Path differenece of light ray to produce first minima

[desmond iking]

Homework Statement

for part a , in order to produce first minima from the central bright ray , the path differenece between 2 ray should be equal to λ/2 or 180 degree am i right? why the notes give the path
differenece = λ
...If path differenece = λ , the two light ray are in phase right? how can destructive intefrence occur?

Homework Equations

The Attempt at a Solution

 

[ehild]

In case of a single slit, the waves emerging from the upper half of the slit interfere with those, emerging from the bottom half.

So the ray starting from the upper edge of the slit interferes with the ray from the centre and their path difference should be half wavelength to produce the first minimum on the screen. The ray from the lower edge interferes also with a central ray.

That means (0.5a)sinθ=0.5λ --->a sinθ =λ

The other minima occur where (0.5a)sinθ=(0.5+k)λ that is when asinθ=(2k+1)λ

ehiild

 

[BvU]

Ha, here's Des again, violating copyright and PF rules simultaneously . Why would I want to help this guy ? Well, because he comes with interesting topics. And he saves his energy for when it really becomes complicated, I suppose.
This time I can be lazy too: just refer him (/her ?) to Fraunhofer diffraction !