The diameter of a plano-convex lens is $6 \, cm$ and its thickness at the centre is $3 \, mm$. If the speed of light in the material of the lens is $2 \times 10^8 \, m/s$,the focal length of the lens is.......$cm$.

Find the velocity of the image of the given object in $cm/sec$.

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

If the aperture of a lens is halved,then the image will be:

$A$ convex lens $T$ is used to form an image whose size is one-fourth that of the size of the object. Then the object distance is (in $f$)

$A$ plano-convex lens having a radius of curvature of the first surface $2 \ cm$ exhibits a focal length of $f_1$ in air. Another plano-convex lens with a first surface radius of curvature $3 \ cm$ has a focal length of $f_2$ when it is immersed in a liquid of refractive index $1.2$. If both lenses are made of the same glass of refractive index $1.5$,the ratio of $f_1$ and $f_2$ will be: