A thick symmetric biconvex lens has axial thickness
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
A thick symmetric biconvex lens has axial thickness tℓ=12mm, front radius R1=+40mm, back radius R2=−40mm, and is made of glass of index n=1.60. It stands in air on both sides. An object is placed 200mm in front of the front vertex. All rays are paraxial.
((a)) Find the position of the final image, measured from the back vertex, by applying the single-surface refraction equation at the front surface and then at the back surface, using the image of the first surface as the object of the second (measuring that object distance from the back vertex).
((b)) Build the vertex-to-vertex system matrix for the lens (refraction, translation by the reduced thickness, refraction) and use it to find the focal length and the positions of the two principal planes, each measured from its nearer vertex.
((c)) Using the system matrix together with the translations before and after the lens, confirm the image position found in part (a).