The relation between $n_1$ and $n_2$,if the behavior of light rays is as shown in the figure,is:

$A$ 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 $f$)

The dispersive powers of crown and flint glasses are $0.02$ and $0.04$ respectively. In an achromatic combination of lenses,the focal length of the flint glass lens is $40 \ cm$. The focal length of the crown glass lens will be $....... \ cm$.

The power (in diopters) of an equiconvex lens with radii of curvature of $10 \ cm$ and refractive index of $1.6$ is

The radii of curvature for a thin convex lens are $10 \ cm$ and $15 \ cm$ respectively. The focal length of the lens is $12 \ cm$. The refractive index of the lens material is:

$A$ thin lens made of glass (refractive index $= 1.5$) of focal length $f = 16 \; cm$ is immersed in a liquid of refractive index $1.42$. If its focal length in liquid is $f_{l}$,then the ratio $f_{l} / f$ is closest to the integer: