Which of the following types of images can be formed by the convex mirror shown? (I) Real image, larger than the object. (II) Real image, smaller than the object. (III) Virtual image. Our answer options are (a) III only, (b) I only, (c) I and II only, (d) I and III only, (e) I, II, and III.
Okay, starting out, let’s take a look at this convex mirror in the diagram. We see this mirror. And we’re told the front surface of the mirror faces left. So that means any objects that we would put in front of the mirror would be on this side of it. Now, mirrors form images. And we want to figure out which of these three types this convex mirror forms. To begin figuring this out, we can sketch in what’s called an optical axis on our diagram. This is a line that goes right through the center of our optical element, be it a lens or, in this case, a mirror.
Now, let’s put an object that we want our mirror to image on this optical axis. Let’s say that we put it right here. Now, the way we’ll figure out what type of image this mirror forms is we’ll trace rays coming from the very tip of our object here that reach the mirror and then will reflect off of it. When we trace enough of these rays, we’ll get a sense for what kind of images this mirror can form. Let’s start out with a ray of light known as a principal ray, coming from our object and moving parallel to the optical axis. This ray would travel like this and then run into the mirror surface. And because this surface is a mirror, we know this incoming ray will be reflected back. According to the law of reflection, it will be reflected in an angle equal to its angle of incidence.
Now, let’s draw another principal ray coming from our object. This one will go right towards the center of our mirror. That ray will look like this. And once again, we know our mirror will reflect it back. That reflected ray will appear something like this. Now, let’s draw in one more principal ray coming from our object. This one will be aimed in such a way that when our mirror reflects it, the reflected ray will travel parallel to our optical axis. So now we’ve drawn these three rays coming from our object. Here is the first one, here is the second one, and this is the third one.
From looking at the directions that these rays are headed, we can tell that no matter how far we move to the left of our mirror, they will never intersect. They’ll never cross one another. We know, though, that in order for an image to be formed, these rays must cross. They must meet at a focal point. What we’re seeing though is that if we start at the surface of our mirror and we go to the left, no matter how far we go, these rays will never cross. Meaning that they’ll never form an image on this side of the mirror.
However, let’s look at what happens if we trace these three reflected rays back to the right side of the mirror. If we trace the dashed pink ray back, that would look like this on the back side of the mirror. And then, if we trace along the dashed blue reflected ray, that would look like this. And lastly, tracing the green reflected ray back behind the mirror would look a bit like this. And look at what we have now, a focal point for these three intersecting imaginary rays. This means that an image of our object would form, but it would form on the back side of the mirror. And it would look something like this.
Now, the object that we’re forming an image of is a real object. It exists in real three-dimensional space. And if this mirror had formed an image of our real object, on the left side of the mirror, then that image would’ve been real as well. That is, it would be an image that we could project on a screen if we wanted to. But what we’re seeing is that no image forms on this side of the mirror. In other words, no real images are created. And we can see that the fact that no real images are formed has nothing to do with the exact position of our object. If we moved our object closer to the mirror or moved it farther away, these three reflected rays would still not meet. And therefore, no real image would form.
However, looking behind the back surface of the mirror, we see that an image does indeed form. It only does so if we take these imaginary or virtual lines and see where they intersect, which tells us that the image that is formed in this case is a virtual image. So when we get back to options (I), (II), and (III), for which of these types of images can be formed by the mirror, since no real images can be formed by this mirror, we’ll cross out (I) and (II). But we do see evidence that a virtual image is formed.
Taking this information to our answer options (a) through (e), we see that it’s answer choice (a) which identifies that only a virtual image, and not a real image, can be formed by this convex mirror.