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jk22
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Is the relativistic Snell's law : $$\frac {sin\theta_1}{sin\theta_2}=\frac {c_2}{c_1}\sqrt {\frac {c^2-c_2^2}{c^2-c_1^2}} $$ ? OR where could I check this ?
There is no proper time or frame applicable to a photon (or light in general). See our FAQ linked below. Thus, this question is meaningless. The question of refraction across a refraction boundary where one one medium is moving relative to the other is, on the other hand, a very meaningful question for which relativity predicts significant modifications to Snell's law, as noted in my prior post.jk22 said:Relativistic in the sense of local time of the photon through the medium not motion of the medium.
jk22 said:Indeed my question was not very clear :
So it is impossible to find the refraction law for a particle (not forcedly a photon) moving at speed c1 then c2 by passing to the frame 1 and then 2 computing the minimum and then come back to the rest frame of the interface ?
Trying to do the latter I came across : the following formula $$\frac{tan(\theta_1)}{tan(\theta_2)}\sqrt{\frac{1+(1-c_2^2/c^2)tan(\theta_2)^2}{1+(1-c_1^2/c^2)tan(\theta_1)^2}}=\frac{c_1}{c_2}$$
Which does not give Snell's law back. I then thought that it is because it lacks a point like infinite acceleration at the interface. Hence doing this problem would need an accelerated frame with a continuous acceleration and then take the limit of the time of the acceleration to zero ? Then computing the minimal time in the moving frame would need the covariant derivative (concept of General relativity).
So I suppose finding Snell's law by passing to a moving frame is simply impossible due to a to high complexity.
Relativistic Snell's law is a formula that describes how light bends at the interface between two different materials. It takes into account the effects of both relativity and the change in light speed as it moves through different materials.
The traditional Snell's law only takes into account the change in light speed as it moves through different materials, while Relativistic Snell's law also considers the effects of relativity, such as time dilation and length contraction.
Relativistic Snell's law tells us that light will bend towards the direction where it travels slower, and that the angle of refraction is dependent on the relative speeds of light in the two different materials.
Relativistic Snell's law is useful in understanding the behavior of light in different materials, such as in fiber optics and lenses. It is also important in the field of astrophysics, where the effects of relativity must be taken into account when studying the bending of light in space.
Yes, Relativistic Snell's law can be applied to any type of wave, not just light. It can be used to describe the behavior of other electromagnetic waves, as well as sound waves and water waves.