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

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The equation 2sqrt(2)x - 2x = 2.5 cm leads to a calculated value of x = 3.02 cm, but the final answer is stated as 6.04 cm. The discrepancy arises from the phase change of 180 degrees due to reflection off mirrors, which requires the path difference to equal a full wavelength rather than half. This understanding clarifies why the expected answer differs from the initial calculation. The intensity should be zero when the path length difference is a full wavelength. Overall, the discussion emphasizes the importance of considering phase changes in wave interference problems.
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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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