HELP pls with Young's double slit experiment formulae (1 Viewer)

[dantheman2211]

Hey guys can someone pls explain how to derive the fringe spacing equation?? y=λL/d
I know that we use the small angle approximation but what angle are we even talking about??
Like I've tried asking Chatgpt and gemini and everything but it doesnt want to explain the relationship between theta, alpha and beta in my diagram attached.
Can someone please explain whats going on.

Thanks

 

[cheesynooby]

beta is equal to theta (you can derive that fairly easily) and that's approximately equal to the angle in the triangle formed by y and L
then tantheta = y/L = sintheta for small theta so you can sub that into the equation on the formula sheet

you don't really need to understand it for the hsc though, you can pretty much just quote the small angle approximation and most cases you won't need the formula anyway (just the relationship between theta, y and L)

 

[dantheman2211]

Thanks for replying so quickly
So the hypotenuse would be from the centre of the two slits to point P right?
So we are just approximating that beta is equal to the angle formed by the line from S2 to P cause the lines are almost parallel
i think i understand know

 

[justletmespeak123]

you need linear algebra and matricies to derive formula

 

[CirrusTheJet]

No, you don't need such maths. If you graph y=tanx and y=sinx, you will notice that tanx is approximately equal to sinx for when x is a small value