A solid glass sphere of radius mm and index is used as a lens 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
A solid glass sphere of radius R=10 mm and index n=1.50 is used as a lens in air, light travelling left to right along a diameter. Treat it as a thick lens whose two surfaces are the front and back of the sphere, so that under CV1 the front surface has R1=+10 mm, the back surface has R2=−10 mm, and the axial thickness is tℓ=2R=20 mm. Rays are paraxial.
((a)) Build the vertex-to-vertex system matrix (refraction, translation through the glass, refraction, multiplied right to left under CV2) and find the focal length.
((b)) Locate both principal planes, each measured from its nearer vertex, and say where in the sphere they fall. Explain why the symmetry of the sphere makes the answer to the second plane predictable once the first is known.
((c)) Find the back focal distance, from the back vertex to the focus of a parallel bundle, and confirm it by tracing a parallel ray through the two surfaces one at a time with the single-surface refraction equation.