$A$ magnifying glass is to be used at a fixed object distance of $1 \text{ inch}$. If it is to produce an erect image magnified $5$ times,its focal length should be ........ $\text{inch}$.

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.)

$A$ luminous object is separated from a screen by a distance $d$. $A$ convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

$A$ lens is made of flint glass (refractive index $= 1.5$). When the lens is immersed in a liquid of refractive index $1.25$,the focal length

$A$ thin convex lens is made of a material of refractive index $1.6$. An object is kept at a distance of $u$ from the lens on the principal axis as shown in the figure. The radii of curvature of the surfaces are $10 \, cm$ and $5 \, cm$. Now,the lens is reversed such that the face having radius of curvature $5 \, cm$ lies close to the object. The difference in image position as obtained for both the cases is equal to ......$u$.

An object of size $3.0 \, cm$ is placed $14 \, cm$ in front of a concave lens of focal length $21 \, cm$. Describe the image produced by the lens. What happens if the object is moved further away from the lens?