Show that the factor `((1)/(R_(1))- (1)/(R_(2)))` (and therefore focal length) does not depend on which surface of the lens strike first.

Explanation

Consider a convex lens of radii of curvature `p` and `q` as shwon.

Case 1: Suppose light is incident form left side and strikes the surface with radius of curvature `p`, first,
Then `R_(1) = +p, R_(2) = -q` and `((1)/(R_(1)) - (1)/(R_(2))) = ((1)/(p) - (1)/(-q)))`
CASE 2: Suppose light is incident form right side and strikes the surface with radius of curvature `q`, first.
Then `R_(1) = +q , R_(2) = -p` and `((1)/(R_(1)) - (1)/(R_(2))) = ((1)/(q) - (1)/(-p)))
Though we have shwon the result for biconvex lens, it is true for every lens.