Intensity conservation during refraction

In summary, the problem can be solved by using the conservation of energy and rewriting the equation using Snell's law. This approach will lead to the same result as Mihallas - I_{\nu}n_{\nu}^{-2} being a constant.
  • #1
lakmus
23
1
Hi,
I try to solve excercises from the book Stellar Atmospheres by Mihallas. I'm stuck on this one:
By use of Snell's law,
[itex]n_1(\nu)\sin{(\theta_1)}=n_2(\nu)\sin{(\theta_2)}[/itex],
in the calculation of the energy passing through an unit area on the interface between two dispersive media with differing indices of refraction, show that
[itex]I_{\nu}n_{\nu}^{-2}[/itex]
is a constant.

Well I tried at firts write just conservation of energy for intensity (here is the assumption that all light goes thru the interface). From definition of intensity and rewriting and solid angle by
[itex]\mathrm{d}\omega=\frac{\mathrm{d}S \cos{\theta}}{r^2}[/itex]
I got:

[itex]I_1 \cos^2{(\theta_1)} = I_2 \cos^2{(\theta_2)}[/itex],
where index 1 is for light in the medium with refraction index [itex]n_1[/itex], index 2 analogically.
Using Snell's law does not helped to get right result.

So I tried calculate some reflection, but I could not get the right result like Mihallas - [itex]I_{\nu}n_{\nu}^{-2}[/itex] .

It's the firt exercise in the whole book, so I supose it should be easy, bud I can't find out, where I'm wrong.
Thank's for all advices!
 
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  • #2
The correct approach is to use the conservation of energy. Since the light is passing through an interface, the total energy must be preserved. From the definition of intensity, we can calculate the total energy of light in medium 1 and medium 2: I_1 n_1^2 = I_2 n_2^2 where n_1 and n_2 are the indices of refraction for the two media. Using Snell's law, we can rewrite this equation as: I_1 n_1^2 (\sin{\theta_1})^2 = I_2 n_2^2 (\sin{\theta_2})^2 Since sin{\theta_1} = sin{\theta_2}, we can thus rewrite the equation as: I_1 n_1^2 = I_2 n_2^2 which is the same as our original equation. Therefore, we can conclude that I_{\nu}n_{\nu}^{-2} is a constant.
 

1. What is intensity conservation during refraction?

Intensity conservation during refraction is a physical principle that states that the total intensity of light remains constant as it passes through a medium with a different refractive index. This means that the amount of light energy remains the same before and after refraction, but the direction and speed of the light may change.

2. How does intensity conservation during refraction relate to Snell's law?

Snell's law, which describes the relationship between the angles of incidence and refraction, is based on the principle of intensity conservation during refraction. This means that when light passes from one medium to another, the total amount of light energy remains the same, but is distributed differently due to changes in the direction and speed of the light.

3. Does intensity conservation during refraction only apply to light?

No, intensity conservation during refraction applies to all types of waves, including sound waves and water waves. The total energy of the wave remains constant, but the direction and speed of the wave may change as it passes through a medium with a different refractive index.

4. What happens to the intensity of light when it is refracted from a less dense medium to a more dense medium?

The intensity of light decreases when it is refracted from a less dense medium to a more dense medium. This is because the light is bending towards the normal and spreading out over a larger area, resulting in a decrease in the intensity of the light.

5. Can intensity conservation during refraction be violated?

No, intensity conservation during refraction is a fundamental physical principle and cannot be violated. The total energy of the light or wave must remain constant, even if the direction and speed of the wave change as it passes through a medium with a different refractive index.

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