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I quote from my textbook, " Consider two vertical slits S1 and S2 placed parallel to each other, and a string is passed through them. The end B is fixed and A is given jerks perpendicular to its length. If on rotating slit S2 till it is perpendicular to S1 the amplitude of vibrations becomes zero then the wave is a transverse wave, otherwise it is a longitudinal wave."

I understand how this works for mechanical transverse waves, but not for light. The electric and magnetic vectors do not have spatial extension, though it is shown that way in animations. The oscillating vectors just show the varying magnitude of the fields at points on the ray of light. Otherwise its like saying a physical arrow(velocity vector) extends in front of a moving body whose size depends on the body"s velocity.

So my question is why should the amplitude of light be affected when the oscillations have no spatial extension(considering just one ray of light passing through the slits)?

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You are right that the oscillations of the electromagnetic field need not have any spatial extent. The oscillations, as you point out, are in the strength of the electric and magnetic fields. If I understand your question correctly, you are asking why then can some objects distinguish between the two different polarizations of light.

This is because anisotropic materials (those which do not have exactly the same structure in all directions) can act differently to electric fields which lie along their different axes. In the image below the material in the middle does not support an electric field in the horizontal direction. When you try to establish an electric field in the horizontal direction, energy is taken out of the source which is trying to establish it (the light in this case). So, this material, which acts as a typical polarizer, only allows light which is polarized in the vertical direction to pass.

There are other ways to distinguish between the two different polarizations of light. Birefringent crystals, for instance, have a different index of refraction for the two different polarizations of light. They therefore deflect the two different polarizations of light by a different amount.

From the Wikipedia article on Polarizers

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If instead of the string Light were to be used then it will pass through both of the slits S1 and S2. The book is using this analogy to explain the concept of polaroids. image
(source: aventalearning.com)
The whole string-slit system that your book quotes is analogus to the above shown light-polaroid system. Light will not pass through the second polaroid. I am not explaining how polaroid works, am explaining what your book aims at.

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light rays are not one dimensional objects. True, in the figures that directed segments are shown. Mathematically, you can think of sort of an infinitesimal vector showing that direction. it can be made infinitely small. is that 0 dimensional small, i don't know. I don't think it is. It would have the dimension of dx.

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  • $\begingroup$ They are not infinitesimal vectors. They show the magnitude of $\vec E$ and $\vec B$. See this image, more the length of the vector means more the magnitude. $\endgroup$
    – user31782
    Commented Apr 5, 2014 at 4:48
  • $\begingroup$ i know exactly what they are showing. However, it seems that the original question comes from a misinterpretation of the diagrams. In any case, light is not made of light of light rays. The field varies continuously, in space. At least in classical mechanics. you may not be able to eliminate the direction of the electric field in a discription of EM interactions. But, the direction of the B field is problem. Its like spin. Spin doesn't point perpendicular to the dynamics. If the spining is taking place in the x y plane, +z and -z are just as good. $\endgroup$
    – user43953
    Commented Apr 7, 2014 at 18:52
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electromagnetism is not a handed force. So i don't think you even need to use vectors that are transverse. I recently, learned about a mathematical object called a differential form. a dx+dy is like the k unit vector and dx-dy is like -k. So spin can be described in a more natural way that does not resort to a perpendicular direction.

Definetly, more than one dimension are required for spin. At least two are required. So, i guess a more accurate picture would be to think of sheets of light coming in rather than beams or rays. A vector pointing up can always be assigned to a fluid vortex. Its just a swirling motion, it doesn't point up or down. The swirl itself can not be eliminated.

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  • $\begingroup$ its probably more accurate to think of a em wave as a water wave on its on sides. The motion of the wave is somewhat circular, rather than strait up and down. So, what you have is more like a propagating vortex. So a water wave is sort of polarized. I don't know if you can devise a polarizing filter for water waves. $\endgroup$
    – user43953
    Commented Apr 5, 2014 at 15:31

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