## Worked Example **Problem:** A thin biconvex lens has a focal length of 20 cm for paraxial rays. Due to spherical aberration, marginal rays (at the edge of the lens) converge 1.5 cm closer to the lens. If an object is placed 60 cm from the lens, what is the difference in image positions for paraxial and marginal rays? **Solution:** For **paraxial rays** using the thin lens equation: $$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$ $$\frac{1}{20} = \frac{1}{v} + \frac{1}{-60}$$ $$\frac{1}{v} = \frac{1}{20} + \frac{1}{60} = \frac{3+1}{60} = \frac{4}{60}$$ $$v_{paraxial} = 30 \text{ cm}$$ For **marginal rays**, effective focal length = 20 - 1.5 = 18.5 cm: $$\frac{1}{18.5} = \frac{1}{v} + \frac{1}{-60}$$ $$v_{marginal} = 26.7 \text{ cm}$$ **Longitudinal spherical aberration** = 30 - 26.7 = **3.3 cm** The image is spread over 3.3 cm along the optical axis, causing blur.