The radii of curvature of both surfaces of a convex lens of focal length $f$ and focal power $P$ are equal. One of the surfaces is made plane by grinding. The new focal length and focal power of the lens are respectively:

Inside a vessel filled with liquid, a converging lens is placed as shown in the figure. The lens has a focal length of $15 \,cm$ when in air and has a refractive index of $\frac{3}{2}$. If the liquid has a refractive index of $\frac{9}{5}$, the focal length of the lens in the liquid is (in $\,cm$)

Two objects $P$ and $Q$ are placed at $10 \ cm$ and $30 \ cm$ in front of a convex lens of focal length $20 \ cm$. The correct option for the image of $P$ and $Q$ is:

You are given two lenses,a converging lens with focal length $+10\, cm$ and a diverging lens with focal length $-20\, cm$. Which of the following would produce a virtual image that is larger than the object?

$A$ lens of focal length $f$ and diameter $d$ forms an image of intensity $I$. If the central part of the lens of diameter $\frac{d}{2}$ is covered with a paper,what will be the new focal length and the new intensity of the image?

$A$ parallel beam of white light falls on a convex lens. Images of blue,red,and green light are formed on the other side of the lens at distances $x$,$y$,and $z$ respectively from the pole of the lens. Then: