If the path-length differences between two identical and coherent beams is two wavelengths when they arrive on a screen, will they produce a dark or a bright spot?
a. bright spotb. dark spot

Bright spot

Explanation:

When we have interference between two identical and coherent beams, the conditions for constructive interference (bright spots) and destructive interference (dark spots) are:

- Costructive interference: the path-length differences between the two waves is an integer multiple of the wavelength of the waves:

where the term on the left is the path difference, and is the wavelength

- Destructive interference: the path-length differences between the two waves is an odd multiple of half the wavelength of the waves:

In this problem, the path-length difference is 2 wavelengths: so, it is an integer multiple of the wavelength, therefore the point is a point of constructive inteference (bright spot).