A convex lens forms the image of the same size of an object placed at a distance of $20 \mathrm{cm}$. If another lens is placed in contact with the first, the image is formed at a distance of $5 \mathrm{cm}$ from the combination on the other side. What are the focal lengths of the lenses used?

The focal length of a lens is$-50 \mathrm{cm}$. What is its power?

The power of a lens is $+5 \mathrm{D}$. What is its focal length and nature?

The radius of curvature of each surface of a convex lens of refractive index $1.5$ is $40 \mathrm{cm}$. Calculate its power.

A person uses spectacles of power $-0.5 \mathrm{D}$ for distant vision. How far is the far point of the person?

A lens has a power of $+5 \mathrm{D}$ in air. What will be its power when immersed deep in water? ${}_a{n}_g=\frac{3}{2}$, ${}_a{n}_w=\frac{4}{3}$.

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.