The focal length of a convex lens of refractive index $1.5$ is $2 \ cm$. What will be the focal length of the lens when it is immersed in a liquid of refractive index $1.25$?

$A$ concave lens (refractive index $n_l = 1.5$) has both surfaces of the same radius of curvature $R$. If it is immersed in a liquid of refractive index $n_m = 1.75$,it will act as a:

Double convex lenses are to be manufactured from a glass of refractive index $1.55$ with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be $20 \ cm$ (in $cm$)?

$A$ 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 of focal length $30 \,cm$ produces $5$ times magnified real image of an object. What is the object distance (in $\,cm$)?

An object and a screen are fixed on the uprights of an optical bench. The distance between them is $100 \, cm$. $A$ convex lens is placed in between the object and the screen and the position of the lens is so adjusted that the image of the object is formed on the screen at two conjugate positions of the lens. The distance between these conjugate positions of the lens is $40 \, cm$. What is the focal length of the lens in $cm$?