The focal length of an equiconvex lens is $1.00 \mathrm{m}$ when it is placed under water. Calculate the focal length of the same lens in air. Take the refractive indices of water and glass as $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ and $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ respectively.

An object is placed at $0.06 \mathrm{m}$ from a convex lens of focal length $0.10 \mathrm{m}$. Find the position of the image.

A convergent beam of light passes through a diverging lens of focal length $0.2 \mathrm{m}$ and comes to a focus on the axis $0.3 \mathrm{m}$ behind the lens. Where would the beam have been focussed in the absence of the lens?

A beam of light converges to a point $P$. A concave lens of focal length $16 \mathrm{cm}$ is placed in the path of the beam at $12 \mathrm{cm}$ from $P$. At what point does the beam now converge?

A double convex lens has $10 \mathrm{cm}$ and $15 \mathrm{cm}$ as its two radii of curvature. The image of an object, placed $30 \mathrm{cm}$ from the lens, is formed at $20 \mathrm{cm}$ from the lens on the other side. Find the focal length and the refractive index of the material of the lens. What will be the focal length of the lens, if it is immersed in water of refractive index $1.33$?

An illuminated object and a screen are $90 \mathrm{cm}$ apart. Find the nature and focal length of a lens required to produce a clear image on the screen, twice the size of the object.

What can you tell about the image of a $3 \mathrm{cm}$ long object placed at a distance of $15 \mathrm{cm}$ from a lens, if the magnification is known to be $-2$?