# Single Slit Diffraction issue with derivation

When deriving the minima, the classical approach is to say

$$\frac d 2 \sin(\theta) = \frac{\lambda}2$$

therefore, $$d \sin(\theta) = \lambda$$ It can then be shown for any integer value of $$\lambda$$. But why couldn't you say that the 2 point sources that interfere destructively are the full width of the slit apart, so $$d\sin(\theta) = \lambda/2$$, therefore $$d\sin(\theta) = \lambda/2$$ for destructive interference, which wouldn't be an integer. Maybe I've misunderstood something.

• What about the sources in between the first and last sources? They are not interfering destructively. – user258881 Apr 25 '20 at 12:06

you really are misunderstanding. You should consider the slit as the source of many or n elementary waves, so every elementary wave of the first half has the Difference $$\lambda/2$$ to one of the second half, while in your picture only two of the n waves have the difference of 1/2 all the rest have less, so the amplitude will be smaller, but never zero