PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging
Optics and Photonics, Ch Stops, pupils and optical instruments
Problem
Two thin lenses in air, an objective of focal length fo and an eyepiece of focal length fe, are separated by a gap ℓ that is not yet fixed. Use the ray transfer matrices of Chapter 1 for the column (y,θ) in air, multiplied right to left under CV2.
((a)) Multiply refraction, translation and refraction to find the system matrix for a general gap ℓ, and show that its bottom-left entry vanishes, so that a parallel bundle in gives a parallel bundle out, only when ℓ=fo+fe.
((b)) With that gap, show that a parallel beam of width D filling the objective leaves the eyepiece with width Dfe/fo and with its angle multiplied by −fo/fe, and say which entry of the matrix carries each fact.
((c)) Now let the eyepiece be diverging, fe=−∣fe∣, the Galilean arrangement. Show that the same two formulas still hold, that the tube is now shorter than fo, that the view is upright, and that the exit beam is still narrower than the objective. For fo=200 mm, fe=−40 mm and D=30 mm, give the tube length, the angular magnification and the exit beam width.