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

## Homework Statement

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
region2

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

## Homework Equations

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

## 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'

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TSny
Homework Helper
Gold Member
sinθ/sinθ'=v/v' [where v=velocity of particle in 1 & v'in 2]
Are you sure this equation is correct? If Vo is positive, which would be larger: v or v'? θ or θ'?

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.

Are you sure this equation is correct? If Vo is positive, which would be larger: v or v'? θ or θ'?
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.

TSny
Homework Helper
Gold Member
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?

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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?
No.
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?
No.

TSny
Homework Helper
Gold Member
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?