If the focal lengths of a lens for red and violet light rays are $f_{R}$ and $f_{V}$ respectively,then which of the following is the true relationship?

The distance between an object and a screen is $100\, cm$. $A$ lens can produce a real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is $40\, cm$. If the power of the lens is close to $\left(\frac{N}{100}\right) D$ where $N$ is an integer,the value of $N$ is.......

An illuminated object and a screen are placed $90 \, cm$ apart. What is the focal length of the lens required to produce an image on the screen,twice the size of the object?.......$cm$

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........$cm$.

$A$ plane wave passes through a convex lens. The geometrical shape of the wavefront that emerges is

$A$ thin lens made of glass of refractive index $\mu_g = 1.5$ has a focal length of $12 \ cm$ in air. If it is immersed in water of refractive index $\mu_w = 4/3$,what will be its new focal length in $cm$?