Hello and welcome to this lesson on convex or converging lenses.

This is from the unit called "Electromagnetic Waves".

My name is Mr. Norris.

Now, I'm sure you'll be familiar with lenses from lots of different applications, especially, something like a magnifying glass.

So if I pop a magnifying glass up here, we can see it makes a lovely magnified image of what's on the paper.

But you might be less familiar with a magnifying glass creating an image like this.

Now, what's happened there, to our person? So the magnifying glass has now distorted that image in a different way.

And so, there are different kinds of lenses, which can create different kinds of images in different conditions.

And these lenses are different.

Again, if I hold this up to my drawing, something like there, you can see it produces a different image again.

It actually has the opposite effect of the magnifying glass.

So lenses are very, very important.

They help people see.

And they've got lots of other important applications too in cameras, on smartphone cameras.

So let's look at how lenses work.

The outcome of this lesson is that, hopefully, by the end of the lesson, you'll be able to use a convex lens to form an image on a screen and describe how the image can vary depending on the object distance.

Here's some key words that will come up this lesson, diminished, convex, principal focus, focal length, and lens power.

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

The lesson is divided into three sections.

The first section explains about how you can use a convex lens to create an image on a blank screen.

The second section is where we can investigate the images that are formed by a convex lens.

And in the third section, we'll form some conclusions and look at how the object distance affects the image that forms. So let's get going with the first section, "Creating an image on a blank screen".

So, "On a bright day, the view outside a window can actually be projected onto a blank screen using only a lens." So here's an example view from outside a window.

There's a nice shed in the background there.

And here is a projected image on a blank screen.

In this case, I'm just using a bit of wall in a room as my blank screen.

And the light passes through the lens.

I'm just using a magnifying glass, which has a lens in it.

And the light passes through the lens.

And that creates this projected image on the wall, which is my blank screen, which is upside down and diminished, which means smaller than life size.

You can see the shed and the sky.

The shed is at the top of the image and the sky is at the bottom of the image.

So the image is upside down.

And the word for that is inverted.

Here's a closer view of the image that I created using that lens.

It's a full colour image of the view from outside my window.

So, "Lenses can be different shapes." I used a convex lens because magnifying glasses always have a convex lens within them.

So a convex lens, which is this shape, "is needed to make light rays converge, which means come together and meet or cross.

So that kind of lens is what's needed to create an image on a screen.

Whereas another kind of lens is called a concave lens.

And that does the opposite.

It makes light rays diverge, which means spread apart.

So that dashed line through the centre of the lens is called the principal axis of a lens.

So a convex lens has a principal axis, and so does a concave lens.

It's the line horizontally through the middle of the lens in diagrams like this.

And each kind of lens also has a symbol.

Now, I'm probably not gonna use the symbols much this lesson, but I'll introduce the symbols now, just so you are aware of them.

So this is the symbol for a convex lens.

And notice if you joins kind of the ends of the arrow heads together, it would kind of trace out the shape of a convex lens.

Whereas this is the symbol for a concave lens, which again, kind of traces out the shape of a concave lens.

Let's do a quick check about convex lenses.

"Which of the following are images of, or symbols, used to represent convex lenses?" Choose as many as you think.

Which of these represent convex lenses? Five seconds, off you go.

Okay, here's the answers.

A, B, C, and F all represent convex lenses.

D and e represent concave lenses.

You might not have identified C as a convex lens.

C is a singly convex lens, whereas A and B are doubly convex lenses.

But they all count as convex lenses.

And they could all be represented by the symbol shown in F.

So how do lenses work? Well, lenses work by refracting light.

And lenses actually can refract rays of light twice.

So once at the air glass boundary, assuming the lens is made of glass.

Often, they're not actually.

They can be made of clear plastic or other materials, polymers.

So when light refract at the air-glass boundary, the light will refract towards the normal.

And then, light will refract again when it leaves the lens, so the glass-air boundary, which is refraction away from the normal.

But because of the shape of the lens, the light is refracted in the same direction both times.

So those two instances of refraction, they're often represented as just one single refraction that occurs at the centre line of the lens.

And we could also represent that using the symbol for this kind of lens as well, like that.

So how can this kind of lens form an image on a blank screen? Well, this is the starting point.

Light from the surroundings reflects in every direction from every point on an object.

