A thin double convex lens of radii of curvature $$R_1=20\ \text{cm}$$ and $$R_2=60\ \text{cm}$$ is made of a transparent material of refractive index $$\mu=1.5$$. Choose the correct options.

The focal length of the lens is $$f=30\ \text{cm}$$ when in air

The lens behaves as a concave mirror of focal length $$f_M=10\ \text{cm}$$ when silvered on the surface of radius $$R_2=60\ \text{cm}$$

The lens behaves as a concave lens (diverging lens) if the image space beyond the $$R_2=60\ \text{cm}$$ radius surface is filled with a transparent liquid of refractive index $$\mu=5/3$$, while the object space prior to the $$R_1=20\ \text{cm}$$ radius surface is air

A beam of rays incident parallel to the principal axis focuses at $$48\ \text{cm}$$ behind the lens if water of refractive index $$\mu=4/3$$ fills the entire space behind the surface of radius $$R_2=60\ \text{cm}$$, while the object space prior to the surface of radius $$R_1=20\ \text{cm}$$ is air