Lesson video

Hello and welcome to this lesson on virtual images from convex and concave lenses.

This is from the unit called Electromagnetic Waves, and my name's Mr. Norris.

So anytime you look in a mirror, a reflection is an example of a virtual image.

This is the object and the image of the object in the mirror appears somewhere over there about here, that's where the image appeared to be.

But of course, there is no object there and no rays of light actually come from here where the image appeared to be into my eyes.

What rays of light are actually doing is from the room reflecting off the frog, hitting the mirror, and then reflecting into my eyes.

And my eyes trace back where those rays appear to have come from, which is here.

And that's why the reflection appears to be here, when in fact, of course there's no object there, that's just the virtual image.

So lenses form virtual images like that as well.

And in this lesson we're gonna look at how that works.

In fact, I'm shortsighted and these are concave lenses.

So anytime I look through concave lenses at the world around me, what I'm actually seeing is a virtual image of all of those objects that I'm looking at.

So let's look at how that works.

How do convex and concave lenses form these virtual images? Here's the outcome of today's lesson.

By the end of the lesson, hopefully you'll be able to describe the formation of virtual images by convex and concave lenses, and you'll be able to draw ray diagrams to find the position and size of a virtual image.

Some keywords that will come up this lesson are principal axis, principal focus, real image, virtual image, and virtual ray.

And each word will be explained as it comes up in the lesson.

The lesson is divided into two parts.

We'll firstly look at real and virtual images formed by convex lenses, and then we'll look at the virtual images formed by concave lenses, 'cause they only form virtual images.

Let's get going with the first section.

So convex lenses can produce an image on a screen and you might have had an opportunity to do that yourself.

Now the image can be far from the lens and magnified like in a projector, like in that diagram, or the image could be close to the lens and diminished like in a camera.

And that all depends on the object, distance and the power of the lens.

The key features of a convex lens are the principal axis, which that line that goes through the middle of the lens horizontally.

The principal focus, which is where parallel rays of light, rays of light parallel to the principal axis from distant objects, that's where they're focused to.

And then you've got the focal length of the lens, which is the distance between the centre of the lens and the principal focus.

And of course, this symbol can be used to represent a convex lens.

Let's do a quick check on the key parts of the lens.

Use only the words focus or axis to fill each gap.

Pause the video now, have a go at that task.

Okay, I'll give you some feedback.

It's the principal focus is the point where rays of light parallel to the principal axis.

Our focus to the focal length is the distance between the centre of the lens and the principal focus.

And of course, that dash line is the principal axis.

Well done if you've got all four.

Now we'll just take a moment to talk about people who are longsighted and we'll talk about people who are shortsighted later.

Now, people who are longsighted or shortsighted that the condition is named after what you can see.

So if you are longsighted, you can see long-distance, but struggle with shorter distance, closer objects like a book.

So the diagram shows rays from distant objects where objects are a long way away being successfully focused onto the retina.

So people who are longsighted can do that fine, but the light from a closer object is more diverging.

So have a look at that second diagram.

And the lens of a longsighted eye can't increase in power enough to converge those more diverging rays onto the retina.

So in other words, when the object distance is short, the focus or image distance is too long in longsighted eyes.

So that's the other way of thinking about long sight and short sight is the focus too long or is the focus too short.

In longsighted eyes, the focus is too long from objects which are too close or close to the eye.

So long-sightedness is corrected using glasses with convex lenses like this, that provide the extra converging power needed to shorten the focus.

So to produce a sharp image, the screen or retina must be exactly at the right distance from the lens called the image distance.

And we know that the shorter the object distance, so the closer the object is to the lens, then the greater the image distance and the image size will be.

And that happens until the distance reaches the focal length or closer.

So that's shown in this animation, but as the object gets closer to the lens, the image gets further from the end, so the lens, the image distance increases and you can see the image size increasing there too.

So an image formed on a screen by a convex lens is an example of a real image.

What does that mean? What it means is it's the kind of image that occurs when rays of light from each point on the object meet or cross, forming a focus.

So from, in this case the object is a tree.

