A symmetric biconvex lens sits in air with surface radii ,

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging

What an Instrument Can See, Ch The paraxial system as an operator

Problem

A symmetric biconvex lens sits in air with surface radii R1=+50 mmR_1 = +50\ \mathrm{mm}, R2=−50 mmR_2 = -50\ \mathrm{mm}, thickness t=10 mmt = 10\ \mathrm{mm} along the axis, and glass index n=1.5n = 1.5. The thin-lens estimate, which neglects the thickness, gives 1/f=(n−1)(1/R1−1/R2)1/f = (n-1)(1/R_1 - 1/R_2), a focal length of 50 mm50\ \mathrm{mm}. Using the refraction matrices (10−(n′−n)/R1)\begin{pmatrix}1&0\\-(n'-n)/R&1\end{pmatrix} and the translation matrix (1t/n01)\begin{pmatrix}1&t/n\\0&1\end{pmatrix}, build the system matrix from the front vertex to the rear vertex. ((a)) Find the effective focal length. ((b)) Find the back focal distance (rear vertex to rear focal point). ((c)) Locate the front principal plane relative to the front vertex (positive to the right). ((d)) Locate the rear principal plane relative to the rear vertex (positive to the right). ((e)) Express the percentage difference between the computed effective focal length and the 50 mm50\ \mathrm{mm} thin-lens estimate.

Browse the problem library