Images formed by cylindrical lens

[jadelamlam]

Cylindrical lenses focus light rays onto a line instead of a point.
Is that means several images will be formed from a point object aftering passing through the lens?
(please see the attached files 1 and 2)
If I am correct,
can anyone explain to me,when you add water to a tall water glass(see attached-->3),why there is only 1 image formed?And why it is laterally inverted but not inverted?
I have been confused by those for several weeks.
thx a lot.

 

[Simon Bridge]

Is that means several images will be formed from a point object aftering passing through the lens?

No.

A glass cylinder will act as a converging lens in one dimension only. In the other dimension is acts as a plain sheet of glass.

You can examine the effects with a glass of water - a converging lens should be able to produce real inverted images as well as imaginary upright images. Compare with the same situation with a regular lens and you'll understand what you see.

 

[jadelamlam]

Please forgive for my foolishness...
Referring to 2 pics provided,light from the same point of object intersects at several points. Why only 1 image is formed?Sorry...But I really don't understand :((((((((

Later,I added water to a glass.I found that it can only produce laterally inverted,diminished,erect image and magnified,erect image(for near object).However,images formed by spherical convex lens must not be laterally inverted,but it is inverted.Why?What leads to the differences in natures of images formed by spherical lens and cylindrical lens?

I hope someone can help me

 

[Simon Bridge]

The picture only shows three pairs of rays from one point ... they converge to three points. But surely there are more than six rays actually radiating from each point on the object? What would happen when you add these ones in the diagram?

Try it with an experiment - put an object (a lit candle will do) on one side of your glass of water and put a screen on the other side ... move the screen back and forth to see if you can find the image(s) :)

Do not rely on just pure thought - do an experiment. It is cheap, easy, and quick; so do it! You've done experiments with lenses before right?

When you use a screen, what kind of image are you trying to find?
When you use just your eye, what kind do you usually find?
Could this account for the differences?

images formed by spherical convex lens must not be laterally inverted

"must not"? Check.

Spherical-convex lenses (which are solid glass in air) are converging lenses - they may produce real-inverted or imaginary-upright images depending on how you use them.
Do you understand how these images form?

 

[jadelamlam]

I have drawn a ray diagram...But I am not sure whether it is correct or not.
The picture only shows three pairs of rays from one point ... they converge to three points.
Image is formed by intersection of real/virtutal light rays.I guess the reason that we can only see 1 image is because other light rays from the same point of object cannot reach our eyes?

I have done the experiment too,but I can only see shadows of the glass and the candle = =,and I can't find any image of the candle,so it is a virtual image?

images formed by spherical convex lens must not be laterally inverted
"must not"? Check.
Yes..My teacher told me that images formed by spherical convex lens are always not laterally inverted.

 

[sophiecentaur]

You can treat the two curvatures separately. In a horizontal plane, you have a convex lens, so the (real) image that is formed will be inverted because light from one side of the axis is focussed on the other side (left -to - right inversion). But there is no vertical curvature so light from above the horizontal will not be bent downwards and light from below will not be bent upwards - so no vertical inversion.

Depending on where you put the object relative to a convex lens, the resulting real image may be magnified, reduced OR the same size, aamof. If you put your candle nearer to the cylinder than its focal length, the image formed will be virtual. If you put your eye in the right place, you should be able to see this virtual image.

It would probably be better to sort out these basics by experimenting with spherical lenses (symmetrical) first and then move on to cylindrical lenses - because they add complication to the problem. Also, the sheer thickness of a full cylinder (or sphere) means that the focal length tends to be very near the surface. Most 'real' lenses are thinner, just having spherical shaped surfaces.

 

[jadelamlam]

thx,now I understand why it is laterally inverted,
but why only 1 image is formed?light intersects in 3 different points in the attached pic?

 

[sophiecentaur]

thx,now I understand why it is laterally inverted,
but why only 1 image is formed?light intersects in 3 different points in the attached pic?

How many did you want??

 

[sophiecentaur]

Sorry about that. The fact is that the three 'rays' used for constructing an image are chosen because that is enough. In fact, two rays are all you need (in anyone plane). If you take one ray, right through the middle of the lens, it won't be deflected at all, because the two faces are parallel. Then take another ray, parallel with the principle axis**. This will be bent so that it goes through the 'focal point'. These are the simplest paths to predict. Where those two rays intersect, that is where all other rays will converge so it's where the image will be formed.
There is a caveat, here. If the lens has truly spherical faces, this construction only works over a limited range of angles (good enough for many applications though). For a wider range of angles, you get 'spherical aberration' (blurring of the image). To avoid this, you need to shape the lens slightly differently - which is one of the reasons that the top quality lens manufacturers charge you £kkk for a good lens.

** The interesting thing is that the lens doesn't actually need to be wide enough for this ray to be actually present for an object way off axis. You can still predict where the image will be, using that non-existent ray.

 

[jadelamlam]

please see the pic that I have just uploaded.
According to ur information,the rays // to the principal axis should be converge to a point instead of a line?

 

[sophiecentaur]

With a cylinder, there are two axes of curvature. The image is not perfect. ( for a start, it is highly distorted) The focus for the axis with zero curvature is at infinity. The convex bit makes the image look sharp but it isn't.

 

[Simon Bridge]

I have drawn a ray diagram...But I am not sure whether it is correct or not.
The picture only shows three pairs of rays from one point ... they converge to three points.
Image is formed by intersection of real/virtutal light rays.I guess the reason that we can only see 1 image is because other light rays from the same point of object cannot reach our eyes?

I have done the experiment too,but I can only see shadows of the glass and the candle = =,and I can't find any image of the candle,so it is a virtual image?

images formed by spherical convex lens must not be laterally inverted
"must not"? Check.
Yes..My teacher told me that images formed by spherical convex lens are always not laterally inverted.

You should check what your teacher says there by experimenting with an actual spherical lens. If you understood (from earlier) why the cylindrical lens image is inverted laterally but not vertically then shouldn't you expect a spherical lens to invert in every direction.

When you are considering the ray diagrams - realize that your eye needs diverging rays to see an image - the image appears at the place where the light appears to diverge from. But this means that you won't see an image at every possible eye position. Also, a screen scatters light that arrives at it so you eye gets diverging light off that and you see any image as a picture on the screen. To see a clear picture, the screen has to be place so that light rays from one point on the object arrive at one point on the screen. When the picture is clear, you are said to have it "focused", and the screen position is the same as the image position. Otherwise it's blurry, sometimes so blurry you cannot make out a picture at all. So you have to move the object and the screen and you eye around to see the full effects.

Note - your last ray diagram does not look right. The vertical part of the ray should be un-deviated while the lateral part should be deflected towards the axis.

And thanks to sophiecentaur for fielding this :)

 

[jadelamlam]

Am I correct?

 

[jadelamlam]

You should check what your teacher says there by experimenting with an actual spherical lens. If you understood (from earlier) why the cylindrical lens image is inverted laterally but not vertically then shouldn't you expect a spherical lens to invert in every direction.

No,when light from a distant object passes through a spherical convex lens,it is inverted.
Now,assume that u are the object,when u raise up your left hand,ur image also raises up his left hand,but ur image is inverted,imagine you can turn you image into the right position(i.e. turn the image from virtual to erect,with the back of image facing ur eyes),LHS of ur image is still equal to LHS of u.

Let's consider about the image formed by a plane mirror,when u raise up your hand,then ur image will raise up his right hand,imagine the back of image facing ur eyes now,you can see that he is raising up his right hand in RHS direction,while you are raising up your left hand in LHS direction.

Sorry,I don't know what I am talking about,it seems that I have made it too complicated.

 

[sophiecentaur]

Sorry,I don't know what I am talking about,it seems that I have made it too complicated.

