Understanding the Answer of 2sqrt(2)x - 2x = 2.5cm: 6.04cm

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The solution to the equation 2sqrt(2)x - 2x = 2.5 cm results in x = 3.02 cm. However, the final answer is stated as 6.04 cm due to the overall phase change of 180 degrees caused by reflection off mirrors. This phase change necessitates that the path difference equals the wavelength rather than half the wavelength, which is crucial for understanding the intensity conditions in wave interference scenarios.

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The answer to the attachment is 6.04 cm. But the intensity should be zero when the difference in path length is half a wavelength.

2sqrt(2)x - 2x = 2.5cm

x = 3.02 cm. However, how come the answer is 6.04cm in stead? Can some one please explain this to me thoroughly? Thanks in advance.
 

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can anyone explain this? thanks...
 
The overall phase change due to reflection off the mirrors is 180, thus the path difference needs to be the wavelenth, not 1/2.
 

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