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Consider the potential field V(x, y) which is 0 and -Vo(Vo>0

  1. Apr 5, 2017 #1
    1. The problem statement, all variables and given/known data
    Consider the potential field V(x, y) which is 0 and -Vo (V0 > 0) respectively in the regions
    of y greater and less than zero . Let θ and θ' be the angles of incidence and refraction of
    the particle with the y-axis at the point of incidence as it crosses the x-axis . The ratio
    sin(θ) / sin(θ ') is given (in terms of Δ = Vo / E) by
    region1
    upload_2017-4-5_19-53-33.png region2



    (a)√(1+2Vο/E)
    (b)√(1+Vο/E)
    (c)1+Vο/E
    (d)1+2Vο/E

    2. Relevant equations
    nsinθ=n'sinθ'
    sinθ/sinθ'=v/v'[where v=velocity of particle in 1 & v'in 2]

    3. The attempt at a solution
    1/2mv2=E=1/2mv'2-Vο
    1/2mv'2-1/2mv2=Vο
    (v'2 -v2)/v2=2Vο/mv2
    (v'2 /v2 )-1=Vο/(1/2mv2)
    ∴sinθ'/sinθ=√(1+Vο/E)

    Which is similar to option b but in question it is sinθ/sinθ'
     
    Last edited: Apr 5, 2017
  2. jcsd
  3. Apr 5, 2017 #2

    TSny

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    Are you sure this equation is correct? If Vo is positive, which would be larger: v or v'? θ or θ'?
     
  4. Apr 6, 2017 #3
    I have just used snell's law.
    θ∝v
    but I am not sure about increase or decrease of kinetic energy in the presence of potential +ve or -ve.
     
  5. Apr 6, 2017 #4
    I have just used snell's law.
    θ∝v
    but I am not sure about increase or decrease of kinetic energy in the presence of potential +ve or -ve.
     
  6. Apr 6, 2017 #5

    TSny

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    This problem deals with a particle moving from a region of zero potential energy to another region of constant potential energy -Vo.

    For this situation, Snell's law as written for light ##\frac{\sin \theta_1}{v_1} = \frac{\sin \theta_2}{v_2}## does not apply. Have you covered how Snell's law is modified for the particle situation?
     
    Last edited: Apr 6, 2017
  7. Apr 6, 2017 #6
    No.
    No.
     
  8. Apr 6, 2017 #7

    TSny

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    Then you will need to derive "Snell's law" for the particle.

    As a start, consider the x and y components of the velocity of the particle.
    Does vx change when the particle passes through the origin?
    Does vy change?
     
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