It's important to remember that.

So that point on the object is reflecting light in all directions.

And so is that point, and so is that point, and so is that point.

And so is every point on that object.

So many rays of light from each point will pass through the lens.

So from the top point on the object, all of those rays of light and the rays of light in between, which we've not drawn, will all pass through the lens.

And the same from that point.

All of those rays of light and the ones in between will pass through the lens.

All of those rays of light reflected from the object from that point will pass through the lens.

And all of the rays of light from that point on the object will also pass through the lens.

And all the rays of light in between those that we've not drawn.

And here's the important bit.

"All of the rays from the same point on the object are refracted so that they meet at a set distance behind the lens," say here.

And if you place a screen at that distance, that will create a bright spot there from all of the rays of light from the original point on the object hit the screen there.

So there's a lot of light rays all from the same point on the object.

So they'll kind of all be like the same colour of light being reflected from the object hitting the screen there.

But light from every point on the object is focused to its own bright spot at the same distance where the screen is, where we've just put the screen, behind the lens.

And that's what creates the image.

So from this point on the object, light is being reflected from that red apple that's in the tree.

So it's mainly red light being reflected.

So all of the rays of light that pass through the lens get refracted to there, creating that red spot on the screen.

And from this part of the object, from this part of the tree, it's mainly green light being reflected.

So all the rays of light, which pass through the lens are going to be refracted to its own point on the screen, there.

And all of the rays of light, which are reflected from this point on the object, they'll pass through the lens.

They're all refracted to their own point at the same distance, which is where we put the screen, creating a point of light there.

So you can see how the image is built up by all of these different points of light from every point on the object, like that.

And you end up with an image of the object on the screen.

But notice how the bottom of the object, light rays from the bottom of the object, they get refracted to the top of the image.

And light rays from the top of the object, the top of the tree, they get refracted to the bottom of the image.

So that's why the image ends up inverted when you create an image on a blank screen using this kind of lens.

Let's do a check on what we've just explained.

"Which of the following help to explain how a convex lens produces a sharp, non-blurry image on a blank screen behind the lens?" So pause video now, read through each option, and decide which of these do you think do help to explain how a convex lens forms an image on the screen.

Pause video now, off you go.

Okay, I'm gonna go through the answers now.

So lenses form images by refracting light.

So A does help to explain how lenses form an image.

B is false, convex lenses cause rays to converge, not diverge.

And C and D both also help to explain how a lens produces an image on a blank screen because all the rays from one point on the object arrive at a single point on the screen.

And the rays from the different points on the object arrive at corresponding points on the screen the same distance from the lens.

So that's where you need to put your screen to get a clear image in that situation.

Well, done if you've got those three.

So you've got to put the screen in the right place where the rays of light from every point on the object are focused to at the correct distance.

So this image shows a screen placed at the wrong distance.

Because on this screen, rays from one point on the object don't arrive at the screen in the same place.

They arrive at the screen in different places.

So that means the image on this screen is blurred.

And the same for an image on this screen that's in this position.

So where do you need to put the screen? Well, you need to put it in this position, so that rays from one point on the object all arrive at the screen in one place.

And that's gonna create a sharp, non blurry image with the screen in the right position.

So how do you work out the right distance? Well, the correct distance between the lens and the screen for a sharp image, it depends on two things, the power of the lens, and secondly, the distance of the object from the lens.

So if an object is too close to a lens, then the rays reflected from that object are diverging.

And the lens might not be powerful enough to make them converge.

Rays from objects which are slightly further from the lens are less diverging.

And the lens might then be powerful enough to refract the rays enough to bring those rays together so they converge to a focus, a point where they cross.

However, rays from very distant objects are effectively parallel when they arrive at the lens.

So this can take a little moment to get your head around.

So have a look at the diagrams. So if those rays were to continue over a very large distance, then effectively, that central ray, we could think of it as being made up of parallel rays when they reach the lens after a very large distance.

So rays the are parallel to the principal axis of the lens, they are focused to a point called the principal focus of a lens, this point here.

So that's where parallel rays, rays that are parallel to the principal axis, are focused to the principal focus of the lens.

That's where parallel rays of lights are focused to.

And the distance from the centre of the lens to that principal focus, where parallel rays of lights are focused to, that distance is called the focal length of the lens.

