An achromatic combination is made with a lens of focal length $f$ and dispersive power $\omega$ with a lens having a dispersive power of $2\omega$. The focal length of the second lens will be:

An object of height $1.5 \ cm$ is placed on the axis of a convex lens of focal length $25 \ cm$. $A$ real image is formed at a distance of $75 \ cm$ from the lens. The size of the image will be........$cm$.

The focal length of a convex lens is $10 \ cm$ and its refractive index is $1.5$. If the radius of curvature of one surface is $7.5 \ cm$,the radius of curvature of the second surface will be......$cm$.

The radius of curvature of each surface of a convex lens having refractive index $1.8$ is $20 \ cm$. The lens is now immersed in a liquid of refractive index $1.5$. The ratio of power of the lens in air to its power in the liquid will be $x : 1$. The value of $x$ is $.....$

$A$ film projector magnifies a film onto a screen of area $100 \, cm^2$. If the linear magnification is $4$,what will be the area of the image on the screen in $cm^2$?

$A$ lens placed $10 \,cm$ away from a wall casts a sharp inverted image of a candle on it. It again casts a sharp image when the lens is moved $20 \,cm$ further away from the wall. Now,the candle and the lens are moved such that a sharp inverted image with unit magnification is formed on the wall. To achieve this configuration,the candle was moved