Aberration of Light: Understanding Transformation Equations for Coordinates

[BareFootKing]

Homework Statement

http://s22.postimg.org/5vp0p2aox/Untitled.png

Homework Equations

The Attempt at a Solution

Here is the solution

I understand everything that must be done after one find the correct transformations for the two coordinates, but I don't understand why the transformation for y' has a minus R at the end. I would think y' = the first two terms x¬0cos + y¬0sin

 

[mfb]

What is ¬?

The last term comes from the squaring of [highlight]+[/highlight] y₀sin(wt) [highlight]-[/highlight] R

 

[BareFootKing]

Sorry, the" ¬" of "y¬0" was not suppose to be there. I was typing my post on word and copied and pasted it to the forum. I meant I thought that y' = x_ocos(wt) + y_osin(wt). Why is there a minus R term for y' and not for x'. I understand if it had the R term and we squared y' and x' and add them up and take the square root we would get the numerator shown in the final answer. But I didn't understand why y' had the minus R term in the begging.

 

[mfb]

Ah, that R.
At the considered point in time, you are at (0,R), so you have to subtract this R to get to the origin again.

 

[Nickie]

+ R.

As a scientist, it is important to not only understand the equations and their solutions, but also the reasoning behind them. In this case, the aberration of light phenomenon can be explained by the motion of the observer and the finite speed of light. The minus R at the end of the transformation for y' represents the correction needed due to the motion of the observer. As the observer moves, the light from the object will reach their eyes at a different angle, causing a shift in the y' coordinate. This shift is represented by the minus R term in the equation. Without this correction, the coordinates would not accurately represent the true position of the object as seen by the observer. Therefore, it is essential to include this term in the transformation equations to properly account for the aberration of light phenomenon.