(a) A point object `O' is kept in a medium of refractive index n1 in front of a convex spherical surface of radius of curvature R which separates a second medium of refractive index n2 from the first one, as shown in the figure. Draw the ray diagram showing the image formation and deduce the relationship between the object distance, the image distance and n1,n2 and R. (b) When the image formed above acts as a virtual object for a concave spherical surface separating the medium n2 from n1, draw the ray diagram and write the similar relation. Hence obtain the expression for the lens maker's formula.
Solution
(a) For refraction at the convex surface (small angles; exterior-angle relations and Snell's law n1i=n2r):
vn2−un1=Rn2−n1(i)
(b) For the second (concave) surface of radius R′, with the first image acting as a virtual object, a similar relation holds; adding it to (i) and writing n21=n1n2, f1=v′1−u1:
