$A$ convex lens has a focal length of $0.3 \ m$ and a refractive index of $3/2$. Find the focal length of the lens in $m$ when it is immersed in water,which has a refractive index of $4/3$.

$A$ 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 $16 \, cm$?

The distance between an object and its $3$ times magnified virtual image produced by a convex lens is $20 \,cm$. The focal length of the lens used is: (in $\,cm$)

$A$ thin glass (refractive index $1.5$) lens has an optical power of $-5\,D$ in air. Its optical power in a liquid medium with a refractive index of $1.6$ will be: (in $,D$)

Explain the first focal centre (first principal focus) and second focal centre (second principal focus) for a biconvex lens and a biconcave lens with the help of diagrams.

If sunlight is focused on a paper using a convex lens, it starts burning the paper in the shortest time when the lens is kept at $30 \text{ cm}$ above the paper. If the radius of curvature of the lens is $60 \text{ cm}$, then the refractive index of the lens material is $\frac{\alpha}{10}$. The value of $\alpha$ is . . . . . . .