A combination consisting of a concave lens in contact of a convex lens of focal length $25 \mathrm{cm}$ produces a real image at a distance of $80 \mathrm{cm}$ when an object is placed at a distance of $40 \mathrm{cm}$ from the combination. Find the focal length and power of the concave lens.

Find the focal length and power of a convex lens which, when put in contact with a concave lens of focal length $25 \mathrm{cm}$ forms a real image $5$ times the size of an object placed $20 \mathrm{cm}$ from the combination.

A compound lens is formed with two lenses of powers $+15.5 \mathrm{D}$ and $-5.5 \mathrm{D}$ kept in contact. A $3 \mathrm{cm}$ long object is placed at a distance of $30 \mathrm{cm}$ from the lens. What is the length of the image?

A spherical surface of radius of curvature $R$ separates air (refractive index $1.0$) from glass (refractive index $1.5$). The centre of curvature is in the glass. A point-object P placed in air is found to have a real image $Q$ in the glass. The line $PQ$ cuts the surface at a point $O$ and $PO=OQ$. The distance $PO$ is equal to:

A thin convex lens made from crown glass $(n=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.)$ has focal Iength $f$. When it is measured in two different liquids having refractive indices $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ and $\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is:

A bi-convex lens of focal length $15 \mathrm{cm}$ is in front of a plane mirror. The distance between the lens and the mirror is $10 \mathrm{cm}$. A small object is kept at a distance of $30 \mathrm{cm}$ from the lens. The final image is:

A lens is formed by pressing mutually the plane faces of two identical plano-convex lenses, each of focal length $40 \mathrm{cm}$. It is used to obtain a real, inverted image of the same size as the object. The object is placed from the lens at a distance of: