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I am a high school student and I am a little confused about a topic, My confusion is that,

(say an object is $1$ dimensional) I doubt optics while studying the formation of image what we do is take $2$ rays from the head of the object and then using laws of reflection we see where the ray meets and we declare that point as a reflection of the head of the object and from the head of the image to the principal axis we say that this is the length of the image now my question is if we take any general point of the object and try to reflect it will result in a point so it means that the for every point on an object there is a point of reflection where the rays meet following this if the object is made up of say $10^{10000000}$ points then the image points can be at max the same no. of points provided no points coincide but we know that in many cases after reflection from mirror an enlarged image is formed how is that possible with considering light as a particle.

I request you to please answer my query I asked this no. of teachers no one explained to me the reason and now I am more confused as my doubt is not getting resolved.

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    $\begingroup$ Could you please paraphrase your question and punctuate it if you can? It is really hard to read and understand and follow at the moment. $\endgroup$
    – Yejus
    Dec 29, 2020 at 10:52
  • $\begingroup$ When talking of "Geometrical Optics" It's better to talk light in terms of waves, not particles at this level. $\endgroup$ Dec 29, 2020 at 12:15
  • $\begingroup$ It is to your benefit to write in standard English syntax. People (i.e., me) will not expend the energy needed to decode your symbols. $\endgroup$
    – garyp
    Dec 29, 2020 at 12:29

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You are thinking in terms of a finite number of points. A finite number of points distributed in what we call the object space will always form an image at a finite set of points in the image space. When you talk of an extended object there are a continuum of points. And this continuum of points will be "mapped" to the image continuum. You can think of this situation like stretching a rubber sheet. Hope this clears your query.

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  • $\begingroup$ but actually nothing is infinite? when I asked it to a professor instead of answering this instantaneously, he had given me an another problem to think about." Draw two parallel lines AB =1 cm and CD = 2 cm . Join AC and BD and let they meet at O. Naw take any point P on AB, Join OP and extend it to cut CD. So for each point on AB you get a corresponding point on CD. Similarly you take any point on CD and join it to O. This will cut AB at a point. So for each point on CD you have a corresponding point on AB. Does it mean the number of points on AB (1cm) is the same as that on CD (2cm)? $\endgroup$ Dec 29, 2020 at 14:21
  • $\begingroup$ The number of points on a line (or object) is infinite (uncountable and inconceivable). As jayheme points out, you need to think in terms of a finite number of points on one line and the corresponding points on the other. $\endgroup$
    – R.W. Bird
    Dec 29, 2020 at 15:13
  • $\begingroup$ Your professor has given you the correct intuition regarding your question. One physical way you can think of it is the stretching of a rubber band. Or a sheet as i have mentioned. When we talk about such sets which are uncountably infinite, we dont really say that this set has more elements than the other. Both the line AB and CD have an uncountably infinite number of points on it. $\endgroup$
    – jayheme
    Dec 29, 2020 at 16:01
  • $\begingroup$ ok thanks, I got it, actually I was confused in this because my subject is not mathematics, so I don't know much about how to deal with these things:) $\endgroup$ Jan 1, 2021 at 5:58

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