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
Homework Helper
Gold Member
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
Gold Member
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