$A$ 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 convex lens of focal length $20 \, cm$ (in $, cm$)?

$A$ convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens material. Then its focal length will

$A$ point object $O$ is placed on the principal axis of a convex lens of focal length $20 \, cm$ at a distance of $40 \, cm$ to the left of it. The diameter of the lens is $10 \, cm$. If the eye is placed $60 \, cm$ to the right of the lens at a distance $h$ below the principal axis,then the maximum value of $h$ to see the image will be.......$cm$.

$A$ lens is made of glass having an index of refraction $1.5$. One side of the lens is flat and the other side is convex with a radius $R$. If an object is placed $60 \ cm$ towards the convex side of the lens, the image is formed at $120 \ cm$ on the other side of the lens. The value of $R$ is (in $cm$)

$A$ convex lens has a focal length of $0.3 \ m$ and a refractive index of $3/2$. Find the focal length of the lens in $m$ when it is immersed in water,which has a refractive index of $4/3$.

At what distance from a biconvex lens of focal length $F$ must an object be placed so that the distance between the object and its real image is minimal?