Video: Concave Lenses

In this video, we will learn how to define a concave lens, describe the paths of light rays refracted through these lenses, and explain how rays are focused by such lenses.

12:44

Video Transcript

In this video, we’re going to be discussing concave lenses. We’ll learn what it means for a lens to be concave and how it affects light passing through it. So let’s start by understanding that the word “concave” is used to refer to something that curves inward, like the inside of a circle or a sphere. Now this is a difficult thing to visualise. So let’s draw a diagram.

Let’s say that we’re looking at an object from this perspective. Let’s say this is our eye. And the object that we’re looking at is shaped like this. This shape is concave from the direction in which we’re looking at it because it curves away from us in the middle. It curves inward, and therefore it curves in the exact same way as the inside of a circle. We can see that the inside of the circle sort of curves away from us and then comes back towards us. And therefore, any shape curved in this way is known as a concave shape.

However, let’s now imagine that we take our object once again and look at it from this perspective. Let’s say this is our eyeball now. Well, in this case, what we’re seeing is that the object curves towards us and then back away from us. This is the exact opposite. This is known as a convex object. And so, in this particular case with our object, this weirdly shaped thing that we have, it is convex when viewed from this side and concave when viewed from this side. And in fact, we can say that a convex object curves exactly like the outside of a circle. So if we place our observer now anywhere outside our circle, we will see that this circle curves towards the observer and then away from the observer again. And that, therefore, is a convex object.

Now, an easy way to remember the difference between convex and concave is the following. Let’s once again come back to our weirdly shaped object over here. Now when viewed from this position, our object is concave, because we can imagine our observer walking into this object just like it’s a cave. Whereas when viewed from this position, it is convex, because they cannot walk into it like it’s a cave. So a concave object you can walk into like a cave and a convex object you cannot.

So now that we’ve looked at the definition of the word “concave,” let’s take a look at concave lenses. A concave lens, just like other lenses, is designed to very specifically manipulate the direction in which light rays passing through it will travel once they leave the lens. Now technically, this lens that we’ve drawn here should be known as a biconcave lens. The word bi- meaning two, because this lens is concave when viewed from this side if we place our eyeball here and concave when viewed from this side if we place our eyeball here.

We can see that the lens curves away from us and then back towards us on the left. And the same is true on the right. It curves away from us and then back towards us. Therefore, it’s concave on both sides, biconcave. However, quite often, we drop this prefix bi- and just call this lens a concave lens.

Now to see the effect of a concave lens on light entering it, let’s first recall that light passing from one medium to another, where this second medium has a different refractive index to the first medium, will undergo refraction. In this particular case, the light is going from air, which is what it’s initially travelling in, to glass, which is what we’ll say the lens is made out of, and then back out to the air again. In other words, we’re moving from a medium with a lower refractive index to a medium with a higher refractive index and then back out to a medium with that same lower refractive index. That is causing this particular light ray, as well as some other light rays entering the concave lens, to change direction every time they meet an air-to-glass or glass-to-air boundary. In other words, the light rays are refracting.

So to simplify things, let’s quickly recall what would happen if a light ray meets a rectangular glass block. So let’s say that this is our rectangular glass block. And on either side of it, we have air. Let’s also imagine that we send in a light ray to this glass block moving in this direction. In other words, it’s meeting the boundary between the air and the glass at some angle. We can measure this angle relative to an imaginary line that we can draw in. That’s this dotted line here, known as the normal to the boundary, where this line is the boundary between the air and the glass and the dotted line is normal to that, or at 90 degrees to that line.

So we can use that normal line to measure the angle of incidence. That’s the angle between the normal line and the direction in which the ray of light is coming into the glass block. Now as we said earlier, the air in which the ray of light is initially travelling has a lower refractive index than the glass in which it will travel momentarily. And the change in refractive index between the air and the glass causes the ray of light to bend slightly.

Specifically, going into a medium of higher refractive index, the ray of light will bend slightly towards the normal line. In other words, this angle here, the angle between the new ray of light in the glass block and the normal line, is slightly smaller than this angle here, which we said was the initial angle of incidence. And this process, this bending of light when moving into a medium of a different refractive index, is, as we’ve mentioned already, known as refraction.

And also rather importantly, when the ray of light gets to the other end of the glass block, it meets a boundary here between glass and air. So once again, we can draw a dotted line that’s normal to this boundary. And it intersects the boundary at the point at which the ray of light is meeting that boundary. And then we can say that this new angle of incidence — that’s the angle between the ray of light and the normal — is going to be different to the angle between the ray of light leaving the glass block and the normal line.

Specifically, when leaving a medium of a higher refractive index and entering one with a lower refractive index, the ray of light will bend away from the normal. And this is the information we need to know in order to understand how concave lenses work. When light enters a medium with a higher refractive index, it bends towards the normal compared to the direction it would’ve carried on going in if that glass block wasn’t there, which would’ve been this direction on our diagram. But as we can see, it’s bent towards our normal line. And equally, we can say that when leaving a medium with a higher refractive index to enter one with a lower refractive index. We can say that the ray of light which would’ve otherwise carried on going this way if the glass block extended out further has now bent away from the normal line. So with all of that in mind, let’s come back to our concave lens.

Now for our own convenience, let’s define something known as the plane of the lens. This is the imaginary plane or flat surface that goes right down the middle of the lens. We’re drawing this as a dotted line because we’re looking at it side on. But this plane does go in and out of the screen.

Additionally, let’s also define the optical axis of the lens. This is an imaginary line that goes straight through the centre point of the lens. And it also goes to the centre point of the lens whilst being perpendicular or at right angles to the plane of the lens.

