Question

Describe the reduction in the spherical aberration for a plano-convex lens for the special case of collimated light (parallel light) focused down to a focal point.

Which orientation of the lens gives the least spherical aberration and why?

Show ray diagrams

Describe how and axial-GRIN lens can further reduce the spherical aberration. Again show a qualitative ray diagram.

Answer 1

Two surfaces of plano convex lens function together as convergent lens by focusing parallel light rays (collimated) to focal point. Hence vanishing the reason behind spherical aberration ie different focus points of marginal and paraxial rays. They form a real image. The curved surface of plano convex lens has focusing effect while the plane surface has no such focusing defocusing effect further reducing the spherical aberration effect.

Maximum sharp focus is achieved when curved portion of lens is oriented towards object. Low spherical aberration is also achieved if lens is oriented in a way that causes the collimated beam to enter or exit the curved surface thereby maing the plano side face towards focus or source.

Gradient index lens (GRIN) have a refraction gradient that varies with radial distance thereby reducing aberration typical of traditional spherical lenses. Lens of eye, Mirage are examples of natural lenses whose refractive index varies along layers allowing ,mages with good resolution and low aberration at both short and long distances.