12. one of the strongest emission lines observed from distant galaxies comes from hydrogen and has a wavelength of 122 nm(in the ultraviolet region).
a) how fast must a galaxy be moving away from us in order for that line to be observed in the visible region at 366 nm?
b) what would be the wavelength of the line if that galaxy were moving toward us at the same speed?
the book im using has the chapter separated into smaller sections as you read through it. so it has the problems separated into these same sections so you know what information to look for or need. book is modern physics 3rd edition by kenneth krane
so this question is in the consequences of einstein's postulates. the first one is the principle of relativity and the second one is the principle of the constancy of the speed of light. i do know that this problem would have to do with relativistic velocity addition.
The Attempt at a Solution
i don't know/understand how to develop equations from these two postulates. the book has an example with equations for the relativistic velocity addition but how does wavelength fit into this? this leads me to believe that i need to somehow draw a picture and develop specific equations for this problem. if this is the case, how do i go about doing such a thing with such minimal information? i know that i would need to use us(earth) as one observer point(o) and the other galaxy as another(o').
thanks for all your continued help.