Determining types of interference

[jaejoon89]

How do you determine whether two rays of light will constructively or destructively interfere? Is it possible neither can occur?

I'm just trying to figure it out for the basic case where they are separated by 'd' in the diffraction grating and later meet up at a point.

My TA said you should divide the length of each ray or something and get a rational number, but that doesn't quite make sense.

 

[Redbelly98]

First you would calculate the difference in path length for the two rays.

If the path difference is an integer multiple of the wavelength, the rays interfere constructively.

If the difference is a "half-integer" multiple of the wavelength, i.e.

(n + ½) λ, where n is an integer​

then the two rays interfere destructively.

If the path difference is anything else, the interference is somewhere in between fully destructive and fully constructive.