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The Proof is Trivial physics edition? Watch

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    (Original post by Phichi)
    The real question is why does light slow down in an optically dense material ?

    Should I make a new thread shortly for this? A formal one? And hope it gets stickied.
    A new thread would be good.

    I don't know quantitatively, but the photons get absorbed and-emitted by electrons. Different frequencies do this to different degrees, but I don't know why, or why purple seems to be more deflected than red since I'd have thought high energy would mean less deflection...
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    (Original post by lerjj)
    A new thread would be good.

    I don't know quantitatively, but the photons get absorbed and-emitted by electrons. Different frequencies do this to different degrees, but I don't know why, or why purple seems to be more deflected than red since I'd have thought high energy would mean less deflection...
    There's lots of theories, all of which don't quite add up, just one of those things we'll have to deal with until another Einstein walks along. The main issue, which also applies to your answer, is that the light, in simplistic terms, stays together, uniform going in and out. If electrons are absorbing the photons and releasing them, as say, a glass block isn't uniform, some photons would be interacting with more electrons than others (in your case).

    Its purely reliant on the wavelength, of which purples is smaller than red.
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    (Original post by Phichi)
    Do you plan on doing M4 and M5 at A-Level? If you're interested in moments of interia and such, it's good fun. It's not as hard as made out to be, I personally found relative motion the hardest thing. Was beneficial when I started my degree.
    I'm going to do M3, but I'm not sure if my school offers M4 and M5. If they don't, I might self-teach some of the material but probably won't sit the exam.
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    What sort of questions are we supposed to post? One that can be answered with A-level knowledge or can they be harder?
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    (Original post by lerjj)
    I'm going to do M3, but I'm not sure if my school offers M4 and M5. If they don't, I might self-teach some of the material but probably won't sit the exam.
    I self taught M4 and M5, most schools won't teach it, but that doesn't mean you can't get help or guidance when you need it. With further maths, you can get another AS or A-Level out of it, personally I got 3 A-Levels in maths alone by self teaching a few of the applieds, which is good.
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    (Original post by langlitz)
    What sort of questions are we supposed to post? One that can be answered with A-level knowledge or can they be harder?
    They can probably be a little harder I guess. Moments of inertia aren't specifically A level, but you told me the formula so I could work it out, because the question was fundamentally based on conservation of energy which is taught at all levels.

    I don't mind if they involve some extra knowledge beyond A level, because I'll get to learn some new stuff. You and Phichi are physics students I guess?
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    (Original post by langlitz)
    What sort of questions are we supposed to post? One that can be answered with A-level knowledge or can they be harder?
    A-Level to undergrad I'd say, gives a nice range and the ability for everyone to have a challenge.

    Something following like the maths thread would be good, they use this legend:


    * = requires only A-level knowledge
    ** = may require a little extra (induction, L'hôpital's etc.)
    *** = requires undergraduate knowledge

    (Original post by lerjj)
    You and Phichi are physics students I guess?
    I am
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    (Original post by lerjj)
    You and Phichi are physics students I guess?
    Well, kind of... chemical physics
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    Explain why a rubber ball floats in water, without assuming Archimedes' principle (you'll probably prove it on the way though).

    Difficulty:*, but knowing where to start might be difficult.
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    Consider a quantum mechanical particle with energy greater than V_o, travelling in the +ive x direction, passing over a potential well of length L such that

    What are the forms of the eigenfunctions in each of the regions defined by the potential? Determine an expression for the reflection coefficient.

    Difficulty: ***
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    Here is one I posted a while back that no one was able to answer.

    Another challenge problem pertaining to this is as follows:
    Consider a two state system with an orthonormal basis |1> and |2>. These two vectors are eigenvectors of the flavour operator, with |1> representing an electron neutrino and |2> representing a muon neutrino.

    If neutrinos are massless, the Hamiltonian for a system like this would have been:
    H = E|1><1| + E |2><2|

    where E is a positive real constant. If the neutrino originally started in the state  | \psi(t=0)&gt; = |1> what is the state of the system at later times t?

    Difficulty: *** (But this is the first part to a longer question I will ask, this should be very simple to anyone with a little knowledge of quantum mechanics)
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    No-one's posted a question in a while (except for the two QM ones. Seriously, unless you two answer each other's questions...)

    Imagine an electron entering with a velocity v between two charged plates with potential difference V across them. The electron enters a vertical distance d from the +ve plate, where the plate separation is 2d. Show that the path of the electron is a parabola, and derive an expression for the (horizontal) distance travelled.

