Lesson video

Hello and welcome to this lesson on virtual images from converging and diverging lenses.

This is from the unit called "electromagnetic waves", and my name is Mr. Norris.

So anytime you look in a mirror at a reflection, that's a virtual image, okay? Because this is the object, the actual toy, and then the image of the object appears somewhere.

Well, it appears to be about here, okay? But of course there's nothing there, that's just a virtual image of the object, and it's called a virtual image because no rays of light actually come from where the image appears to be into my eyes.

Rays of light actually, from the room, hit the object, reflect to the mirror, and then reflect into my eyes.

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

So that's why the image appears to be there.

So it turns out that converging and diverging lenses can both create this same kind of image, called a virtual image, where rays of light appear to have come from.

And in fact, I'm shortsighted.

So these are diverging lenses, and every time I look through diverging lenses, and light from the world comes through the lens and goes into my eyes, what I'm actually seeing is a virtual image of any object I look at, created by these diverging lenses in my glasses.

So in this lesson, we're gonna have a look at how all of that works.

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 converging and diverging lenses, and you'll be able to draw ray diagrams to find the position and size of the virtual images formed.

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.

In the first section, we'll look at real and virtual images formed by converging lenses.

And in the second part of the lesson we'll look at virtual images, which are formed by diverging lenses.

So diverging lenses only form virtual images.

So let's get going with the first section.

So converging lenses can produce an image on a screen, and you might have had a go at doing 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 converging lens are the principal axis, which is that horizontal line that goes through the middle of the lens.

We've got the principal focus, and that's the point where rays of light parallel to the principal axis from distant objects are 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 converging lens.

Let's do a quick check on the key part 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.

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

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

And of course that dashed line is the principal 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 shortsighted later.

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

So if you're 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 where objects are 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 or contact lenses with converging lenses.

And they are gonna provide the extra converging power needed to shorten the focus, like this.

Watch the second diagram.

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, so the image distance increases, and you can see the image size increasing there too.

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

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

So in this case, the object is a tree.

So rays of light from the top of the tree are refracted by the lens, and then meet or cross on the screen.

And then the rays of light from that point on the tree also meet or cross at the same distance, the image distance, and the same for rays of light from that part of the tree, they meet or cross also at the image distance, and the same from four rays of light from the bottom part of the tree, which are refracted by the lens, and then meet or cross at the same distance, the image distance.

So the image is then made up from all of the individual foci from each point on the object.

And all of those occur at the same distance, which is the image distance, creating a real image on the screen.

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're not seeing the object, we're seeing a magnified inverted real image of the object.

Now these, again, it's a real image because rays of light 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, ie, 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, when the object distance is smaller than the focal length, what you can do is you can look back through a converging lens, and observe a virtual image behind the lens or behind the object, like that.

And it's always upright and magnified.

And that's how a magnifying glass works.

A magnifying glass is simply a converging lens being used in that way, with the object within a focal length of the lens, behind the lens, and you look back through the lens and you see a magnified, upright virtual image.

Let's do a check of what we've just said.

So in which object positions can a virtual image of the object be seen by looking back through a converging lens? So pause the video now and choose which you think could give a virtual image.

Off you go.

Okay, I'll give you the answer now.

The only correct answer is D.

You can only get a virtual image by looking back through a converging lens, if the object distance is less than the focal length.

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

In A and B, you get a real image, because the rays cross.

And in C, there's no image because the rays end up parallel, so they never cross.

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 dashed lines which have been added, which are effectively what the eye is doing, tracing back where the rays of light appear to have come from, and 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 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 rays of light meet.

Well done if you got both of those.

This is a good point now where we can summarise all of the different kinds of image that could be formed by a converging lens with the object at different distances from that lens.

So a very large object distance, a converging lens forms a real, inverted image that's diminished.

And as the object distance decreases, so 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 is closer than twice the focal length.

And that's shown in this animation here, until we get to the focal length, because of course the object distances below the focal length, no real image forms, that's what we've just said.