So an object can be classed as distant if it's basically very many times further away than the focal length of the lens.

Right, "Which of the following diagrams correctly shows the principal focus, labelled as PF, and the focal length of the lens?" Only one of these diagrams correctly shows the location of the principal focus of this lens.

Which diagram is it, A, B, C, or D? Pause the video now, make your decision.

The answer is A.

And it's only A because the principal focus is where parallel rays of light are focused to.

And the rays of light are not parallel incident on the lens, in B, C, or D.

The rays of light incident on the lens are only parallel in A.

Okay, so the lens are brought.

The rays are brought to a focus in all of these options.

But it's only the principal focus in A, because the principal focus is where parallel rays of lights are focused to.

Let's talk about lens power now.

So this second lens on the screen is wider.

It has greater curvature.

Think of it as a fatter lens.

And that increases its power.

That means it refracts light through greater angles, so it's got a shorter focal length.

However, this lens has the same curvature as the first lens.

But it's got a greater power and a shorter focal length, because it's made of a different material that refracts the light more.

So a material where the speed of light is even slower, so it's got.

It can reflect the light through greater angles, even though the lens has got the same curvature.

So these are the two factors that affect the power of a lens, the curvature, or fatness of a lens, or the material that the lens is made from and how much that refracts light.

Let's do a check on that.

"Use the words greater or smaller to complete the following sentences about the power of a lens.

The power of a lens is greater if.

." And then, read the three bullet points and fill in each blank with either the word greater or smaller.

Off you go.

Okay, I'll go through the answers now.

Pause the video if you need more time.

So the power of a lens is greater if the material it is made from refracts light through greater angles.

The power of the lens is also greater if the lens has greater curvature.

If it's fatter, so it has to be more curved than if it's thinner.

And the power of the lens is also greater if the focal length is a smaller distance from the lens.

Well done if you've got all three of those.

Okay, time for your first task of this lesson.

"Make an approximate measurement of the focal length," which is given the symbol f, "of a lens." So collect a convex lens, a ruler, and a blank sheet of paper, and dim the lighting in the room you're in.

Then, "Identify a bright object," like a lamp or an object outside a window on a bright day.

It should be at least 1 1/2 metres away, so it should be many times further away than the focal length of the lens, so it counts as a distant object.

And then, "Hold up the lens between the distant object and the paper," like in the diagram.

And then, "Adjust the distance between the lens and the paper." So you're kind of adjusting the distance of them both, "until a clear image forms on the paper," of what's outside the window.

And then, ask another person to measure that distance, which should be equal to the focal length of the lens to a good approximation.

Because the object is classed as a distant object, it's should be very many times further away than the focal length if it's over 1.

5 to two metres away.

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

Now, the exact result you'll get for that task will depend on the focal length of the actual lens that you used.

So here are some example results.

Here's the view from a window.

Here's the image of a window on paper with a ruler held up.

And here is the position of the lens compared to the screen.

So it's about 14.

4 centimetres from the screen.

But we need to add on 0.

8 centimetres for the end of the ruler.

So 15.

2 centimetres, so about 15 centimetres for an approximate measurement of the focal length of this lens.

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

What we are going to do next is investigate the different images that can be formed on a screen by a convex lens.

So, "A convex lens focuses rays from a distant object that are parallel to the principal axis." They get focused to the principal focus.

That's labelled as PF In this diagram.

Parallel rays are focused to the principal focus.

And the projected image we know is gonna be inverted, which means upside down, and diminished, smaller than life size.

But you're gonna investigate the images formed when the object is closer to the lens.

So the objects will be a light bulb, a torch, or a lap.

What you're gonna do is you're gonna vary the distance of the object to the lens.

So you're gonna start with a large distance, or a large object distance, and then move the object closer to the lens.

And each time, you're gonna work out, or measure, the distance from the lens at which a sharp image appears on a screen.

And that's called the image distance.

You will also record the nature of each image.

Is it magnified or diminished? And is it outright or inverted? So the following setup can be used in this experiment.

We've got a lens in a holder that's fixed in position.

There's a bulb in a holder.

And that should be movable along that metre rule on the left to set the object distance.

You then should have a screen, which is movable along that second metre rule, to find where a sharp image forms. And a box with a white side can work well.

And that's the image distance where a sharp image forms of your object.

Consider these two predictions.

Here's the first one.

Lucas suggests that the ray diagrams are always gonna be symmetrical, because he's noticed that symmetry is important a lot of the time in physics.

So the closer the object of the lens, then the closer the image will form.

That's his prediction.

But Sophia suggests something different.

She suggests that rays from a closer object, when the object is closer to the lens, she's noticed that they're more diverging.

So after the lens applies the same amount of refraction, she thinks the rays will meet and the image will form at a point further from the lens.

Whereas Lucas thought the closer the object.

The closer the object distance, the closer the image distance.

Sophia thinks the closer the object distance, the further the image distance.

Whose prediction do you agree with? Take a moment to consider that now.

Or you might think something different.

Let's do a check on possible sources of error in this investigation, because this will show that you've understood what you're gonna do in the experiment.

So, "Which the following could be sources of error in this investigation?" Pause the video, read through each option, and decide which you think could be sources of error in this investigation.

Off you go.

I'm gonna give some feedback now.

I'll take each one in turn.

It may be difficult to judge the position of the object, especially, if you use a light bulb as the object because the bulb filament is inside the bulb.

So you'll have to judge that.

You might only be able to judge that to within half a centimetre, for example.

Well, that's definitely a source of error because it's difficult to judge.

B, different parts of the object, different parts of the bulb Filament, may have parts at slightly different distances, making it hard to judge a single object distance.

That's another reason why your object distances might not be exactly what you want 'em to be.

So that's a source of error too.

Well, then if you've got that.

C, there may be a range of screen distances at which the image looks sharp, causing uncertainty in the image distances.

That's true.

And the bulb could get hot.

Well, that's not a source of error.

That is a safety consideration that you need to be aware of.

So well done if you identified A, B, and C could be sources of error in this investigation.

Okay, so it's now time to do that investigation.

So step one, set up the equipment as shown, including a power supply and wires for the bulb, if needed.

And then, dim the room lighting.

Step two, place a screen at a distance equal to the focal length, which is given the symbol f, of the lens.

And that's the focal length you found in task A.

So use the same lens that you used in task A, so you already know the focal length of this lens.

And then, by placing the screen there, that should be the image distance where an image should appear if an object is distant from the lens.

Step three, using trial and improvement, adjust the position of the bulb to find the greatest object distance that produces a sharp, bright image on the screen when the screen is at a distance of, or close to, f, the focal length.

You can adjust the screen slightly if you need to.

But the image should appear somewhere close to f, if not exactly at your predicted f.

Step four, record that first result in a table, as shown below.

Step five, slowly move the bulb closer to the lens, reducing the object distance until there is a measurable change in the image distance by, say, one centimetres or more.

So what that will involve doing is moving the bulb close to the lens a little bit, and then moving the screen a little bit to see which way the image moves.

And then, keep on adjusting the bulb, the object distance to the lens and the screen distance to the lens until you've moved the bulb closer and you've moved the screen to a new position to get the image distance at the new position of the bulb.

Then step six, record the new result for object distance, image distance, and the details of the image in the table.

And repeat step five until the object is as close to the lens as possible, ideally, within one focal length.

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

So here are some results from this investigation.

And this was done for a lens with a 15 centimetre focal length.

But you might have used a lens with a completely different focal length.

So your results might look different.

But hopefully, the overall pattern should look roughly the same.

The first pattern that should be the same is that as the object distance decreased, the image distance should have increased.

So moving the object closer to the lens pushes the image further away from the ends, from the lens.

Another thing you should have seen is that the.

At the greatest object distance, so the first object distance you tested, you should have had a very small image.

But as the object distance decreased, then the size of the image should have increased towards a similar size at a certain point.

But then, beyond that point, if you decrease the object distance further, so made the object closer to the lens, then you would've found that the image became magnified.

So the image started as diminished when the object was very far from the lens.

But as the object moves closer to the lens, the image moves further away and gets bigger and bigger.

So it goes from diminished to the same size, as life size, and then becomes magnified, and then continues to increase in size if the object distance is brought closer and closer to the lens.

Until, that is, that the object distance is brought so close to the lens that it's only about a focal length away.

And at that point and beyond, no image can be formed.

So you shouldn't have been able to form an image on a screen if you brought your object to the focal length, or closer to the lens.

Well done if your results broadly fit those patterns.

So let's draw some conclusions then about how the object distance affects the image.

So the results could be plotted on a graph like this.

It would need to be a line graph because the independent variable, which is object distance, is continuous.

The values that object distance can take run on a continuous scale of numbers.

Doesn't come in categories.

It's not a categoric variable.

So we don't do a bar chart.

We do a line graph 'cause the independent variable is continuous.

And the graph clearly shows one of the key trends from the results, which is that the greater the object distance, the shorter the image distance was.

Or if we looked at the other way around, the way we did it in the experiments, the shorter the object distance, the greater the image distance.

So in the experiment we saw that when the object distance decreases, both the image distance and the image size increase.

And that happened until the object distance equaled the focal length.

We'll talk about what happens if you've managed to get the object to the focal length or closer in a moment.

And as we saw from the very start of the lesson, the image formed on a screen by a convex lens is always inverted.

So the image actually switches from being diminished to being magnified when the object distance is 2f.

And that's when the animation pauses.

It pauses at when the object distance is 2f because that is the object distance where the image is the same size as the object, at 2f, double the focal length there.

So that's when the image switches from being diminished to being magnified.

And as I just said, when the object distance was at double the focal length, the image distance was also double the focal length.

So the object distance was equal to the image distance.

And also the object, the image size, was equal to the object size in real life.

So it was neither magnified nor diminished at that distance.

And then, when the object distance decreased from 2f, from double the focal length, the image distance and size both increased at an increasing rate.

They increased very quickly with tiny increases in distance towards the lens, until the object distance reached the focal length.

So let's look at that now.

But when the object was at the focal length, the refracted rays became parallel.

And if the object is closer than the focal length, the refracted rays weren't converging anymore.

They were diverging here, diverging.

So in both of those cases with the object at the focal length or closest to the lens on the focal length, no image can form on a screen, as the rays from a single point on the object, then never meet or cross after being refracted by the lens.

Okay, let's do a check on the conclusions from this experiment.

"Identify the correct option from each pair of words." Pause the video now and have a go at that.

I'm gonna go through the answers now.

So with the large object distance, the image was diminished and close to the principal focus of the lens.

Well done if you've got both of those.

But then as the object distance decreases, then the image distance and the image size both increase.

Well done if you've got that.

Okay, so it's time for a task to summarise how the object distance affected the image.

So there's two parts to this task.

Part one, "Complete the table to describe how the object distance affects the image formed on a screen by a convex lens." And in the table, f stands for focal length, as it has done throughout this lesson.

And then, part two of the task, it's actually something to watch out for within the task.

There are two object locations, so two rows in the table, where no image forms on a screen, so two rows in the table that you can't fill in because no image forms on a screen.

So in those two rows, you could explain why no image forms on a screen.

Pause the video now.

And have a good go at that task with your best effort.

I'm gonna give some feedback now on that task.

When the object is very distant, the image is found at the focal length, at f.

It's a diminished image.

And the image is always inverted, so I'm gonna miss out that column for now.

Then when the object is brought closer, but it's still further away than 2f, the image moves backwards from f towards 2f, the other side of the lens.

The image is still diminished, but it's increasing in size as the object is brought towards 2f.

Then when the object is at double the focal length, at 2f, the image is at 2f and it's not magnified or diminished.

It's life size.

Then when the object is brought closer to the lens from 2f to f, the image becomes further and further away.

And it's magnified.

And then, when the object is put at the focal length or closer than the focal length, then no image forms on a screen because after a refraction by the lens, the rays are parallel, or diverging, so they never cross or meet.

Well done if you've got answers along those lines.

Make any improvements to your work now.

Here's a summary of the lesson.

A convex lens can produce an inverted image on a screen by refracting light.

Rays of light from distant objects, which are parallel to the principal axis, are refracted to the principal focus of a lens, which is located at a distance from the centre of the lens called the focal length, represented by the symbol f.

A greater power lens has a shorter focal length.

The image distance and size or magnification depend on the power of the lens and the object distance.

And as the object distance decreases, the image distance and size both increase, until the object reaches the focal length or closer.

Because at those distances, the rays leaving the lens are parallel, or diverging, so cannot form an image on a screen.