Change of Frequency Through Different Medium

[stongio]

Homework Statement

A beam of light of frequency f is shot from point P in medium one ( refractive index = n ) to a point Q in medium two ( refractive index = N ) . Imagine a plane interface separates the two mediums. The perpendicular distance from P to the plane interface is a . The perpendicular distance from Q to the plane interface is b .The distance from P to where the beam intersects the plane interface is A . The distance from Q to where the beam intersects the plane interface is B . The speed of light in vacuum is c .

In terms of f , c , n , N , a , b , A , B , or a subset of these quantities what is the change in frequency \deltaf as the light passes from medium one to medium two . Give your answer for the two cases where N > n and N < n and indicate whether the shift is up or down as the light moves from mediul one to medium two.

Homework Equations

\lambda=c/f

The Attempt at a Solution

I tried to mess around with the geometry to calculate the change in speed and then convert that to change in frequency, but it just doesn't make any sense to me. Wouldn't the frequency only change if the second medium had a different polarization? If so, is it possible to compute this change using the given data?

sorry about the huge image couldn't figure out how to resize it >:/

 

[Redbelly98]

Welcome to Physics Forums.

In terms of f , c , n , N , a , b , A , B , or a subset of these quantities what is the change in frequency \deltaf as the light passes from medium one to medium two . Give your answer for the two cases where N > n and N < n and indicate whether the shift is up or down as the light moves from mediul one to medium two.

Are you sure they ask for change in frequency?

3. The Attempt at a Solution
I tried to mess around with the geometry to calculate the change in speed and then convert that to change in frequency, but it just doesn't make any sense to me. Wouldn't the frequency only change if the second medium had a different polarization? If so, is it possible to compute this change using the given data?

Can you show your work please?

Note: the equation λ=c/f is only true when n=1. For n≠1, you need to use the speed of light in the medium of index n.

 

[stongio]

Yes, this is only the first half of the problem, but it does ask for change in frequency. And you are right \lambda= c/f is only true for n=1... I meant to write v/f.

Ok I have been having a lot of trouble conceptualizing the change in frequency but here is what i know:

v=c/n

n sin\theta_{1} = N sin\theta_{2}

or

n\frac{a}{A}=N\frac{b}{B}

also,

The time, \tau = \frac{A}{v_{1}} = \frac{B}{v_{2}}

where v_{1} is the velocity of light in medium with index of refraction n, and v_{2} is the velocity of light with index of refraction N.

I just have no idea how to arrive at an equation for change in frequency. Perhaps I need to take the derivative of time with respect to distance? I'm really lost.

 

[berkeman]

Yes, this is only the first half of the problem, but it does ask for change in frequency.

Hint: Remember that zero is a valid answer for the change in frequency

Also remember that E = h \nu for a photon, so for its frequency to change, energy would have to come from somewhere...

 

[stongio]

Yes, I was thinking that might be the case. However, the frequency of light can change if the second medium has a different polarization. I don't know much about polarization but is it possible that the parameters listed in the problem would be indicative of a polarization change?
And how would one go about solving for the change in wavelength, \delta\lambda?

 

[Redbelly98]

I'm unaware of a polarization change ever causing a change in frequency, and at any rate there is nothing here that indicates a polarization change happens.

If the frequency does not change, and we know how speed depends on wavelength, then it's possible to see what happens to wavelength using f=v/λ