Here's a question on ray optics. We say that the focal length of a lens is half times the radius of curvature, right. Now, consider any lens(say convex), made of any material(say glass). Now a beam of light parallel to the principle axis, passes through the lens. All the rays in the beam will converge at a point, which we call the focus. For now, let us assume that the focal length of this particular lens is half time the radius of curvature of the lens. Now, take another lens whose structure is identical to that of the previous lens, i.e., it has the same radius of curvature and everything, the only difference being that this time the lens is made of a material that is denser than that of the previous lens. This time, if we pass a beam of light parallel to the principle axis through the lens, all the rays in the beam will converge at a different focus, with focal length shorter than that in case of the previous lens. So, we can see that, this time the focal length is not equal to half times the radius of curvature. This shows that saying that the focal length of a lens is half times the radius of curvature is not always true. Please comment.