A ray crossing 2 media of different indices and energy conservation

In summary, the conversation discusses the intensity of rays and solid angles. The equation p75 is being discussed and there is confusion about its form, which appears to be the projection of intensities along the x-axis. It is noted that only the total energy going through dS should matter, and there is a suggestion that ##I_1## may be independent of spacetime coordinates and large enough to wrap around dS. However, there is uncertainty about this and the reasons for it.
  • #1
Paulpaulpa
6
2
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The ##I_i## are the intensity of the rays, in other words energy per surface units per radians by seconds.

The d##\Omega## are the solid angles

The equation p75 isis what I don't understand. I suppose that each side represent the energy going and out of the surface dS but I don't understand why it has this form. It looks like the projection of the intensities along the x-axis, as if energy was a a vector quantity (like the momentum, for which the three components are conserved separately). But only the total energy going through dS should matter and I don't understand why it has this form.

If we say that ##I_1## is independant of the spacetime coordinates and is large enough to wrap around dS, the energy going in should be ##I_1 d\Omega dS## since the surface is totally exposed to the ray. I am probably wrong but I don't know why.
 
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  • #2
Some energy is reflected.
 
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FAQ: A ray crossing 2 media of different indices and energy conservation

What is a ray crossing 2 media of different indices?

A ray crossing 2 media of different indices refers to a situation where a light ray travels from one medium to another, where the two media have different refractive indices. This can occur, for example, when light travels from air to water, or from water to glass.

How does the refractive index affect the path of the light ray?

The refractive index of a medium is a measure of how much the speed of light is reduced when it travels through that medium. When a light ray crosses from one medium to another with a different refractive index, it will change direction, or refract, due to the change in speed.

What is energy conservation in the context of a ray crossing 2 media?

Energy conservation refers to the principle that energy cannot be created or destroyed, only transferred or transformed. In the context of a ray crossing 2 media, this means that the total energy of the light ray remains constant as it travels from one medium to another, even though its direction and speed may change.

How does the angle of incidence affect the path of the light ray?

The angle of incidence is the angle at which the light ray hits the interface between the two media. The angle of refraction, or the angle at which the light ray changes direction, is determined by the angle of incidence and the refractive indices of the two media. As the angle of incidence increases, the angle of refraction also increases, causing the light ray to bend more.

What is Snell's law and how does it relate to a ray crossing 2 media?

Snell's law is a formula that relates the angles of incidence and refraction to the refractive indices of the two media. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media. This law helps to predict the path of a light ray as it crosses from one medium to another with a different refractive index.

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