Rays of light from the top of the tree meet or cross at a point on the screen forming a focus.

And the same for rays of light.

From this point on the object, they meet at a different point on the screen and rays of light, actually meet somewhere which is on the screen at the image distance and rays of light from the bottom of the tree also meet at the same distance, the image distance.

So the image is made up from all of those individual foci from each point on the object, which all occur at the same distance, which is the image distance.

That's how an image is built up.

So when a real image is seen, rays of light actually come from the image into your eyes, because they might reflect off the screen and go into your eyes.

But you could also see a real image actually without a screen, and we'll come onto that now.

So we've said that real images can appear on a screen, however they can also be observed without a screen.

I'm gonna show you two examples of that now.

Now it might be best to start with looking at this diagram, so the diagram shows the viewpoints when you're looking back through a convex lens towards the object, but you don't actually see the object as it is, you see in this case a diminished, inverted real image of the object.

So when you're looking back through the lens, we're seeing the image not the object.

And it's the same in this situation.

We've just changed the object distance here.

So the object, that sheet of paper is closer to the lens.

So when we are looking back through the lens at the object, we've not seen the object, we're seeing a magnified inverted real image of the object.

Now these, again, it's a real image, because rays of lights are actually coming from the image into your eyes in both cases.

So let's do a check of that, which are correct reasons why this is a real image.

Pause the video and decide, tick as many as you think are correct reasons why this is a real image.

Okay, I'll give you some feedback now.

So a, the image could be formed on a screen.

Well, that image could be formed on a screen and that's one of the reasons why it's a real image.

Real images can be formed on a screen.

b, the image is formed by rays of light crossing.

That's true, and it's a reason why this is a real image.

Real images are formed by rays of light crossing.

That's why they can be formed on a screen.

And then c, when the image is seen, rays of light pass from the image to your eye.

And that's true and it's a reason why it's a real image.

So real images have all of these properties, they can be formed on a screen, they're formed by rays of light crossing.

And when you see the image, rays of light actually come from the image to your eye.

Now when the object is too close to the lens, i.

e.

at the focal length or closer, a real image does not form.

And that's because when objects are too close to the lens, the rays are type II diverging and the lens can't refract the rays enough to make them converge and form a focus, a real image.

The rays leave the lens parallel if the object's at the focal length.

So that's here when the rays are parallel, or the rays leave the lens diverging, so they're never cross and form an image if the object is too close to the lens.

However, what can happen when the object distance is smaller than the focal length is you can look back through the convex lens and observe a virtual image behind the lens or behind the object here.

And it's always upright and magnified.

And that's how a magnifying glass works, is simply a convex lens being used in that way.

The object is within a focal length of the lens and you're looking back through the lens of the object.

But what you actually see is a virtual image of the object.

Let's do a check in which object positions can a virtual image of the object be seen by looking back through a convex lens? Pause the video and choose what you think are the correct option or options.

Okay, I'll tell you the answer.

Now, the only correct answer is d, you only get a virtual image looking back through a convex lens, if the object distance is smaller than the focal length.

So if the object is very close to the lens within one focal length.

In a and b, the object distance is longer and the lens will refract the rays to form a real image, so the rays cross.

In c, the rays are refracted so they never cross, so they never form any kind of image.

You only get a virtual image with a convex lens when the object distance is less than the focal length and you have to look back through the lens to see it.

Well done if you got that right.

Let's make sure we understand how virtual images are created.

It's all because your eye can't actually detect that the rays change direction at the lens.

So what your eyes effectively doing is tracing back where rays of light appear to have come from like this.

Look where the rays of light that reach your eye appear to have come from.

Those dash lines which have been added, which are effectively what the eye's doing, tracing back where the rays of light appear to have come from, they're called virtual rays.

So they're not actual rays of light, they're just lines which have been added to show where rays of light look like they've come from.

And a virtual image will form where the rays of light appear to have come from, the point where the virtual rays meet.

And you can see that in the diagram.

Now virtual images can't form on a screen, because if you put a screen where the image appears to be coming from, there's no light rays there.