Now both the plane of the lens and the optical axis will help us orientate ourselves relative to the lens itself. And this will be very helpful when we discuss rays of light coming in towards the lens. In fact, let’s do this now.

Let’s imagine that we’ve got a ray of light moving in towards our lens that is parallel to the optical axis. And let’s also zoom in to this part of the lens to work out exactly what will happen when our ray of light arrives at the boundary between the air in which it was travelling earlier and the lens itself. So here’s that same green rectangle just zoomed in. This is the air in which the ray of light was travelling in, and this is the lens.

Now the boundary at which this ray of light arrives at is angled in this direction, which means that the line normal to this boundary is this line here. We can see that it’s at 90 degrees to the boundary. And hence, the angle of incidence — that’s the angle between the ray of light and the normal line — is this angle here.

But remember, we said earlier that when a ray of light leaves a boundary with a lower refractive index and enters a boundary with a higher refractive index, it refracts towards the normal. In other words, instead of continuing on in this direction as it would have, if the glass lens wasn’t there, our ray of light will refract slightly towards the normal. And so if we come back to this diagram showing what’s happening with our ray of light going into the glass lens, we’ll see that it bends or refracts in this way. And it continues to move in this direction until it reaches the boundary between the glass block and the air once again.

So now let’s think about what happens at this boundary. At this boundary, what we have is our ray of light arriving at a boundary angled in this direction. And remember, this time, this is the glass block and this is the air. And we can even label this on both diagrams just to help us remember more clearly.

So anyway, this time, the line that’s normal to our surface is this line here, which means that the angle between our ray of light and the normal is this angle here. But then we can recall that when light goes from a material with a higher refractive index to one with a lower refractive index. Instead of carrying on in the same direction that it would have if the glass block had extended further, our ray of light will actually bend away from the normal. In other words, this angle between our ray of light leaving the glass block and entering the air and the normal line gets larger.

Therefore, coming back to our larger diagram, we can see that the ray of light now moves this way. And so this is how the two surfaces of a concave lens will refract this particular ray of light entering the concave lens parallel to the optical axis.

Now one thing that we can do is to draw lots of different rays of light moving in parallel to the optical axis going towards our concave lens. And we can see how our concave lens would refract all of these rays of light. This is what they would end up doing.

Now we can see that rays of light initially moving in this direction parallel to our optical axis all seem to spread outwards away from the optical axis as they leave the concave lens. In other words, they are said to diverge or spread out or move away from each other. And hence, for this reason, a concave lens is also sometimes known as a diverging lens.

Now there are a few interesting points to be made here. Firstly, we can see that the rays of light nearest to our optical axis are the ones refracted the least. They’re the ones closest to just carrying straight on. In other words, the final ray of light is not quite as refracted as compared to, for say, this ray of light, which would’ve otherwise carried on in this direction. And it ends up refracting quite a lot.

Now we can take this to mean the following. If we send in a ray of light along the optical axis and it goes straight through the centre of our lens, then that ray of light will not refract. It will just go straight through. However, we can approximate this to be the case for any ray of light moving through the very centre point of the lens in any direction. In other words, if we have this concave lens here and we send in a ray of light, let’s say in this direction. As long as it goes through the very centre of our lens, we can approximate it as not changing direction at all. We can imagine it just passes straight through the lens.

Now, strictly speaking, this is not 100 percent true. It does refract slightly. But we can approximate it as not refracting at all, which makes our life a lot easier when working out what happens to rays of light coming from an object placed on one side of the lens. Secondly, let’s once again look at the rays of light leaving our lens when the incoming rays were parallel to our optical axis.

If we trace these rays of light backwards, so, for example, if we take this ray of light and trace it backwards, then we can see that all of these rays appear to be emanating or coming from one particular point. This point is known as the focus of the lens, or sometimes known as the focal point of the lens. And to an observer on this side of the lens, all they can see is the rays of light leaving the lens. Therefore, to them, it looks like these rays of light are coming from the focus.

Now remember, the focus can only be found by tracing back the rays of light leaving a lens if the incoming rays of light were parallel to the optical axis. And these two points that we’ve just seen are very important to remember. Firstly, any ray of light passing through the very centre of the lens, regardless of what direction that ray of light is travelling in, can be approximated as travelling straight through the lens without being refracted.

Now, strictly speaking, this is not necessarily true. Even rays of light going through the centre of the lens will be slightly refracted except for the one particular ray of light going exactly along the optical axis through the centre of the lens. But we can approximate all rays of light going through the centre as passing straight through the lens.

And secondly, if we have lots of rays of light passing parallel to the optical axis into the lens, then the rays of light leaving the lens will all appear to be emanating from a point known as the focus of the lens, or sometimes known as the focal point of the lens.

So now that we’ve learned all of this about a concave lens, sometimes also known as a diverging lens, let’s summarise what we’ve talked about in this lesson. Firstly, we saw that the word “concave” refers to something that curves inward, like the inside of a circle or a sphere. We can imagine this as a cave to walk into, hence the word “concave.” And this little diagram here shows that when viewed from this position, an object shaped like this is indeed concave.

Secondly, we saw that a concave lens is also known as a diverging lens. Light rays entering parallel to the optical axis are refracted. So they diverge or spread out when leaving the lens. And finally, we saw that an observer on the same side as the outgoing rays from the lens. Meaning that they cannot see the rays of light on the other side of the lens. Will see the outgoing rays of light coming from what is known as the focus of the lens.

And one last point worth mentioning is that we saw that any ray of light passing straight through the centre of the concave lens can be approximated as passing straight through the lens without being refracted.

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