I think too many words cloud the issue. If you just look at any of the hundreds of diagrams that show image formation by a convex lens then they make it obvious that the rays from an object come to a focus on the other side of the principle axis. This gives a totally inverted image and the diagrams explain why.
A plane sheet of glass will not form an image at all and certainly no inversion. Your cylinder is a combination of the two (also the image is very distorted and not focussed well).
p.s. You can obviously spell the words "Your" and "Your". Why not do it? This isn't text messaging or twitter.

 

[Drakkith]

Am I correct?

Not quite. You won't have an oval, you will have a line.

 

[Drakkith]

Look here: http://en.wikipedia.org/wiki/Convex_lens#Types_of_simple_lenses

See how the three light rays in the picture converge? Now imagine stacking identical lenses on top of each other to make a cylinder-like object. Light that is shined through will focus in a line running from the bottom of the focal plane to the top.

 

[sophiecentaur]

Look here: http://en.wikipedia.org/wiki/Convex_lens#Types_of_simple_lenses

See how the three light rays in the picture converge? Now imagine stacking identical lenses on top of each other to make a cylinder-like object. Light that is shined through will focus in a line running from the bottom of the focal plane to the top.

I'm not sure that's a valid model. There is no 'vertical focussing' in the case of a vertical cylinder. The light will just 'spread out vertically from any point on the object.

 

[Drakkith]

I'm not sure that's a valid model. There is no 'vertical focussing' in the case of a vertical cylinder. The light will just 'spread out vertically from any point on the object.

Yes, that is why there is merely a line formed at the image plane instead of an image.
Edit: Or you could say that is why a line is formed instead of a point. The rays emitted from a point source will not be focused vertically at all.

 

[sophiecentaur]

But how can you justify replacing the cylinder with a set of lenses? They will produce a set of discrete images and not a vertical line. I think you have gone a step too far with your explanation.

 

[Drakkith]

But how can you justify replacing the cylinder with a set of lenses? They will produce a set of discrete images and not a vertical line. I think you have gone a step too far with your explanation.

The lens in the picture linked only focuses in one dimension. It just isn't round like a cylinder, so I called it "cylinder-like".
Here's the bigger version of the picture: http://en.wikipedia.org/wiki/File:Large_convex_lens.jpg

 

[jadelamlam]

Sorry,there is still a question,
in the diagram attached,
1.The pink ray or the orange ray is correct?
2.Let the purple point be an object placed under the green object perpendicularly.
Is it means that the image of purple object overlaps the image of green object?

 

[sophiecentaur]

Sorry,there is still a question,
in the diagram attached,
1.The pink ray or the orange ray is correct?
2.Let the purple point be an object placed under the green object perpendicularly.
Is it means that the image of purple object overlaps the image of green object?

1. Obviously the orange ray is correct because there is no curvature, vertically to change the vertical direction of the rays. What could possibly be making that orange ray take the path it does on your diagram?
2. Of course, as there is no focussing in the vertical sense light from all sources on the vertical line with the green and purple dot will be spread out all over the place and every point on that line becomes a line in the image plane.
If you put two coloured lights in a vertical line, you would not expect any image to be formed on a screen - even if you put a plane piece of glass in the way. The cylinder is identical when considering the vertical axis. There can be no vertical focussing.

It's time that you did an experiment or two. You only need a bottle or straight sided water glass.

 

[jadelamlam]

However,when we put a pen infront of a glass filled with water.We can see that the top of the pen is on the top of image,while the bottom of pen is at the bottom of the image.
Cylindrical lens form a line image,the image of the top of pen should overlap the image of bottom of pen,so why we still can identify the top and bottom of the pen?

 

[sophiecentaur]

However,when we put a pen infront of a glass filled with water.We can see that the top of the pen is on the top of image,while the bottom of pen is at the bottom of the image.
Cylindrical lens form a line image,the image of the top of pen should overlap the image of bottom of pen,so why we still can identify the top and bottom of the pen?

You are looking at a Virtual Image in that case and not a Projected, Real Image. Without the glass, you can 'see' the pen but that doesn't mean you can expect to see a projected image of that pen on a screen placed where your eye is. You mustn't confuse the two phenomena. The ray diagrams are totally different.

