$A$ glass concave lens is placed in a liquid in which it behaves like a convergent lens. If the refractive indices of glass and liquid with respect to air are $_a \mu_g$ and $_a \mu_l$ respectively,then

$A$ 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?

$A$ biconvex lens of radius of curvature $R$ is made up of a variable refractive index $\mu = 2[1 + \frac{|y|}{d}]$. Assume $2d << R$. $A$ point object is placed at a distance $R$ on the principal axis as shown in the figure. If the spread of the image lies over a span of $n$ meters,find the value of $n$.

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.)

$A$ screen is placed $90 \ cm$ from an object. The image is formed on the screen by a convex lens placed at two different locations separated by $20 \ cm$. The focal length of the lens is approximately equal to: (in $cm$)

$A$ plano-convex lens is made of refractive index $1.6$. The radius of curvature of the curved surface is $60 \ cm$. The focal length of the lens is $..... \ cm$.