A thin convex lens forms the distinct image of an object on a screen placed at a distance of $30 \mathrm{cm}$ from the lens. When the lens is displaced $5 \mathrm{cm}$ towards the screen, then in order to obtain distinct image the screen is displaced $5 \mathrm{cm}$ towards the lens. Find the focal length of the lens.

An object is placed infront a convex lens at such a distance that its real image of the same size is formed. When the object is displaced $16 \mathrm{cm}$ towards the lens, still a real image is formed but now its size is 3 times the size of the object. Calculate the focal length of the lens.

A convex lens of $20 \mathrm{cm}$ focal length is placed in contact with a concave lens of $25 \mathrm{cm}$ focal length. Find the position and nature of the image of an object placed at a distance of $2 \mathrm{m}$ from this combination.

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.