Light Interference: Find Condition of d for Constructive Interference

[Hamal_Arietis]

Homework Statement

[/B]
Find condition of d that constructive interference occurs
with m=1,2,3,...
a)$(m-\frac{1}{2})\frac{\lambda}{2}$
b)$m\frac{\lambda}{2}$
c)$(m-\frac{1}{2})\lambda$
d)$m\lambda$

Homework Equations

optical path difference (OPD) must equal $m\lambda$

The Attempt at a Solution

The optical path difference i finded is:
$$2d+\frac{\lambda}{2}=m\lambda$$
So $d=(m-\frac{1}{2})\frac{\lambda}{2}$ and I choose A
But the answer is B)$d=m\lambda$
Where is wrong?
Thanks for helping

 

[TSny]

Your work looks correct to me. I also think (a) is the right answer.