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Consider the following image from Wikipedia and based on it I have a doubt.

Image Credits: Wikipedia

I do not understand why are the light waves represented like the waves in water. Shouldn't the waves be like sine waves. Why is the slit part the starting of a new wave. Secondly, Why does this lead to to destructive interference rather than constructive because the waves are emitted at the same time. And if anyone can tell me how is double slit possible even when there is a single photon?

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That's rather a lot of questions. May I recommend you read amazon.com/Introduction-Modern-Optics-Dover-Physics/dp/… ? –  Carl Witthoft Feb 13 at 16:02
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In the representation here the curves mark the peaks of sinusoidal waves (and "gravity waves" on the surface of a fluid are sinusoidal in the limit of amplitude small compared to depth). This is just a different visualization. It is always important to distinguish between the visualization and the thing visualized. –  dmckee Feb 13 at 16:22
    
@rahulgarg12342: You can see my answer here to understand waves. In order to understand photon's wave nature you can see my answer here. –  GODPARTICLE Feb 13 at 18:22
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2 Answers

Shouldn't the waves be like sine waves.

That depends on what you want to show. In this particular case, what is shown is the propagation of a particular ray of light.

Why is the slit part the starting of a new wave.

A slit acts as a source of spherical waves. This is the Huygens-Fresnel principle. This is done to produce a new single source of light.

Why does this lead to to destructive interference rather than constructive because the waves are emitted at the same time.

It produces constructive and destructive interference. The black spots are maximum destructive interference while the bright spots are maximum constructive one. Both phenomena always come together.

How is double slit possible even when there is a single photon.

The photon is not only a particle but also a wave that can interfere with itself. That's what the experiment shows, that's its nature. This is the "weirdness" of quantum mechanics.

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Well thanks for a good short answer but I still have two doubts as I am only 15 and have a hard time in understanding high level mathematical mumbo-jumbo. If we show it as sine waves then I do not get it how it will be possible. If you show watery waves it is easier to interpret but I do not understand how are the light waves are converted to watery waves? –  rahulgarg12342 Feb 13 at 16:10
    
Because the mathematics behind a wave in water is the same as in electromagnetic phenomena. In this case, int eh picture it's shown as if you're standing at the peak of it and move with it. This is the same as if you focus on the peak traveling wave on water. –  Ignacio Vergara Kausel Feb 13 at 16:14
    
I don't even get how can a photon interfere with itself? Even if it interferes with itself how can it split and form a multiple interference pattern? Its interference should either be only constructive or only destructive according to me. –  rahulgarg12342 Feb 13 at 16:17
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@rahlulgarg12342 You used the phrase "are represented like" in your question and it is important to keep that phrase in mind. Representing light as a "water wave" or "sine wave" is just a tool. Such representations allow us to use our intuition about water waves and sine waves to help describe light. Light is neither a "water wave", "sine wave", nor even a "particle". It is a phenomenon that has some aspects of all these and we switch between these descriptions as needed to describe a particular aspect. –  Jason A Feb 13 at 16:18
    
@rahlulgarg12342 because a single photon is like one of the yellow lines after the first slit and then when going to the second two-slit opening it acts as two sources which can interfere with itself producing constructive and destructive pattern on the screen. –  Ignacio Vergara Kausel Feb 13 at 16:23
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Yes, the waves are and should be (approximately) sine waves. A proper animation would show the intensity at each point, so it would need a continuum of colors. For the sake of simplicity, the Wikipedia animation only shows the places where the sine wave approaches the maximum in orange.

Each slit is the source of the waves according to the Huygens-Fresnel principle. That principle holds for all waves – it is really a method to find some solutions to the wave equation. Because the waves on water, classical electromagnetic waves, as well as wave functions for a single particle in quantum mechanics obey a wave equation that is mathematically identical (except for some polarization details and corrections) in all these cases, methods – like the Huygens-Fresnel principle – to find a solution in one case are good for other cases, too.

The double slit experiment leads to the interference pattern even if individual particles are being sent through the experiment. It's what the experiments show. Well, people knew that this would be the result before they did this exact experiment. The theoretical description associates a wave function, a complex-valued "probability wave", with a particle. This wave function follows an equation (Schrödinger's equation) that is analogous to the wave equations for water and especially classical electromagnetic fields, so it interferes just like the classical examples. However, the wave function is interpreted differently: $|\psi(x,y,z)|^2$ isn't the "energy density" but instead, it is the probability density that a particle will make a "dot" at a particular place. When many particles are collected, they produce many dots that recover the probability distribution. So the pattern inevitably looks increasingly like the usual interference pattern we can see in the case of water waves and classical electromagnetic waves, too. That's how Nature works.

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