The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is $40\,cm$. The area of the image is $9$ times that of the square. The focal length of the lens is........$cm$.

$A$ convex lens of refractive index $1.5$ has power $3D$. It is placed in a liquid of refractive index $2$. The new power of the lens is (in $D$)

Parallel rays are incident on a thick plano-convex lens having radius of curvature $R$,refractive index $\mu$ and thickness $t$. When rays are incident on the plane surface,they converge at a distance $x$ from the plane surface. When rays are incident on the curved surface,they converge at a distance $y$ from the curved surface. Then:

If the focal length of a double convex lens for red light is $f_R$,what is its focal length for violet light?

$A$ concave lens (refractive index $n_l = 1.5$) has both surfaces of the same radius of curvature $R$. If it is immersed in a liquid of refractive index $n_m = 1.75$,it will act as a:

$A$ 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 $..... \ cm$.