No light rays actually come from the image and go into your eye, the light rays are coming from somewhere else.

So that's why a virtual image can't be projected on a screen with a virtual image, light rays only appear to have come from the image, they haven't actually come from the image into your eyes.

So let's do a quick check of that, which are correct reasons why this is a virtual image? Pause video now and choose which ones you think.

Okay, I'll give you some feedback now.

a, the image could be formed on a screen.

Well, that's not true because this is a virtual image and virtual images cannot be formed on a screen.

So hopefully you didn't choose a.

b, the image is formed by virtual rays crossing.

That is a correct reason why it's a virtual image.

The virtual rays show where the rays of light appear to have come from, but they've actually come from somewhere else.

So that is a property of virtual images.

And c, rays of light only seem to be originating from the image.

No real rays of light actually pass from the image to your eye.

Yes, that's a reason why it's a virtual image as well.

So virtual images can't be formed on a screen, because they're formed by rays of light, appear to have come from not where they've actually come from.

They're formed at the positions where the virtual rays meet, not where actual ray of light meet.

Well done if you've got both of those.

So this is actually a good point to do a bit of a summary of all of the different kinds of image that can be produced by a convex lens with the object to different distances from the lens.

So at a large object distance, a convex lens forms a real and inverted image that's diminished.

And then as the object distance decreases and the object gets closer to the lens, both the image distance and the image size increase and the image becomes magnified when the object distance becomes smaller than twice the focal length.

And that's shown in this diagram here, up to the this point up to the focal length, 'cause at object distance below the focal length, no real image forms a virtual upright and magnified image appears instead behind the image.

So closer than the focal length, there's that magnified upright virtual image.

Okay, let's draw some ray diagrams then to work out the location and size of a virtual image.

So what you do is you draw the first and second principal rays for this kind of lens.

You can't draw the third principal ray for this kind of lens, so we don't include it.

So what we've got here is an eight-centimeter high object that's 10 centimetres from a lens with a focal length of 15 centimetres.

So the object is within the focal length of the lens.

It's gonna act like a magnifying glass and produce that magnified upright virtual image behind the object.

So this is how we can work out the exact size and distance of that image.

We draw our principal rays.

So a ray that's parallel to the principal axis, that's this one, that's gonna be refracted through the principal focus.

So this is exactly the same rules as we've done previously for this kind of lens.

A ray incident on the centre of the lens is not refracted, and then we can't draw the third ray.

So what we've got to do now is trace where those rays look like they've come from.

So add in the virtual rays as dash lines for that ray, where does that ray look like it's come from? And where does this ray look like it's come from? And where they meet, that's where the virtual image forms, and you should label it with the word image, just so it's clear in your diagram? Right, what we should do now then is, let's just get the hang of what these ray diagrams for magnifying glasses or this kind of lens, but with the object within the focal length, what do these diagrams look like? Let's get the hang of drawing them.

So make a quick copy of this diagram.

It should still be neat, but it doesn't have to be to scale, 'cause this is just about getting the hang of it.

And then add the rays and the image just so you have a few practises of drawing the rays and the image before we do these proper scale diagrams in a moment.

So firstly, make a copy of what's on the screen, then add the rays and the image to show what our ray diagram should look like for a magnifying glass.

Pause the video now, off you go.

Right, I'll just remind you what this should look like.

So a ray parallel to the principal axis should have been added that's refracted through the principal focus and then a ray through the middle of the lens isn't refracted so it should look like that.

And then you trace the rays back, where do they look like they've come from.

Dashed lines, these are virtual rays.

And then you draw in an image which should be magnified and upright.

Well done if yours looks like that.

Right, time to do a proper scaled version of these ray diagrams then.

So this is designed to be done on the sheet that accompanies this lesson where this diagram is printed for you.

But if you don't have access to that, you should copy this diagram first onto graph paper or square paper, and then you can do parts 1 and 2 of the task.

So part 1 is to complete the ray diagram to show the size and position of the image.

And then part 2 is to give me three words that describe the nature of the image that is created in this situation.

