Video: Identifying the Focal Point of a Concave Lens

Which of the points 𝐴, 𝐵, 𝐶, and 𝐷 shown in the diagram is closest to the focal point of the concave lens?

02:22

Video Transcript

Which of the points 𝐴, 𝐵, 𝐶, and 𝐷 shown in the diagram is closest to the focal point of the concave lens?

Now to answer this question, we need to know what the focal point of a concave lens actually is. So let’s imagine we’re looking through the concave lens on the right-hand side. This little eyeball drawing shows where we’re looking from. In other words, we’re looking straight along the direction that the beams are coming from.

This side of the lens is known as the image side of the lens. This is because the rays are coming from the opposite side. So any images formed would be on this side of the lens. The other side of the lens, this is because the rays that are going into the lens are coming from this side of the lens. And they could be coming from some objects.

So for a concave lens, the focal point is the following. If the beams of light entering the concave lens that is on the object’s side are parallel to each other and perpendicular to the plane of the lens, then the focal point is defined as the point at which the rays of light on the image side appear to be coming from.

This is quite a complicated description. So let’s break it down a bit. Essentially what we’re saying is that the rays that are going into the lens, that’s these ones here, have to be parallel to each other. Well, yes, they are. They’re all travelling towards the right. And they have to be perpendicular to the plane of the lens.

Well, this here is the plane of the lens. And if we were to draw the lens very simply, we wouldn’t draw these curvy parts. We’d just draw a straight line along the plane of the lens. And yes, all of these beams are perpendicular to the plane of the lens because if we put the plane of the lens here, for example, we can see that all of these angles are 90 degrees.

So we’ve satisfied all of the necessary conditions that we were talking about earlier on, which means that if we go to the other side, to the image side, and look from where we’ve drawn the little eye, then the focal point is the point from which all of the beams coming out towards us appear to be coming from.

In other words, that’s this point here. We just need to follow these beams back to where it would appear they were coming from if we were looking from where the little eye is. And they all seem to be converging on a point roughly about here. So the nearest letter to that point, which is a focal point, is 𝐵. And hence, our final answer is that 𝐵 is nearest to the focal point of the lens.

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