Optical Path Length Difference & Constructive Interference: Normal Incidence

[fredrick08]

Homework Statement

Light falls at normal incidence onto a transparent film on a substrate as shown

i. what is the optical path length difference in the case of normal incidence?
ii. if nf>no and nf>ns, what is the condition for constructive interference in the case of normal incidence? explain your answer.

Homework Equations

OPL=nd

The Attempt at a Solution

ok I am studying for an exam and this qn has been on the last 2 exams, and i have absolutely no idea how to do it, it can't be that, just an understanding issue. ok i know that the OPL=nd, i got no idea what the questions is asking me, or how to do it, please can anyone give me some info?

 

[fredrick08]

anyone is it something like OPLn(AB+BA)=2nt?

 

[fredrick08]

anyone

 

[maverick_starstrider]

Your condition for constructive interference is such that twice the thickness of the glass is equal to an integer number of wavelength (the wavelength is taken from inside the film) MINUS Pi (because the rays reflected off the air-film boundary will be given a Pi phase boost because nf>no, however the rays reflecting off the film-substrate boundary will not, since ns<nf)

 

[fredrick08]

so it it just for constructive, 2ntCos(theta)=m*lambda and for destructive 2ntCos(theta)=(m+0.5)*lambda, when m is an integer?

 

[fredrick08]

so it it just for constructive, 2ntCos(theta)=m*lambda and for destructive 2ntCos(theta)=(m+0.5)*lambda, when m is an integer?

 

[Redbelly98]

No, but you almost have the right idea. As Maverick said, you need to account for the extra π phase shift that happens at A, but not at B. This is essentially equivalent to adding half a wavelength to the path difference.

 

[fredrick08]

ahh ok... so then for constructive interference it is the opposite? 2nt=(0.5+m)lambda... its the A and B part I am confused about, becasue some gets reflected and some goes straight through.. or something.

i understand but still lost lol, for part a. the phase difference is pi?

 

[fredrick08]

or is it (m-0.5)lambda?

 

[fredrick08]

sorry for some reason my computer is laggy and saying the same thing over and over again every time i make a post...

 

[Redbelly98]

ahh ok... so then for constructive interference it is the opposite? 2nt=(0.5+m)lambda

or is it (m-0.5)lambda?

Yes, either one of those would be fine.