So pause the video now and have a good go at that task.

Okay, I'll give you some feedback now.

So the ray diagram should look like this.

A ray that's parallel to the principal axis is refracted through the principal focus and a ray that passes through the middle of the lens is not refracted.

And then you trace those rays back with dashed lines, 'cause these are the virtual rays that you are adding.

And where they meet, that's where the image forms, should be an arrow that's labelled image.

So it should look like that.

And then what three words describe the nature of this image? Well, it's a virtual image, 'cause it's form where rays of light appears to come from where the virtual rays cross, not where rays of light actually come from.

It's a magnified image, because it's bigger than the object to start with and it's upright.

Well done if you've got all of that right.

So that takes us to the second part of the lesson.

We now need to look at how concave lenses form virtual images in a very similar way.

So concave lenses fold inwards, they make light rays diverge, which means spread apart.

The principal focus of a concave lens is a similar idea.

It has a slightly different definition for a concave lens.

It's the point where rays parallel to the principal axis, like in this diagram, appear to have been diverged from.

So where do these rays appear to have been diverged from? They appear to have been diverged from here.

So that is the principal focus of this concave lens.

And again, we've got focal length, which is the distance between the centre of the lens and the principal focus.

And there's a reminder of the symbol for a concave lens.

Now I mentioned earlier we would come back to talk about shortsighted people.

Now's the time.

So someone who's shortsighted like me, they can focus on closer objects, but not distant objects.

So remember, if you are shortsighted or longsighted, that's named after what you can see well.

So someone who's shortsighted can see objects which are close.

So the rays from closer object are diverging and the lens power can, if people who are shortsighted can increase enough to bring these to a focus on the retina, like in that top diagram.

Rays from a close object can be successfully brought to a focus on the back of the eye, the retina.

However, the lens power can't decrease enough in a shortsighted person to focus rays from distant objects which are parallel, like in this diagram.

The focus or the image distance is too short.

So although the rays still hit the retina and not brought to a focus on the retina, which is what they need to be to get a clear image.

So that's the other way of thinking about shortsightedness.

The focus is too short from objects which are very far away.

So shortsightedness is corrected with concave lenses.

Instant light is made more diverging like this.

So parallel rays of light were refracted too much and brought to a focus too soon.

So if a concave lens used to diverge the light a little bit, then the eye's too powerful lens in a shortsighted person can then focus the light successfully on the retina at a longer distance.

Let's do a check about short sight and long sight.

So put an S or an L by each statement to identify if it relates to short-sightedness, put an S, or if it the statement relates to long-sightedness person L.

Pause the video now read each statement and decide S or L.

Okay, I'll give you some feedback now.

Statement 1, a person can focus on close objects, but they can't focus on distant objects.

Now short and long-sightedness is named after what you can see, so if you can focus on close objects, that's short sight.

Number 2, when the object distance is short, the image distance is too long, or if the image distance is too long, that's long sight.

And which one is corrected using concave lenses? That's shortsightedness.

Well done if you've got all three.

So concave lenses cannot form images on a screen, real images, because they don't make light rays converge.

However, you can look back through a concave lens just like looking through a magnifying glass, except this is with a concave lens, and observe a virtual image formed by where rays of lights appear to originate from.

So here's a virtual image seen looking through my glasses.

So I'm shortsighted, so they're concave lenses in those glasses.

And the image is always upright, diminished, and between the focal length and the lens.

So have a look at this animation.

Wherever the object distance is, the image distance is always between f and the lens, it's always upright and diminished.

Now for a concave lens, the image size and location can be found by drawing a scale ray diagram, just like for a convex lens.

But be really careful, because the principal rays that you draw for a concave lens are slightly different to the principal rays that you draw for a convex lens.

So here we go.

A 15-centimeter high object is 26 centimetres from this kind of lens, of focal length 16 centimetres.

So the first principal ray that you draw for this kind of lens is as follows.

