$A$ double convex lens of focal length $20 \ cm$ is made of glass of refractive index $3/2$. When placed completely in water $(_{a}\mu_{w} = 4/3)$,its focal length will be.....$cm$.

$A$ lens of refractive index $n$ is placed in a liquid of refractive index $n'$. If the focal length of the lens in air is $f$,what will be its focal length in the liquid?

$A$ point object is placed on the axis of a thin convex lens of focal length $0.05 \ m$ at a distance of $0.2 \ m$ from the lens and its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of $A \ cm,$ then what is the amplitude of oscillation of the image? [You may assume $\frac{1}{1+x} \approx 1-x,$ where $x << 1$]

The power of a biconvex lens is $1.25\,m^{-1}$ in a particular medium. The refractive index of the lens is $1.5$ and the radii of curvature are $20\,cm$ and $40\,cm$ respectively. Find the refractive index of the surrounding medium.

$A$ thin convex lens of focal length $f$ made of crown glass is immersed in a liquid of refractive index $\mu_l$ $(\mu_l > \mu_c)$, where $\mu_c$ is the refractive index of the crown glass. The convex lens now acts as:

The radii of curvature of a double convex lens are $4 \ cm$ and $8 \ cm$. If the refractive index of the material of the lens is $1.5$,the focal length of the lens is nearly (in $cm$)