Two waves of light in air travel through a layer

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SUMMARY

The discussion centers on calculating the phase difference between two light waves traveling through different layers of plastic. Given the wavelengths and refractive indices, the calculations yield a phase difference of 5.71 radians after both waves emerge from the layers. The equations used include N1 = L1*n1/λ and N2 = L2*n2/λ, with the final phase difference expressed in radians rather than wavelengths. The confusion arises from interpreting the results, as the answer sheet presents the phase difference without units, which is deemed "bad form."

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Homework Statement



Two waves of light in air, of wavelength 550 nm, are initially in phase. They then both travel through a layer of plastic as shown in the figure, with L1 = 4.00 μm, n1 = 1.40, L2 = 3.50 μm , and n2 = 1.60. What is their phase difference after they both have emerged from the layers, when they arrive at the same point?
halliday_9e_fig_35_35-177-1408377159428.jpg


Homework Equations


N is the numbers of lemdas
N1=L1*n1/λ
N2=L2*n2/λ
N in air = (L1-L2)/λ n(air)=1

The Attempt at a Solution


N2+Nair-N2=0.909 but the correct answer is 5.71?
 
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"Phase difference" is an angle (in radians), not the number of λ's.
 
TSny said:
"Phase difference" is an angle (in radians), not the number of λ's.
What is the name of the difference in wavelengths?
 
Any Help said:
What is the name of the difference in wavelengths?
You could also call the difference in wavelengths the "phase difference". So, the answer of .909 wavelengths is a correct answer. However, does the answer of 5.71 include any units?
 
TSny said:
You could also call the difference in wavelengths the "phase difference". However, does the answer of 5.71 include any units?
no only number
 
Any Help said:
no only number
"Bad form" on the part of the answer sheet.
 
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