5. The path length difference for the waves exiting the two slits of the double slit experiment must be equal to for a bright fringe to appear.

An integral or whole multiple of the wavelength λ

or d sin θ = mλ,

for m = 0, 1, −1, 2, −2, ...,

Explanation:

In the double slit interference pattern, if we consider how two waves travel from the slits to the screen, we'll see that each slit is a different distance from a given point on the screen hence, they posses different wavelengths. Waves in a double slit experiment will be in phase if they interfere constructively by starting out crest to crest, or trough to trough. If the waves arrive crest to trough, they will interfere destructively, and arrive out of phase. A constructive interference occurs when the path length difference of the waves exiting the two slits forms an integral multiple of wavelength at the screen. A destructive interference occurs if the path length  differs by half a wavelength. Constructive interference forms the bright fringes, while the dark fringes are formed by destructive interference.

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