The focal length of a lens with a refractive index of $1.5$ in air is $0.30 \ m$. When it is immersed in a liquid of refractive index $\frac{4}{3}$,its focal length in the liquid will be ...... $cm$.

In the diagram shown,the lens is moving towards the object with a velocity $V \, m/s$ and the object is also moving towards the lens with the same speed. What is the speed of the image with respect to the earth when the object is at a distance $2f$ from the lens? ($f$ is the focal length.)

Two transparent media of refractive indices $\mu_1$ and $\mu_3$ have a solid lens-shaped transparent material of refractive index $\mu_2$ between them as shown in the figures in Column $II$. $A$ ray traversing these media is also shown in the figures. In Column $I$,different relationships between $\mu_1, \mu_2$,and $\mu_3$ are given. Match them to the ray diagram shown in Column $II$.

$A$ convex lens of glass $(\mu_g = 1.45)$ has a focal length $f_a$ in air. The lens is immersed in a liquid of refractive index $(\mu_l) = 1.3$. The ratio of the $f_l / f_a$ is

$A$ thin double convex lens has radii of curvature each of magnitude $40 \; cm$ and is made of glass with refractive index $1.65$. Its focal length is nearly....... $cm$.

$A$ biconvex lens has a focal length $2/3$ times the radius of curvature of either surface. The refractive index of the material is: