An object is placed at a distance of $1.50 \, m$ from a screen. $A$ convex lens is placed between them to produce a four times magnified image on the screen. The focal length of the lens is ..... $cm$.

$A$ magnifying lens has a focal length of $10 \, cm$. If an image is to be formed at a distance of $30 \, cm$ from the lens,the object should be placed at a distance of ..... $cm$.

Derive the thin lens equation.

The thickness at the centre of a plano-convex lens is $3 \, mm$ and the diameter is $6 \, cm$. If the speed of light in the material of the lens is $2 \times 10^{8} \, m/s$,the focal length of the lens is ............ $cm$.

The refractive index of a material of a plano-concave lens is $5/3$, and the radius of curvature is $0.3 \,m$. The focal length of the lens in air is (in $\,m$)

$A$ concave lens made of material of refractive index $1.6$ is immersed in a medium of refractive index $2.0$. The two surfaces of the concave lens have the same radius of curvature $0.2 \, m$. The lens will behave as a