For a ray that's parallel to the principal axis, so go from the top of the arrow again, and parallel to the principal axis and where will that be refracted? Well, it's a diverging lens and it's a parallel ray, so it's refracted as if it originated from the left-hand principal focus, because that's the definition of principal focus from this kind of ray.

Now that to get that angle right from that, what you'll need to do is get your ruler and put your ruler between the point where the parallel ray hits the lens and that principal focus.

So effectively, you'll put your ruler against that whole line and do the line from the principal focus to the lens as dashed, 'cause that's the virtual ray tracing back where the actual light ray looks like it's come from.

Secondly, a ray incident on the centre of the lens is not refracted.

So straight through the middle of the lens, no refraction.

Now that's the same as for the the other kind of lens.

So that's easy to remember that one.

If in doubt, always put a ray from the top of the arrow straight through the centre of the lens, so it's not refracted, because that works for both kinds of lens.

So the point where the virtual rays cross indicates the position of the image, the point where all of the light rays appear to have come from, which is here.

So you can draw in the image up to that point.

And this could be confirmed by drawing the third principal ray, a ray that was heading to the right-hand principal focus, so that's here, but don't draw it all the way there, because it needs to be refracted by the lens, so it becomes parallel.

And where that ray appears to have come from, drawing a virtual ray as well, and it should lead you back to the same point.

So let's do a quick check to check that we are on the right track with getting the hang off what these diagrams should look like.

So the first thing to do is do a copy of this diagram.

It needs to be neat, so use a ruler, but it doesn't need to be to scale, 'cause this is just practise to get the hang of what these diagrams look like.

Once you've made a copy of this diagram, add the rays and the image to show what a rare diagram should look like for a concave lens.

Pause video now and have a go at that.

Right, I'll give you some feedback now about what this diagram should look like.

The first principal ray is parallel to the principal axis and that gets refracted as if it's come from the principal focus on the left of the lens.

Then the second principal ray goes straight through the middle of the lens without being refracted and that is enough to give the image, but you could draw in the third principal ray if you like.

And that would go towards the right-hand principal focus, so in that direction, but don't draw it all the way there, 'cause it gets refracted parallel to the principal axis and trace it back and it should come from the same point.

A really good idea to practise drawing that out a few times now, because you need to get it clear in your head what ray diagrams look like for this kind of lens compared to the other kind of lens.

Okay, time to do a proper task now for a scale ray diagram for this kind of lens.

This is designed to be done on the worksheet that goes with this lesson.

But if you don't have access to that, what you'll need to do first is draw out the diagram on square paper or graph paper and then you can do parts 1 and 2 of the task.

So part 1, complete the ray diagram to show the size and position of the image in this situation.

And part 2, what three words describe the nature of the image that you found? Pause video now and have a good go at that task.

Right, I'm gonna give some feedback now.

So completing the ray diagram, you should have drawn a ray as parallel to the principal axis, and that is diverged as if it's come from that left-hand principal focus.

So you should probably draw both those rays together.

Draw the virtual ray dashed and the actual ray solid.

The second principal ray goes straight through the middle of the lens and everyone should have done that one, 'cause it's the easiest one straight through the middle of the lens.

And that is actually enough to locate whether image is, if everything's been done correctly should be labelled image.

But the third principal ray, which you could draw to confirm that you've got this right is a ray that was going to the right-hand principal focus.

But don't draw it all the way, 'cause it's refracted at the lens, so it becomes parallel to the principal axis and trace it back and it should have come from the same point.

And what three words describe that image that you found? Well, it is a virtual image that's formed by where rays of light appear to have come from.

It's a diminished image and it's upright.

Well done if you've got that.

Here's a summary of the lesson.

When rays of light are brought to a focus, a real image forms, a real image can be projected onto a screen.

Virtual images occur at points where rays appear to, but do not actually originate from.

They cannot form on a screen.

The size and position of a virtual image is found by drawing virtual rays to find where rays appear to originate from.

Objects within a focal length of a convex lens, produce upright, magnified virtual images, whereas concave lenses produce upright and diminished virtual images.

Convex lenses correct long sight by shortening the focus and concave lenses correct short sight by lengthening the focus.