Constructive and Destructive interference

thehabsonice

Hello guys I have a question about constructive/ destructive interference.

I know that in single slit and double slit patterns that the
dark fringes=destructive interference (minima)
bright fringes = constructive interference (maxima)

I do know that the formula's are as follows:
Single slit:
constructive: path differene= mlambda
(a)sin(theta)= m lambda where m=1,2,3,4 etc...
destructive: path difference= 1/2(m) (lambda)
(a) sin (theta)= (m)lambda where m= 1,3,5,7 etc...

double slit:
constructive interfernce: path differene= mlambda
(d)sin(theta)= m lambda where m=1,2,3,4 etc...
destructive: path difference= 1/2(m) (lambda)
(d) sin (theta)= (m)lambda where m= 1,3,5,7 etc...

So yes I would like you guys to tell me if these formula's are right.... i have been looking in my notes and it really isn't clear.

One last thing... how do you know if you have a constructive pattern or a destructive pattern just by looking at the quesition (if it doesn't tell you to find minima or maxima).


Thank you