Two thin lenses, one convex and the other concave of focal lengths $15 \mathrm{cm}$ and $20 \mathrm{cm}$ respectively, are put in contact. Find the focal length of the doublet lens.

A thin converging lens of focal length $15 \mathrm{cm}$ is kept in contact with a thin diverging lens of focal length $20 \mathrm{cm}$. Find the focal length of this combination.

Two thin lenses of focal lengths $15 \mathrm{cm}$ and $30 \mathrm{cm}$ are placed in contact. What is the power of the system?

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?