A thin lens of focal length mm and clear diameter mm
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 thin lens of focal length f=100 mm and clear diameter 25 mm, in air, forms a real image of a small object 4.0 mm tall placed 150 mm in front of it. Rays are paraxial and CV1 applies. The object stands on the axis and reaches h=4.0 mm above it.
((a)) Find the image distance, the transverse magnification and the image height.
((b)) Find the half-angle of the cone of rays the lens accepts from the axial object point, u, and the half-angle of the cone converging on the axial image point, u′.
((c)) Both half-angles are counted positive, so compare magnitudes: show numerically that ∣h∣u=∣h′∣u′ for these two heights and half-angles, and say which two rays of the chapter's similar-triangle argument this product belongs to.
((d)) The same lens is now to throw a 40 mm tall image of the same object, and the cone converging on the image must have a half-angle of at least 0.010 rad. Using the invariant alone, find the half-angle the lens must accept from the object, then find the object distance that gives this magnification and hence the smallest clear diameter the lens could have. Is the 25 mm lens wide enough?