Which of the following statements is a correct statement about virtual images? A) A virtual image can be produced by a convex lens and by a concave lens. B) A virtual image is inverted compared to the object that it is an image of. C) A virtual image can be projected on a screen. D) A Virtual image is produced on the side of a lens opposite to the object that produces the image.
Okay, so, we’re looking at four different statements here that could potentially apply to virtual images. So, to pick which one is correct, we first need to recall what a virtual image actually is. Well, a virtual image is an image formed due to the apparent divergence of light from a point. So, what do we mean by that? Well, let’s consider how a virtual image is produced by a concave lens.
So, here is our concave lens. And here is the optical axis of the lens, which is the imaginary line that goes straight through the center of the lens and is also perpendicular to the surface that cuts the lens straight down the middle. In other words, this pink dotted line is the surface that we’re talking about, which is what the lens would be if it were completely flat. And the optical axis, the orange dotted line, is perpendicular to, or at right angles to, this surface.
Additionally, we can label the focal points of the lens, which are two points either side of the lens, the same distance away from the lens’ center. And the focal points are where light rays going into the lens or coming from that lens will converge, or at least appear to converge.
Now, let’s imagine that we place an object, let’s say we place this arrow, in front of our lens. And we’re imagining that the arrow is an actual object. Let’s say it’s an arrow made from wood. And we’re placing the base of the arrow on the optical axis. From this point, we can consider the image that is formed by the lens of the arrow-shaped object. To do this, we can first consider the light that is reflecting off, let’s say, the tip of the arrow.
And in particular, we will consider two rays of light coming from the tip of the arrow. The first one is the ray of light that’s moving parallel to the optical axis. And the second is the ray of light moving straight through the center of the lens. Now, based on the refraction of light through lenses, the ray of light traveling straight through the center of the lens continues to travel in the same direction. It does not refract. However, the ray of light that’s parallel to the optical axis will actually diverge in a concave lens. Such that if we trace the outgoing ray of light backwards, it will appear to an observer on this side of the lens to be emanating from the focus of the lens, or the focal point of the lens.
And remember, this happens because the observer on this side of the lens can only see this ray of light and this ray of light. They cannot see these two rays of light, which is what those rays of light where before going through the lens. And so, to this observer, it looks like this ray of light is actually coming from where the focus of the lens is. And then, based on this information, what the observer sees when looking through the lens is an image of our object, which looks something like this.
In other words, when the observer traces back the rays of light that they can actually see, the point at which they meet is the point at which they will see the image of the object. And in this particular case, the point at which they meet will be where the tip of the arrow is seen by the observer. And hence, if we place our object in this position on this side of the lens, then this observer will see an image which looks like this, where the image is actually smaller than the object itself and seems to be closer to the lens than the actual object is.
And it’s a virtual image because it’s formed by the apparent crossing over of light rays when those light rays are traced back through the lens. And so, that’s what we mean when we say virtual image, an image formed by an apparent divergence of light. And this light is apparently diverging from the point at which the observer seems to think those light rays will have crossed. So, now, that we know this, let’s look through options A to D, starting with option A.
Option A says that a virtual image can be produced by a convex lens and by a concave lens. Well, we’ve already seen that a virtual image can be produced by concave lens. And as it turns out, if we were to take a convex lens with its optical axis drawn in as well as its focal points. And we were to take our object and place it less than one focal length away from the lens, in other words, closer to the lens than the focal point is itself. And then, consider the two rays of light coming from the tip of the arrow. Then, what we’d see is that the first ray of light is the one that’s parallel to the optical axis, and the second ray of light is the one going straight through the center of the lens.
Now, a convex lens will take rays of light that are parallel to the optical axis and refract them so they go through the focus of the lens. Whereas the ray of light going straight through the center of the lens will once again continue to go in the same direction. And at this point, we can see that on this side of the lens, the rays of light are not going to meet because they are moving away from each other.
However, if we trace the two rays of light back through the lens, then what we will see is that they appear to cross on the left-hand side of the lens as we’ve drawn it. In other words, if there’s an observer on this side of the lens looking through the lens, then to them it will seem like the light coming through the lens originated at this point here. And hence, they will see a virtual image of our object, which will look like this.
Now, it’s worth noting that a virtual image can only be produced by a convex lens if the object itself is placed closer than the focal length to the lens itself. But the point is that convex lenses can also produce virtual images. And therefore, statement A is actually correct, which means that we might have already found the answer to our question since we’re trying to find the correct statement about virtual images. But let’s go through options B to D, just to be sure.
Option B says that a virtual image is inverted compared to the object that it is an image of. Now, when an image is inverted, it actually appears the wrong way up compared to the object itself. In other words, if our object was an upward-pointing arrow, then an inverted image would be a downward-pointing arrow. However, as we’ve seen in both cases for the concave and for the convex lens, the images we’ve produced are both the right way up. Therefore, it is not true that a virtual image is inverted, because in both cases we’ve seen that’s not correct. And hence option B is not the answer we’re looking for.
Moving on to Option C then, this one says that a virtual image can projected on a screen. Well, as we’ve said already, in both cases, the virtual images are seen by an observer who is looking through the lens. However, because both of these images are only formed due to the apparent meeting of the light rays when we trace them backward. This means that placing a screen at these positions — so let’s say we took a screen and we put one here and we put one here — would do nothing at all. Because light rays aren’t actually meeting at that point for there to be an image produced on the screen.
A real image, on the other hand, is a very different story because those are formed because light rays actually meet to produce those images. And hence, if we put a screen in the position of a real image, we would see that onscreen. However, this is not true for virtual images, which means we can move on to option D.
Option D says that a virtual image is produced on the side of the lens opposite to the object that produces the image. In other words, what this statement is saying is that if we place an object on this side of the lens, then the virtual image will be produced on the opposite side. So, for example, if we place an object on the left, then the virtual image is produced on the right. But once again, in both cases that we’ve seen so far, the virtual image is placed on the same side as the object.
And that’s true for the convex lens as well. The object and the image are on the same side. And so, we can rule out option D as the answer to our question as well. So, at this point, we can say that the correct statement about virtual images out of the four given is that a virtual image can be produced by a convex lens and by a concave lens.