 

[jadelamlam]

virtual image?
please see the attached,I have just done an experiment.
I have also drawn some ray diagrams(sorry for my ugly drawings)
Light rays intersect before our eyes,so it is a real image?
Moreover,please see:
http://upload.lsforum.net/users/public/z427157w144.jpg
purple rays come from the top of object,while green rays come from the bottom of image.They overlap each other.
But we when we look at the image,we can clearly distinguish the top and bottom of object from the image.However,from http://upload.lsforum.net/users/public/o370183f144.jpg
It should be a line image that we cannot classify the top and bottom of image?

see also:

http://hk.image.search.yahoo.com/images/view;_ylt=A2oKiHMpJApQzj4AQ1K1ygt.;_ylu=X3oDMTBlMTQ4cGxyBHNlYwNzcgRzbGsDaW1n?back=http%3A%2F%2Fhk.image.search.yahoo.com%2Fsearch%2Fimages%3Fp%3Dcylindrical%2Bconcave%2Blens%26fr%3DFP-tab-web-t%26fr2%3Dpiv-web%26tab%3Dorganic%26ri%3D14&w=640&h=480&imgurl=www.shokabo.co.jp%2Fsp_e%2Foptical%2Flabo%2Flens%2Flens_c3.jpg&rurl=http%3A%2F%2Fwww.shokabo.co.jp%2Fsp_e%2Foptical%2Flabo%2Flens%2Flens.htm&size=47.6+KB&name=cylindrical+lens+lens+formula&p=cylindrical+concave+lens&oid=0888140787f73798e7fb1dadf61a21be&fr2=piv-web&fr=FP-tab-web-t&tt=cylindrical%2Blens%2Blens%2Bformula&b=0&ni=21&no=14&ts=&tab=organic&sigr=11obfb6lp&sigb=13nmt10po&sigi=11kb00tio&.crumb=Z9hJ4Hw5kI6

the above diagram is similar to the diagram of rays passing through a glass with water

 

[Drakkith]

Moreover,please see:
http://upload.lsforum.net/users/public/z427157w144.jpg
purple rays come from the top of object,while green rays come from the bottom of image.They overlap each other.
But we when we look at the image,we can clearly distinguish the top and bottom of object from the image.However,from http://upload.lsforum.net/users/public/o370183f144.jpg
It should be a line image that we cannot classify the top and bottom of image?

No, our eyes are not a flat surface that we are projecting light onto, they use real lenses to converge the light. When you look through the cylinder your eye causes light going in different directions to focus on different spots on the retina. Even though they overlap at the focal plane, we are looking at light that has already passed the focal plane and has entered our eye. This results in a distorted view horizontally, and a non distorted view vertically. (By distorted I simply mean it doesn't look like it would if the cylinder were flat glass)

 

[sophiecentaur]

It is essential that you appreciate the difference between a virtual and a real image. When you look into the cylinder, your eye is seeing a virtual image in one plane and a real image in the other. Tricky to appreciate, perhaps.
As I have said before, this is a difficult example of a lens to start your learning process with. A cylinder never forms a proper coherent real image because the focal lengths in the two plane are not the same (it's an extreme case of what's called astigmatism and many people's eyes suffer from this). Rays converge on a vertical line, parallel with the cylinder but, at any point on that line, you get rays from the whole height of the object. For a very short cylinder, you could expect to get the same effect as for a pinhole camera, which could give some vertical discrimination between different parts of the object. If you google images of pinhole cameras you will see that a single small hole behaves like a tiny lens - producing a real inverted image because only rays from one part of the object reach a particular part of the projection screen. The height of the cylinder is equivalent to having a vertical slot rather than a pinhole and the image is blurred out in the vertical direction to the extent of the length of the slot. Light from the very lowest parts of the object will not reach the bottom of the projected image because the light rays can't bend. So you will get a slight 'clue' about the object because the general colour / brightness of the image may be a bit different at the bottom and the top.

 

[jadelamlam]

thx a lot,I understand it now!

 

[sophiecentaur]

WE got there! Well done.