A doublet consists of two thin lenses in air

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 doublet consists of two thin lenses in air, each of focal length f=100 mmf=100~\text{mm}, separated by d=50 mmd=50~\text{mm}. Between the front vertex of lens 1 (the input reference plane) and the back vertex of lens 2 (the output reference plane) the system matrix in the plain-angle (y,θ)(y,\theta) column is M=(0.550 mm−0.015 mm−10.5).\mathbf{M}=\begin{pmatrix}0.5 & 50~\text{mm}\\ -0.015~\text{mm}^{-1} & 0.5\end{pmatrix}. ((a)) Translate M\mathbf{M} into cardinal-point language by stating the effective focal length. ((b)) Locate the front principal plane relative to the front vertex and the back principal plane relative to the back vertex (distances positive to the right). ((c)) An object stands 200 mm200~\text{mm} in front of the front vertex. Using the thin-lens conjugate equation applied between the principal planes, find the image distance measured from the back vertex and the transverse magnification.

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