Question Video: Recognising Concave Lenses | Nagwa Question Video: Recognising Concave Lenses | Nagwa

Question Video: Recognising Concave Lenses Science • Third Year of Preparatory School

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The image shows a box of lenses and prisms of different sizes. How many concave lenses are there in the box?

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Video Transcript

The image below shows a box of lenses and prisms of different sizes. How many concave lenses are there in the box?

In this question, we are given an image of a box that contains 11 different lenses and prisms with varying shapes and sizes. We are asked to look through this group of lenses and prisms and find out how many concave lenses are in this group.

Let’s start by recalling what exactly a concave lens is and how we can identify them. To understand the shape of a concave lens, imagine we are starting with a cylinder with the circular ends along the horizontal axis. Now, imagine that we take two spheres represented by circles in this image and overlap them with our cylinder with the edges of the circle lining up with the corners of the cylinder like shown. If we remove this overlapping material from the cylinder, we will get the shape of a concave lens.

Notice that a concave lens is thickest at the edges of the lens and thinnest in the middle of the lens. So, when we look at the objects in the box, we are looking for two attributes, curved surfaces and being thicker at the edges and thinner in the middle. With this in mind, let’s take a look at these lenses and prisms and find out how many here are concave.

Starting in the top-left corner, we have our first lens to look at. This lens is thinner along the middle and thicker on the edges with curved surfaces, which means this is a concave lens. Moving to the right, we have our second object. This one is the same thickness along the whole shape and is distinctly in the shape of an S. So this is not concave. Looking now at object three, we see that it is thinner on the edge and is made up of straight surfaces. So this is not what we want.

Starting on a new line for the fourth object, we see that it is not only shaped like a triangle, but it also has no curved surfaces, so it is not a concave lens. Object five is thinner on the edges and thicker in the middle, but it has curved surfaces, meaning that this is our first convex lens of the group. Now, object six has thicker edges, a thin middle, and the surface is curved. So everything checks out, and we have our second concave lens. Now to object seven, it is thinner on the edge and its straight edges make it a distinct diamond. So it is not what we are looking for.

Going below to the eighth object, its surfaces are curved, but they are thicker along the edge and thinner in the middle, meaning this is a convex, not concave, lens. This is the same for object nine. It is thinner on the edge and thicker in the middle, meaning it is a convex lens.

Now, moving to object 10, we can see that it is thicker on the edge and thinner in the middle. So it may at first appear to be concave, but notice that the surface is made up of straight lines. Since they are not curved, it cannot be a concave lens. Our final object, number 11, is thinner on the edge and thicker in the middle and has a curved surface, meaning this is another convex lens. And that’s all of the objects in the diagram.

So, out of these 11 lenses and prisms in the box, there are a total of two concave lenses.

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