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March 29, 2024, 07:39:29 pm

Author Topic: Optical Path Difference  (Read 3896 times)  Share 

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/0

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Optical Path Difference
« on: October 07, 2010, 02:45:12 pm »
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Can anyone who's done path differences or interference help me?

In the diagram we need to find the path difference between the two beams of light. The blue material has refractive index while the white material has refractive index . (refractive index of a medium is defined as: )

The book gives . (taking I presume)

However, my reasoning goes differently:...

In the blue material, the speed of light is , so in a time t it covers distance . The total distance traveled inside the blue material is (by trig), so .
In this same time , the total distance traveled outside the blue material is

Hence, . (assuming )
The cos theta is on the bottom
Taking ,
Can anyone see what's wrong? Thanks
« Last Edit: October 07, 2010, 02:58:07 pm by /0 »

appianway

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Re: Optical Path Difference
« Reply #1 on: October 30, 2010, 02:11:57 pm »
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Does path difference need to take time into account? Surely it's purely just the number of wavelengths that differ bewteen two paths. I thinkkk you need to compare this different at points A and D, as this is essentially the difference attributed to passing through the medium. The optical path length is defined as nL, where L is the actual length travelled (as the refractive index larger than 1 causes smaller wavelengths). So you just multiply dcostheta by two (as this gives the actual length) and then multiply this by n (which gives 2ndcostheta, as needed). I think you considered the time, which isn't relevant here - if you leave a torch shining for a period of time, you can still get interference between photons which were emitted later and photons which were emitted earlier.