$A$ lens behaves as a converging lens in air and a diverging lens in water. The refractive index of the lens is

$A$ screen is placed $90 \, cm$ from an object. The image of the object is formed on the screen by a convex lens at two different locations separated by $20 \, cm$. If the sizes of the images formed at these positions are $6 \, cm$ and $3 \, cm$,then the height of the object is.....$cm$.

$A$ thin equiconvex lens is made of glass of refractive index $1.5$ and its focal length is $0.2 \ m$. If it acts as a concave lens of $0.5 \ m$ focal length when dipped in a liquid,the refractive index of the liquid is:

$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a concave lens of focal length $16 \, cm$ (in $, cm$)?

$A$ convex lens forms a real image of an object for its two different positions on a screen. If the height of the image in both cases is $8 \ cm$ and $2 \ cm$,then the height of the object is ........ $cm$.

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