Two thin lenses are mounted on a common axis in air
PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging
Optics and Photonics, Ch Image formation by mirrors and lenses
Problem
Two thin lenses are mounted on a common axis in air, light travelling left to right. Lens 1 is converging with focal length f1=+15cm. Lens 2, a distance d=40cm to the right of lens 1, is diverging with focal length f2=−20cm. An object is placed so1=30cm in front of lens 1. Both lenses are thin, and only paraxial rays are considered.
((a)) Locate the image formed by lens 1 alone, then treat it as the object for lens 2 (measuring its distance from lens 2), and find the position of the final image and the overall transverse magnification.
((b)) Build the system ray-transfer matrix for the whole set-up, from just before lens 1 to just after lens 2 (a refraction matrix, then a translation matrix, then a refraction matrix, multiplied in the order the book states). By requiring the height of the outgoing ray at the image plane to be independent of the angle it left the object with, confirm the image position found in part (a).