# Does the classical aberration formula make sense?

• I
Kairos
I believe I have understood the formula of aberration of light ##\tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} \sqrt{1-\beta^{2}} ##

but I wonder if the non-relativistic formula ## \tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} ## has a physical relevance. Does this formula apply to a real physical situation (for sound ?) or is it just an approximation for small ## \beta ##?

Staff Emeritus
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Did you ever drive a car in rain? Did the rain seem to be coming from ahead?

• vanhees71
Kairos
Yes I did. But as the point of emission of the rain is not well defined, I have difficulty in defining ## \sin \theta ## and ## \sin \theta' ##

Staff Emeritus
Homework Helper
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Yes I did. But as the point of emission of the rain is not well defined, I have difficulty in defining ## \sin \theta ## and ## \sin \theta' ##
The emission point is irrelevant. The only relevant thing is the angle of the rain relative to the velocity of the car.

• vanhees71
Kairos
Does this mean that this formula is valid for an emission by a plane but not for a point source?

ergospherical
But as the point of emission of the rain is not well defined, I have difficulty in defining ## \sin \theta ## and ## \sin \theta' ##
##\theta## and ##\theta'## have nothing a priori to do with the emission point, they're related to the angle between the velocity of the particle and the coordinate axes i.e. ##\mathbf{v} = (v\cos{\theta}, v\sin{\theta})## and ##\mathbf{v}' = (v'\cos{\theta'}, v'\sin{\theta'})##.

Kairos
thank you