A convex lens is used to make a magnified virtual image of an object as shown in the diagram. What is the magnification produced by the lens?
Okay, so in this question, we know that we’ve got a convex lens. And it’s used to make a magnified virtual image of an object, which is what we’ve been given in the diagram. We need to find the magnification produced by the lens.
So first of all, we know that we’ve got a convex lens. Now we can recall that convex lenses can produce both real and virtual images. And the condition for a convex lens to produce a virtual image is that the object must be less than one focal distance away from the lens.
Now the diagram actually shows us what the focal distance of the lens is. It’s from here to here, because all of the rays of light converge at the focal point. So the focal distance is how far away this focal point is from the lens. And, of course, the focal length applies on both sides of the lens, so roughly maybe about that much. Let’s say that is the focal length on the other side of the lens.
Now we can see that the smaller grey arrow, this one here, is less than one focal distance away from the lens. In other words, it’s nearer to the lens than this point here, which is the focal point of the lens on the left-hand side of the lens. So this grey arrow, therefore, must be the object. And so the large grey arrow, this one here, must be the image, more specifically the virtual image.
Now we can work out the magnification of the lens using the following equation. The magnification of the lens is given by the size of the image divided by the size of the object.
Now generally, when we draw ray diagrams, we refer to the size of the image or the object as the distance between the axis, which is this line here, and the very edge of the object or image, which for the object is here — so this distance is the size — and for the image that’s here. So we’re looking at this distance.
However, because these object and images are symmetric about the axis, in other words they go as far in this direction as they go in this direction, we can just use the lengths that we’ve been given as the sizes of the object and the image.
So we say that the magnification, which we’ll call 𝑀, is equal to the size of the image, which is equal to 20 centimeters, because remember we said that the large grey triangle is the image. And we divide this by the size of the object, which is 2.5 centimeters.
When we evaluate this fraction, we find that the magnification of the lens is eight times. Therefore, the lens magnifies an object by eight times in order to produce an image.