Young's double slits exact formula without small angle approximation

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metalmaniac
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Have a look at this.

http://www.matter.org.uk/schools/content/interference/formula.html"

I follow the derivation of the formula. However it seems to follow from the diagram that:

λ=ssin(arctan(w/D))

Without the need for the approximation sinx ≈ tanx.

I can't see how this can be true because why would we use λ=sw/D if we have an exact form.
 
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Often you don't need the extra precision, and the approximation highlights the key concepts/features for a cursory understanding of the matter.
There's nothing wrong with the exact solution, of course.