Here's a question on ray optics.?

Question

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, 2F is not=R.PLEAZZZZZZ COMMENT

Answer 1

2f = r applies to a spherical concave mirror (see ref.), not a lens. Maybe that's the source of your confusion.
It's not in the thin-lens formula either, although that formula does lead to one special case involving 2f; with a converging lens, when the object is at distance 2f from the lens, the real image is at the same distance.

Answer 2

We DON'T say that the focal length of a lens is half times the radius of curvature.

For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot.

Answer 3

2f = R only according to the thin lens formula.
the actual formula is
u2/v - u1/u = u2 - u1 / f
where u2 and u 1 are the 2 consecutive refractive indices of media through which light is passing through.

Answer 4

yep.
if you've been told that 2f=r it's probably because, for the situations you'll be looking at, it's a good enough approximation

that's physics.. the universe is far too complicated to model perfectly.
so why not use something that's imperfect but easy?!