A virtual, upright, and magnified image appears instead, behind the object.

And that's here.

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 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 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 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.

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 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 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 one and two of the task.

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

And then part two 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're adding.

And where they meet, that's where the image forms, it 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 formed where rays of light appear 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 got all of that right.

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

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

So diverging lenses bulge inwards.

They make light rays spread apart, like in the diagram.

Now, the principal focus for a diverging lens is a similar idea, but it's got a slightly different definition, because the lens does a different thing.

It diverges the line.

So the principal focus of a diverging lens is the point where rays parallel to the principal axis, like in this diagram, it's where they appear to have been diverged from.

So if you trace those rays back, where do they look like they've been diverged from? Here.

So that's the principal focus of this diverging lens.

And the focal length has the same definition.

It's the distance between the centre of the lens and the principal focus.

So that's the distance here.

And just a reminder of the symbol for a diverging lens, which is this symbol here.

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're shortsighted or long sighted, 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 of 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, 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 shortsightedness.

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

So shortsightedness is corrected using diverging lenses.

Instant light is spread out more, like this.

Look at the diagram.

So parallel rays of lights were refracted too much, so brought to a focus too soon.

By making the light rays more diverging, the eye's too-powerful lens can then focus it at the correct distance, which is on the retina.

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 shortsightedness, 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 diverging lenses? That's shortsightedness.

Well done if you got all three.

So, diverging lenses cannot form images on a screen.

Real images, because they don't make light rays converge.

However, you can look back through a diverging lens and observe a virtual image, just like when you're looking through a magnifying glass.

Except this time it's a diverging lens.

And that virtual image is formed from where rays of light appear to originate from.

So here is a virtual image formed by looking back through my glasses.

I'm shortsighted, so they've got concave lenses.

And the image is always upright or diminished, and between F and the lens.

So have a look at this animation.

Wherever the object is, the image is always virtual, upright, and diminished.

Now the image size and location for the virtual image formed by a diverging lens, it can also be formed by drawing a scale ray diagram.

However, be really careful, because the principal rays that you draw for diverging lenses are different to the principal rays that you draw for converging lenses.

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 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, 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 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 can 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, I draw in a virtual ray as well, and it should lead you back to the same point.

Okay, let's do a check now that we're getting the hang of how to draw these ray diagrams for diverging lenses.

So could you copy out the diagram, as it looks like now on the screen.

It doesn't need to be to scale, but it does need to be neat.

So use a ruler.

And then once you've done that, add rays and the image to show what a ray diagram should look like for a diverging lens.

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

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

So the first principal ray is parallel to the principal axis, so it should look like that.

And it's a diverging lens, so that ray gets diverged as if it's come from that principal focus.

So you can draw both of those together.

The diverge ray and the virtual ray, by using a ruler.

Make sure the virtual ray is dashed.

Then the second principal ray goes straight through the middle of the lens, and you can always draw a ray that goes straight through the middle of the lens, and is not refracted, so you can always do that one.

And actually that is enough to locate where the size and position of the image.

But you could draw the third principal ray as well, which would be going towards the right hand principal focus, but don't draw it all the way there.

Okay, you need to stop at the lens, because that ray, that was going to the right hand principal focus, becomes parallel.

And trace it back, and it should have come from the same point.

So make sure your diagram looks like that.

It's a good idea to spend a couple of moments just practising , drawing that out, just so you get the hang of these ray diagrams for diverging lenses, and how they're different to the ray diagrams for converging lenses.

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 one and two of the task.

So part one, complete the ray diagram to show the size and position of the image in this situation, and part two, what three words describe the nature of the image that you found? Pause the 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 from, that's 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 where the 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 got that.

Here's a summary of the lesson.

When rays of lights are brought to a focus, a real image forms, and 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 converging lens produce upright and magnified virtual images, whereas diverging lenses produce upright and diminished virtual images.

Converging lenses correct long sight by shortening the focus, whereas diverging lenses correct short sight by lengthening the focus.