Change of Frequency Through Different Medium

In summary: In the first medium, v=c/n. So,λ=c/fand in the second medium,λ=N/fTherefore, the wavelength of the light in the first medium is longer than the wavelength of the light in the second medium.
  • #1
stongio
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0

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 [tex]\delta[/tex]f 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



[tex]\lambda[/tex]=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?
Picture45.jpg

sorry about the huge image couldn't figure out how to resize it >:/
 
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  • #2
Welcome to Physics Forums.
stongio said:
In terms of f , c , n , N , a , b , A , B , or a subset of these quantities what is the change in frequency [tex]\delta[/tex]f 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.
 
  • #3
Yes, this is only the first half of the problem, but it does ask for change in frequency. And you are right [tex]\lambda[/tex]= 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[tex]\theta_{1}[/tex] = N sin[tex]\theta_{2}[/tex]

or

n[tex]\frac{a}{A}[/tex]=N[tex]\frac{b}{B}[/tex]

also,

The time, [tex]\tau[/tex] = [tex]\frac{A}{v_{1}}[/tex] = [tex]\frac{B}{v_{2}}[/tex]

where v[tex]_{1}[/tex] is the velocity of light in medium with index of refraction n, and v[tex]_{2}[/tex] 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.
 
  • #4
stongio said:
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 :wink:

Also remember that [tex]E = h \nu [/tex] for a photon, so for its frequency to change, energy would have to come from somewhere...
 
  • #5
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, [tex]\delta\lambda[/tex]?
 
  • #6
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
 

What is change of frequency through different medium?

Change of frequency through different medium refers to the phenomenon of a change in the frequency of a wave as it travels from one medium to another. This change can be caused by various factors, such as the change in the speed of the wave or the change in the wavelength.

How does the change of frequency occur?

The change of frequency occurs due to the difference in the properties of the two mediums. When a wave travels from one medium to another, its speed and wavelength change, which results in a change in its frequency. This change can also be affected by the density and temperature of the mediums.

What is the relationship between frequency and wavelength?

Frequency and wavelength are inversely proportional to each other. This means that as the frequency of a wave increases, its wavelength decreases and vice versa. This relationship is expressed by the formula: v = fλ, where v is the speed of the wave, f is the frequency, and λ is the wavelength.

How does the change of frequency affect the wave's properties?

The change of frequency can affect the wave's properties in various ways. For example, a higher frequency means a higher energy and a shorter wavelength, which can result in more powerful and dangerous waves, such as X-rays and gamma rays. On the other hand, a lower frequency can result in less energy and longer wavelengths, which can be used for communication purposes, such as radio waves.

What are some real-life examples of change of frequency through different mediums?

Some real-life examples of change of frequency through different mediums include the change in the color of light as it passes through a prism, the change in the pitch of sound as it travels from air to water, and the change in the frequency of radio waves as they travel through different materials, such as buildings and mountains.

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