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
Three independent paraxial calculations. Throughout use the book's sign convention CV1: light travels left to right, so>0 for a real object on the left, si>0 for a real image on the outgoing side (to the right for a surface or a lens, in front of the mirror, to the left, for a mirror), and R>0 when the centre of curvature lies to the right of the vertex. All media other than the glass named are air, of index 1.00. Every surface is treated in the paraxial approximation.
((a)) A long solid glass rod of index 1.50 has a polished convex spherical end of radius of curvature R=+6.0 cm. A small object sits on the axis in the air, 24 cm to the left of that end. Where, measured from the vertex of the end surface, is the image formed inside the glass?
((b)) A concave spherical mirror has radius of curvature R=−50 cm under CV1, so that f=−R/2. A candle stands on the axis 75 cm in front of the mirror. Find si.
((c)) A thin lens of glass of index 1.60 in air has R1=+10 cm and R2=−15 cm. Use the lensmaker's equation to find its focal length.