    Difficulty: * (maybe **, depends how you go about it)
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    (Original post by lerjj)
    No-one's posted a question in a while (except for the two QM ones. Seriously, unless you two answer each other's questions...)

    Imagine an electron entering with a velocity v between two charged plates with potential difference V across them. The electron enters a vertical distance d from the +ve plate, where the plate separation is 2d. Show that the path of the electron is a parabola, and derive an expression for the (horizontal) distance travelled.

    Difficulty: * (maybe **, depends how you go about it)
    Isn't that just a projectile motion problem since the force is constant?


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    (Original post by langlitz)
    Isn't that just a projectile motion problem since the force is constant?


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    Yes, you could show that the force is constant I suppose. It's going to be difficult for me to write questions that most people on this thread find difficult, I suspect.
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    Will make the thread in a minute, any suggestion for names? How about: "The Proof is 'not-so' trivial - Physics Edition"
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    (Original post by lerjj)
    No-one's posted a question in a while (except for the two QM ones. Seriously, unless you two answer each other's questions...)

    Imagine an electron entering with a velocity v between two charged plates with potential difference V across them. The electron enters a vertical distance d from the +ve plate, where the plate separation is 2d. Show that the path of the electron is a parabola, and derive an expression for the (horizontal) distance travelled.

    Difficulty: * (maybe **, depends how you go about it)
    Spoiler:
    Show


    F=\dfrac{eV}{2d} = ma (1) - Force on electron due to electric field.

    Using a suvat for vertical motion towards the plate. s = ut + \frac{1}{2}at^2 u=0 in the vertical direction.

    y= \frac{1}{2}at^2 (2)

    Using (1)  a = \dfrac{eV}{2dm}

    Plugging this into (2) y= \dfrac{1}{2} \dfrac{eV}{2dm}t^2 \, \, \Rightarrow y = \dfrac{eV}{4dm}t^2 (3)

    The horizontal velocity, v, is constant, thus the distance travelled in positive x-direction is x = vt

    Thus, t = \dfrac{x}{v}

    Making equation (3) become;

     y = \dfrac{eV}{4dmv^2}x^2

    Proving the motion is parabolic.

    When the electron strikes the plate, it's vertical displacement is d.

     d = \dfrac{eV}{4dmv^2}x^2

    The horizontal distance travelled is just a rearrangement.

    x^2 = \dfrac{4md^2v^2}{eV}

    \Rightarrow

    x = 2dv \sqrt{\dfrac{m}{eV}}



    Might have some errors, rushed it.

    Will crack at the others later, new years dinner now!
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    (Original post by Phichi)
    Spoiler:
    Show


    F=\dfrac{eV}{2d} = ma (1) - Force on electron due to electric field.

    Using a suvat for vertical motion towards the plate. s = ut + \frac{1}{2}at^2 u=0 in the vertical direction.

    d = \frac{1}{2}at^2 (2)

    Using (1)  a = \dfrac{eV}{2dm}

    Plugging this into (2) d = \dfrac{1}{2} \dfrac{eV}{2dm}t^2 \, \, \Rightarrow d = \dfrac{eV}{4dm}t^2 (3)

    The horizontal velocity, v, is constant, thus the distance travelled in positive x-direction is x = vt

    Thus, t = \dfrac{x}{v}

    Making equation (3) become;

     d = \dfrac{eV}{4dmv^2}x^2

    The y displacement would be y = \dfrac{eV}{4dmv^2}x^2

    Proving the motion is parabolic.

    The horizontal distance travelled is just a rearrangement.

    x^2 = \dfrac{4md^2v^2}{eV}

    \Rightarrow

    x = 2dv \sqrt{\dfrac{m}{eV}}




    Might have some errors, rushed it.
    That looks correct.
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    Thread name suggestions? Gonna make it on my phone.

    My last post:

    Will make the thread in a minute, any suggestion for names? How about: "The Proof is 'not-so' trivial - Physics edition"


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    (Original post by Phichi)
    Thread name suggestions? Gonna make it on my phone.

    My last post:

    Will make the thread in a minute, any suggestion for names? How about: "The Proof is 'not-so' trivial - Physics edition"


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    Have you made it?

    Happy new year btw!
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    (Original post by langlitz)
    Have you made it?

    Happy new year btw!
    Making it shortly today, was hoping someone would give name suggestions.



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