The focal length of a glass convex lens is $2 \, cm$. What will be its focal length in $cm$ when it is immersed in a liquid of refractive index $1.25$?

$A$ point source of light is moving at a rate of $2 \,cm \,s^{-1}$ towards a thin convex lens of focal length $10 \,cm$ along its optical axis. When the source is $15 \,cm$ away from the lens,the image is moving at:

$A$ 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 refractive index of the material of a concave lens is $\mu$. It is immersed in a medium of refractive index $\mu_1$. $A$ parallel beam of light is incident on the lens. The path of the emergent rays when $\mu_1 > \mu$ is

The graph between the lateral magnification $(m)$ produced by a lens and the distance of the image $(v)$ is given by

The focal length of an equi-convex lens is greater than the radius of curvature of any of the surfaces. Then the refractive index of the material of the lens is