Thin Lens Formula — Prelims Questions

An object is placed $30,\text{cm}$ from a convex lens of focal length $15,\text{cm}$. What is the position and nature of the image formed?

A concave lens has a focal length of $20,\text{cm}$. An object is placed $10,\text{cm}$ from the lens. Where is the image formed?

A convex lens forms a real image of an object at a distance of $40,\text{cm}$ from the lens. If the image is twice the size of the object, what is the focal length of the lens?

An object is placed at a distance of $F/2$ from a convex lens of focal length $F$. What is the nature of the image formed?

Two thin lenses of focal lengths $f_1 = +10,\text{cm}$ and $f_2 = -20,\text{cm}$ are placed in contact. What is the focal length of the combination?

A lens of power $+2.5,\text{D}$ is used to form an image of an object placed $40,\text{cm}$ from it. What is the image distance?