The focal length of a convex lens is maximum for which of the following?

$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is
$(a)$ a convex lens of focal length $20 \, cm$,and
$(b)$ a concave lens of focal length $16 \, cm$?

$A$ thin equiconvex glass lens of refractive index $1.5$ has a power of $5 \,D$. When the lens is immersed in a liquid of refractive index $\mu$, it acts as a divergent lens of focal length $100 \,cm$. The value of $\mu$ of the liquid is:

Provide the object distance,image distance,type,size,and magnification for an object placed in front of a thin convex lens for different positions.

$A$ thin plano-convex lens of focal length $73.5 \ cm$ has a circular aperture of diameter $8.4 \ cm$. If the refractive index of the material of the lens is $\frac{5}{3}$, then the thickness of the lens is nearly

$A$ plane wave passes through a convex lens. The geometrical shape of the wavefront that emerges is