Question

Can a concave lens form an image of size two times that of an object?
A) Yes
B) No
C) Sometimes
D) None of the above

Answer 1

A concave lens is a lens that possesses surfaces that curves inwards. It is a diverging lens that spreads out light rays that have been refracted through it. A concave lens is thinner at its center than at its edges. A concave lens always forms a virtual, erect, and diminished image between the F and 2F of the lens. Let’s see in the following steps how a concave lens forms an image.

Complete solution:
We will analyze the above situation with the help of a ray diagram. There are two cases, first, when the object is at an infinite distance from the optical center, and second when the object is at a finite distance from the optical point.
Step 1: Consider the following figure.

In this case, the object is kept far from the lens (at infinity). When the focal length is negligible in comparison to the distance between the optical point and the object then the object is considered at infinity. Now draw the rays parallel to the principal axis. Since the concave lens diverges the rays and every ray parallel to the principal axis appears to pass through the focus F1 of the lens, therefore all rays appear to meet at focus F1. Hence the virtual, erected and highly diminished image is formed at the focus. In this case, we saw that the size of the image is very smaller than the size of the object.

Step 2: Now consider the following figure-2

In this case, the object AB is kept at a finite distance (between F1 and 2F1). Similarly, draw a ray parallel to the principal axis. It appears to pass through the focus F1. We draw another ray passes through the optical center O. Now in the same way all refracted ray will meet at A’ therefore the formed image is A’B’. Here also the formed image is diminished.
In the above cases, you see that the image cannot be bigger than the object.

Hence, the option B is the correct option.

Note: Always remember that the concave lens forms a diminished image. We can also consider the magnification produced formula $m = \dfrac{{h'}}{h}$ where h is the size of the object and h’ is the size of the image. The value of $m$ for the concave lens is always less than 1. If the value of $m$ is less than 1 it implies that $h' < h$ therefore the size of the image can not be bigger than the size of the object.