Review of Basic Geometrical Optics n1 n2 s P The image P is an image of the object S if all the rays from S are refracted by the interface so that they go through P The Snell’s law has to satisfy at all point of the interface.

sp Following Wavefronts The other view how lenses works is that they alters the wavefront of the incoming wave

Cartesian lens (aspherical lens) Spherical lens Over this range, the two surfaces Are nearly the same Spherical and Aspherical Lenses The imperfections in the image due to the deviations from the correct surface are Called “spherical aberrations.”

Plano-ConvexPlano-ConcaveBiconvexMeniscus (Concave-Convex) Commercial Lenses

Thin Lens Equaton s S’ S P Sign convention: distances to the left of the lens are negative, distances to the right of the lens are positive. f : f is positive for focusing lenses, f is negative for diverging lenses

(i) S=  S’=f (a) f>0 (positive lens), rays converge to focus f P (b) f<0 (negative lens), rays diverge, but they appear to come from point P. In this case, P is called a virtual image P

(ii) S=-f and f>0, we have S=  f s The lens is said to “collimate” the rays from s

(iii) S<-f (a) f>0, P is a real image f P (b) f<0, P is a virtual image (S’<0) P f S f S’

(iv) f>0, -f <S<0, we have S’<0 (negative image) f s P

Simple Graphical method of ray tracing and image magification a ray through the center of a thin lens is undeviated collimated ray pass through the focus and vice versa. ff ss’ x x’ (i) Positive thin lens Magnification = x’/x=s’/s <0, so image is inverted but real

(i) Negative thin lens The image is upright but virutal f