Question

How do you identify that any lens which forms an image has a positive or negative focal length?

Answer 1

Focal length

1. When parallel rays coming from infinity, undergoes refraction through the lens, they converge at a point on the principle axis.
2. In the case of a concave lens, the ray diverges, but when these diverged rays are traced back they meet at this point on the principle axis.
3. This point of intersection is called the focus of a lens.
4. Focal length is defined as the distance from the focus of the lens to the optical center of the lens.

Focal length sign convention-

1. If the image formed by a lens is formed on the other side of the lens that is on the opposite side of the object then the image will be a real image.
2. In that case, the focal length of the lens will be positive.
3. If the image formed by a lens is formed on the same side of the lens that is on the same side of an object then the image will be a virtual image.
4. In that case, the focus will be negative.
5. Convex lenses have a positive focal length and concave lenses have a negative focal length, as shown below.
6. By sign convention, positive $x$ direction is taken as positive and negative $x$ direction as negative and hence convex and concave lenses have their focal length as positive and negative respectively.