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If the path-length difference between two identical and coherent beams is two wavelengths when...

Question:

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

Interference

If the difference between the optical path lengths of two co-propagating coherent rays equals an integer multiple of the wavelength {eq}\lambda {/eq}, the two reflected rays interfere constructively, since the maxima of the electric field coincide. If the difference between the optical path lengths coincides with an odd multiple of {eq}\lambda / 2 {/eq}, a minimum and a maximum of the electric field coincide and the interference is destructive.

Answer and Explanation:

A bright spot.

Two coherent waves interfer constructively, when the path difference between them is an integer multiple of the wavelength {eq}n \, \lambda {/eq}. This is the case here {eq}(n = 2) {/eq}. They interfer destructively, when the path difference is an odd multiple of half a wavelength.


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Constructive and Destructive Interference

from CLEP Natural Sciences: Study Guide & Test Prep

Chapter 8 / Lesson 16
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