[Physics] Does a biconvex lens have a shorter focal length than a plano-convex lens

Question

Is there a ray-tracing diagram somewhere that shows precisely the difference between a Biconvex and Plano-convex lens?

Answer 1

First. While asking this question, you should clarify the specific properties of the two lenses.. Let's say, their Radius of Curvature, optical density/refractive index and the medium in which they are put.

So as you have not mentioned any of these, I conclude that the radii of curvature is same for both lenses. So now there can be two cases.

Case 1: Lenses are placed in a medium of less refractive index So for a biconvex lens The focal length would be: 1/f = (Π-1)(1/R -1/R). { where Π = refractive index of lens/ refractive index of surrounding)

Putting the values you will get f = R/2(Π--1)

And for a plano convex lens it will be.,.. f= R/(Π-1)

Now its clear that :: focal length (plano convex) > focal length (biconvex)

Case 2: Lens putted in a refractive index greater that those of lens.

Then for bi convex f= R/2(Π-1) and here Π-1 is negative..

For plano convex, f=R/(Π-1)

So both have -ve value and in this case as well focal length (plano convex) > focal length (biconvex)

In magnitude, plano convex lens has always greater focal length than a bi convex lens.