Video Transcript
A convex lens is used to produce a virtual image, as shown in the diagram. Which of the points 𝐴, 𝐵, and 𝐶 shown in the diagram is located at a distance from the lens equal to the lens’s focal length?
Okay, so, in this question, we’ve been given a diagram that firstly consists of a convex lens. And secondly, we’ve been told that this convex lens is used to produce a virtual image. Now, in this case, we can see two purple triangles, one of which is the object, and the other is the image. And these two triangles seem to be placed along this line here, which is actually the optical axis of our convex lens.
Let’s recall that the optical axis is the imaginary line that goes straight through the middle of the lens. And it specifically passes through the middle of the lens perpendicular to the plane of the lens. Now, out of these two pink triangles here, like we’ve already said, one of them is the object and the other is the image. And we can work out which is which by realising that the rays of light that are shown in this diagram are the ones that are coming from the tip of this smaller triangle here.
Normally, when understanding how images are produced by a lens, we look at two particular rays of light coming from the object. One ray of light which is initially travelling parallel to the optical axis and the other ray of light which is passing straight through the centre of the lens. And those are the exact two rays of light drawn to be coming from the tip of this triangle here. That means that our smaller triangle is the object and this larger triangle is the image produced by the convex lens.
Additionally, we’ve been told that this image is a virtual image. Which makes sense because we can see that the image produced of the tip of this smaller triangle, that’s our object, is found by tracing backwards the two refracted rays. So, this is one of the rays because we can see that the ray coming out of the convex lens is actually going this way. And so, if we trace it backward, it seems to be coming from this point here to an observer on this side of the lens, who can only see the ray of light leaving the lens.
And actually, since this ray of light is coming out this way through the lens, the observer on the right-hand side of the lens can only see that ray of light. And so, if we trace it backward to the observer on the right of the lens, it appears as if it’s emanating from this point once again. And so, this is the point at which the two rays of light, when traced backward, seem to emanate. And we can actually recall that a virtual image is one that is found by tracing backwards rays of light that are leaving a lens.
So, we’ve clarified that this triangle is the object, and this is the image. Now, what we’ve been asked to do is to find which one of the points 𝐴, 𝐵, or 𝐶 is located at a distance from the lens equal to the lens’s focal length. In other words, point 𝐴 is located this distance from the lens, point 𝐵 is located this distance from the lens, and point 𝐶 is located this distance from the lens. So, is it point 𝐴, point 𝐵, or point 𝐶 that’s located the focal distance away from the lens? Another way to phrase this question is, which of the points 𝐴, 𝐵, or 𝐶 is the focus of the lens? And the way we can answer this question is the following.
We can recall that with a convex lens, any ray of light passing through a convex lens that is parallel to the optical axis of the lens will be refracted in such a way that it ends up passing through the focal point, which is a point that lies along the optical axis. Therefore, the ray of light that we were considering that is initially travelling parallel to the optical access before it passes through the lens is refracted so it bends in this direction and it ends up passing through point 𝐶. Hence, the answer to our question is that point 𝐶, shown in the diagram, is located at a distance from the lens equal to the lens’s focal length. We can also say that 𝐶 is the focus of the lens.
