Question

A lens is a piece of transparent material with two refracting surfaces such that at least one is curved and refractive index of its material is different from that of the surroundings.
A thin spherical lens with refractive index greater than that of surroundings behaves as a convergent or convex lens, i.e., converges parallel rays if its central (i.e., paraxial) portion is thicker than marginal one.
However if the central portion of a lens is thinner than marginal, it diverges parallel rays and behaves as divergent or concave lens. show this and classify identify convergent and divergent lenses.

Answer 1

The nature of the lens will not change, shape and size, density etc will remain the same.

Now, the focal length will change,

The lens maker's formula will change.

The lens maker's formula is

$\frac{1}{f}=\left(\frac{n_2-n_1}{n_1}\right)(\frac{1}{R_1}-\frac{1}{R_2})=\left(\frac{n_2-n_1}{n_1}\right)A$

Where $f$ is the focal length, $m_2$ the refractive index of the lens, n, the refractive index of the medium and $R_1$ and $R_2$ the curvature radius of each lens face

$\frac{1}{f_{air}}=\left(\frac{n_2-1}{1}\right)A$

In a medium where, $n_1>n_2$ for this particular lens we will have

$\frac{1}{f_{med}}=\left(\frac{n_2-n_1}{n_1}\right)A$

and finally

$f_{med}=f_{air}\frac{n_1(n-2-1)}{n_2-n_1}$

with $f_{med}\ne f_{air}$ and negative , i.e, the lens will change to diverging lens.