The radii of curvature of both the 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:

The focal lengths of a converging lens are $f_V$ and $f_R$ for violet and red light,respectively. Which of the following relations is correct?

Will the focal length of a lens for red light be more,same,or less than that for blue light?

$A$ convex lens focuses an object $20 \ cm$ from it on a screen placed $5 \ cm$ away from it. $A$ glass plate (refractive index $\mu = \frac{7}{5}$) of thickness $t = 1.4 \ cm$ is inserted between the lens and the screen. What is the new distance of the object from the lens so that its image is again focused on the screen (in $cm$)?

$A$ thin converging lens of focal length $25 \,cm$ forms a sharp image of an object on a screen placed at a distance of $75 \,cm$ from the lens. Later, the screen is moved closer to the lens by a distance of $25 \,cm$. The distance through which the object is to be shifted so that its image on the screen is sharp again is

$A$ lens forms real and virtual images of an object when the object is at $u_1$ and $u_2$ distances respectively. If the size of the virtual image is double that of the real image,then the focal length of the lens is (Take the magnification of the real image as $m$)