A thin convex lens of focal length $20 \mathrm{cm}$ is kept in coaxial contact with another thin lens so that the combination becomes a converging lens of focal length $100 \mathrm{cm}$. What is the focal length of the second lens?

A convex lens of focal length $30 \mathrm{cm}$ is placed in contact with a concave lens of focal length $20 \mathrm{cm}$. Find the focal length and power of the combination. Is the combination converging or diverging?

Lenses of powers $+3 \mathrm{D}$ and $-5 \mathrm{D}$ are combined to form a compound lens. An object is placed at a distance of $50 \mathrm{cm}$ from this lens. Calculate the position of its image.

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?

Parallel rays of sun fall upon a concave lens of $10 \mathrm{cm}$ focal length. At a distance of $20 \mathrm{cm}$ from this lens, a convex lens of $15 \mathrm{cm}$ focal length is placed. Where should the screen be placed to get the image of the sun?

A point-object is situated at the centre of a solid glass sphere of radius $6 \mathrm{cm}$ and refractive index $1.5$. The distance of its virtual image from the surface of the sphere is:

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: