Question

The figure shows an object and its image formed by a converging lens. One ray from the tip of the object to the tip of the image is shown. Which of the following options correctly describe the image?

A) Diminished
B) Enlarged
C) Inverted
D) Real
E) Virtual

Answer 1

We know that a converging lens forms an image by focusing the incident parallel light rays to a point on the optic axis of the lens. We see that the image is formed on the opposite side of the lens as the object. Think of what this would mean in terms of the physicality of the image. The image also appears to be flipped about the optic axis. Arrive at how you would describe its orientation relative to the object. Finally, we see that the image appears to be slightly scaled down in size. Use these statements to choose the appropriate options.

Complete Step-by-Step Solution:
Let us begin by understanding how a converging lens works, following which we shall define the characteristics of an image.

A converging lens, or a convex lens is the kind of lens that focuses the light rays incident on it to a point on the optical axis of the lens.

Now, the image formed by the lens varies based on the position of the incident light rays from the object. Let us look at a few terms related to image formation.

Converging lens can produce both real and virtual images. The image is said to be real if it is formed by the actual convergence of rays, whereas it is said to be virtual if it is formed by the convergence of the extensions of diverging rays. An easy way to distinguish the two is to see if the image formed is on the same side of the lens as the object or not. If it’s on the same side then the image is likely to be a virtual one, else it is a real image.

Converging lens can produce both inverted and upright images. An image is said to be inverted if it has a vertical orientation opposite to that of the object, this means that the image is upside-down compared to the object. But if it is vertically oriented in the same way as that of the object, then the image is said to be upright.

Converging lens can produce both diminished and enlarged images. An image is said to be diminished if its size is smaller than that of the object, and is said to be enlarged if it looks bigger than the object.

Now, from the figure given to us, we see that the image is formed on the other side of the lens than the object. This means that it is a real image.

We also see that the image appears to be upside down about the optic axis when compared to the object. This means that the image is inverted.

Additionally, we can make out that the image appears to be smaller in height when compared to the object. This means that the image is diminished.

Therefore, the correct options would be A. Diminished, C. Inverted and D. Real.

Note:
We can summarize the image formation of a converging lens for a fact that it forms both real (inverted) and virtual (erect) images. Also, it is a common mistake to interchangeably use the terms enlarged and magnified. Note that enlarged means that the image is bigger relative to the object, whereas magnified can imply either an enlarged image or a diminished image. This is usually defined as magnification and is quantitatively expressed as:
$Magnification\; M = \dfrac{Image\;height}{Object\;height}$.
If $M <1$ then the image is diminished, and if $M>1$ then the object is enlarged. If $M=1$ it means there is no magnification and the image is the same size as that of the object.