Step 4 of 8: Find the curvature of each surface

We need to know the curvature of the first (AST) surface. The lensmaker's equation for a thin lens is

lensmakers eqn

where, of course, R1 is the radius of curvature of the first surface, R2 is for the second surface, and f is the focal length of the lens. Now, since the lens is equi-convex, the radius of curvature of one side is the negative of the radius of the other side so R1=R=-R2so

biconvex eqn

Now we can solve for the radius of curvature

solution

The radius of curvature of the first surface is positive because the sphere's center is to the right of the vertex.

curvature AST

The second surface has a negative radius of curvature because the sphere's center is to the left of the vertex

curvature 2

The object and image surfaces also have radii of curvatures. Since they are flat, this corresponds to a circle that is infinitely big and so, of course, we write 0 (zero).

curvature OBJ IMS

Now, collect all the curvatures in one place

curvature all

Collect these curvatures into a table describing your optical system.

Surface Curvature Distance Height Material
OBJ 0
AST Rast
2 R2
IMS 0