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Images formed by cylindrical lens

  1. Jul 18, 2012 #1
    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.
     

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  3. Jul 19, 2012 #2

    Simon Bridge

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    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.
     
  4. Jul 19, 2012 #3
    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
     
    Last edited: Jul 19, 2012
  5. Jul 19, 2012 #4

    Simon Bridge

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    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?

    "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?
     
    Last edited: Jul 19, 2012
  6. Jul 19, 2012 #5
    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.
     
  7. Jul 19, 2012 #6

    sophiecentaur

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    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.
     
  8. Jul 19, 2012 #7
    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?
     
  9. Jul 19, 2012 #8

    sophiecentaur

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    How many did you want?? :confused:
     
  10. Jul 19, 2012 #9

    sophiecentaur

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    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 any one 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.
     
  11. Jul 19, 2012 #10
    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?
     

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  12. Jul 19, 2012 #11

    sophiecentaur

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    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.
     
  13. Jul 19, 2012 #12

    Simon Bridge

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    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 :)
     
  14. Jul 19, 2012 #13
    Am I correct?
     

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  15. Jul 19, 2012 #14
    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.
     
  16. Jul 19, 2012 #15

    sophiecentaur

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    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.
     
  17. Jul 19, 2012 #16

    Drakkith

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    Not quite. You won't have an oval, you will have a line.
     
  18. Jul 19, 2012 #17

    Drakkith

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    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.
     
  19. Jul 19, 2012 #18

    sophiecentaur

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    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.
     
  20. Jul 19, 2012 #19

    Drakkith

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    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.
     
    Last edited: Jul 19, 2012
  21. Jul 19, 2012 #20

    sophiecentaur

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    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.
     
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