Finding path difference of EM waves received by radio telecopes

AI Thread Summary
The discussion revolves around the calculation of path difference for electromagnetic waves received by radio telescopes. The initial attempt incorrectly identified the path difference as ##x = d \sin \theta##, while the correct formula is ##d \cos \theta##. The user realized their mistake and clarified that their calculation represented the difference between path lines, not the actual path length difference. A tip was provided to check results against extreme cases to avoid such errors. The conversation emphasizes the importance of understanding the distinction between path lines and path length in wave physics.
songoku
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Homework Statement
Please see below
Relevant Equations
Trigonometry
1626158609238.png


My attempt:
1626158751799.png

I think ##x## is the path difference so by using trigonometry, I got ##x=d \sin \theta##

But my teacher said the answer is ##d \cos \theta##

What is my mistake? Thanks

Edit: Sorry, I found my mistake. My ##x## is not the path difference
 
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OK, well done.

Tip: Always check a result for extreme cases (like here: ##\theta = 0## and ##\theta = \pi/2##)

##\ ##
 
songoku said:
My x is not the path difference
Well, it is the difference between the path lines, but not the path length difference.
 
Thank you very much BvU and haruspex
 
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