Trace the rays of light showing the formation of an image due to a point object placed on the axis of a spherical surface separating two media of refractive indices n1 and n2. Establish the relation between the distances of the object, the image and the radius of curvature from the central point of the spherical surface. Hence derive the expression of the lens maker's formula.
Solution
For a ray from axial point O refracting at the spherical surface (small-angle approximation, exterior-angle relations i=α+γ, r=γ−β) and Snell's law n1i=n2r, one obtains
vn2−un1=Rn2−n1(refraction at a single surface)
Applying this to the two surfaces of a thin lens (radii R1, R2; medium n1 outside, n2 glass) and adding the two equations, with the intermediate image acting as object for the second surface:
