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 short-sighted 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 this lesson.

Hopefully by the end of the lesson, 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 magnification of the virtual image formed.

Some keywords that will come up this lesson are principle axis, principle 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 principle axis, which that line that goes through the middle of the lens horizontally, the principle focus, which is where parallel rays of light, rays of light parallel to the principle 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 principle 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 access to fill each gap.

Pause the video now.

Have a go at that task.

Okay, I'll give you some feedback.

The principle focus is the point where rays of light parallel to the principle axis are focused to.

The focal length is the distance between the centre of the lens and the principle focus.

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

Well done if you got all four.

Now we'll just take a moment to talk about people who are long-sighted, and we'll talk about people who are short-sighted later.

Now, people who are long-sighted or short-sighted, the condition is named after what you can see.

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

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

So people who are long-sighted 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 long-sighted 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 long-sighted eyes.

So that's the other way of thinking about long-sight and short-sight is, is the focus too long or is the focus too short? In long-sighted 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.

They'll 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 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.

Well, 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, 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're 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 too 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'll 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.

It's simply a convex lens being used in that way.

The object is within focal length of the lens, and you're looking back through the lens at 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 eye is 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 the 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 the correct reason why it's a virtual image.

The virtual rays show where the rays of light appear to have come from.

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 rays 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 at 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.

because 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 principle rays for this kind of lens.

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

So what we've got here is an 8 centimetre 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 principle rays.

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

What you can then do is you can then calculate the image magnification using our magnification equation, image height divided by the actual height.

In this case, the image height is 21 centimetres on my diagram, and the actual height is 8 centimetres.

So 21 divided by 8, the unit's cancelled giving the magnification with no units, which is basically the magnification ratio.

How many times bigger is the image than the object? In this case, 2.

6 times bigger.

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 a 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 principle axis should have been added that's refracted through the principle 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? Dash 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, so now let's do some proper scale diagrams. Now, this is designed to be done on the worksheet that accompanies this lesson, but if you don't have access to that worksheet, you can still draw this out on square paper or graph paper first, and then you can do parts one, two, and three of the task.

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

Part two, what three words describe the nature of this image? And part three, calculate the magnification of the image.

Pause the video now.

Off you go.

Right, I'll give you some feedback.

So completing the ray diagram, you should draw a ray that's parallel to the principle axis, that's refracted through the principle focus.

A ray that passes through the centre of the lens is not refracted.

Then you trace those rays back.

Where do they look like they've come from? They're the virtual rays that you've added in.

And then you should have drawn in an image and labelled it with the word image.

What three words describe the nature of the image? It's virtual image 'cause it's formed from the point where virtual rays cross, where rays of light look like they've come from, not where they've actually come from.

It's a magnified image because it's bigger than the object, and it is upright, it's not inverted.

And the magnification of this image, there's the magnification equation.

The image height, I got is 29 centimetres.

It might have come out slightly differently on your diagram, but it should be about that.

The actual height of the object to start with was 10 centimetres, giving a magnification of about 2.

9.

Now you might not get exactly those numbers, but it should be pretty close.

Well done.

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 ray diverge, which means spread apart.

The principle focus of a concave lens is a similar idea, has a slightly different definition for a concave lens.

It's the point where rays parallel to the principle 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 principle focus of this concave lens.

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

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

Now, I mentioned earlier we would come back to talk about short-sighted people.

Now's the time.

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

So remember if you're short-sighted or long-sighted, that's named after what you can see well.

So someone who's short-sighted can see objects which are close.

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

Rays from a closer 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 short-sighted 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, they're 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 short-sightedness.

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

So short-sightedness 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 is used to diverge the light a little bit, then the eye's too powerful lens in a short-sighted 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 the statement relates to long-sightedness, put an L.

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

Okay, I'll give you some feedback now.

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

Now, short and long-sight is named after what you can see.

So if you can focus on close objects, that's short-sight.

Number two, 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 short-sightedness.

Well done if you 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.

I'm short-sighted, 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 principle rays that you draw for a concave lens are slightly different to the principle rays that you draw for a convex lens.

So here we go.

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

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

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

Now 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 principle focus.

So effectively, you'll put your ruler against that whole line, and do the line from the principle 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 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.

And then the point where the virtual rays cross indicates the position of the image, or the point where all of the rays of light look like they've come from, which is here.

So that is the image.

And this can be confirmed by drawing the third principle ray for this kind of lens.

A ray that was heading to the right hand principle focus, so it was heading here, but don't draw it all the way there.

Only draw it up to the lens, because it's gonna be refracted, so it becomes parallel.

So it was heading to the right hand focus and it's become parallel.

And if you trace where that ray looks like it's come from, it should be the same point, the virtual image.

And finally, the image magnification can be calculated using our magnification equation, image height divided by actual height.

So for this example, the image height appears to be five centimetres there or thereabouts, and the actual height appears to be 15 centimetres, giving a magnification of about 0.

33.

So let's do a quick check to check that we are on the right track with getting the hang of 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 ray diagram should look like for a concave lens.

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

Then the second principle 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 principle ray, if you like.

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

It's 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.

Right, time to do a proper scale diagram now for the virtual image formed by a concave lens.

So this is designed to be done on the worksheet that accompanies this lesson, but if you've not got that worksheet, then just draw it out on square paper or graph paper, and then you can do parts one, two, and three of the task.

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

Part two, what three words describe the nature of the image that you've drawn? And part three, calculate the magnification of the image.

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

Okay, I'll give you some feedback now.

So completing the ray diagram, so a ray that's parallel to the principle axis is diverged as if it's come from that principle focus, so trace the ray back, so make sure it's come from that principle focus.

In fact, draw both those rays together when you draw them.

Then a ray goes right through the middle of the lens, is not refracted.

Everyone should have drawn that one.

That's the easiest one to do, straight through the middle of the lens, not refracted.

And actually that is enough to locate the position of the image and it should be labelled image.

Okay, and then finally the third principle ray, which you could draw just to confirm you've got everything in the right place, is a ray that is heading towards the other principle focus, the right hand principle focus.

Don't draw it all the way there 'cause it's refracted at the lens, and becomes parallel to the principle axis.

Trace it back and it should come from the same point.

And that image you found is a virtual image.

It's formed where rays of light appear to have come from.

It's diminished and it's upright.

And the magnification is found by the image height divided by the actual height.

The image height in this case appears to be about eight centimetres, or thereabouts, divided by the object height, which was 15 centimetres, the original arrow, giving you a magnification of about 0.

53 or thereabouts.

Well done if you got answers in that region.

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.