An object of height $25 \ cm$ is placed in front of a convex lens of focal length $30 \ cm$. If the height of the formed image is $50 \ cm$,then the distance between the object and the image is ..... $cm$.

$A$ plano-convex lens is made of a material with a refractive index of $1.6$. The radius of curvature of the curved surface is $60 \ cm$. The focal length of the lens is.....$cm$.

$A$ bi-concave glass lens having refractive index $1.5$ has both surfaces of same radius of curvature $R$. On immersion in a medium of refractive index $1.75$,it will behave as a

The focal lengths for violet,green,and red light rays are ${f_V}$,${f_G}$,and ${f_R}$ respectively. Which of the following is the true relationship?

When a convex lens is immersed in a liquid of refractive index equal to $80 \%$ of the refractive index of the material of the lens,the focal length of the lens increases by $100 \%$. The refractive index of the liquid is

$A$ double convex lens made of glass has both radii of curvature of magnitude $20 \,cm$. Incident light rays parallel to the axis of the lens will converge to a point at a distance $L$ from the common pole $P$. The value of $L$ is [Refractive index of glass $= 1.5$].