I don't have a particular homework inquiry to ask, just some questions I have about thin-film interference and its related equations. I was told by my instructor to learn these concepts on my own and I am just having a few problems I want to clarify.(adsbygoogle = window.adsbygoogle || []).push({});

1)Equations related to thin-film interference

The only equation given about this concept is one relating wavelengths of light in vacuum and in film;[tex]\lambda[/tex] film = ([tex]\lambda[/tex] vacuum) / n

There aren't any others explicitly stated, but the examples uses some parts of some equations dealing with the previous section which is about Young's double-slit experiment. I believe the examples do not explain how the equations were manipulated or used. These equations are for constructive and destructive interference and use m, which is the order of the bright fringe, and d, the distance between the slits:

sin[tex]\theta[/tex] = m([tex]\lambda[/tex]/d); m=0,1,2,3....

sin[tex]\theta[/tex] = [m+(1/2)] ([tex]\lambda[/tex]/d); m=0,1,2,3....

In one specific example, a typical thin-film interface is presented where white light reflects off the film and yellow light is observed. In the interface, soap is surrounded by air. Destructive interference is said to occur, eliminating the blue color. A minimum thickness is asked for.

In presenting a solution and after calculating in-film wavelengths, the book states that the condition for destructive interference must be:

(m+(1/2))([tex]\lambda[/tex]film) =the sum ofthe extra distance travelled by wave(2) and the net phase change of the waves

where the extra distance travelled by wave(2) is denoted as2t, t being the thickness; and where the net phase change is (1/2)([tex]\lambda[/tex]film)

My questions so far are,how was that equation producedandhow is the value of m decided, this being destructive interference and when minimum thickness is asked for? (The book chooses m=1 for this purpose)

2)More Thin-Film Interference

Some problems given for exercise dealing with thin-film interference have a mixture of light reflected off the film, and therefore two wavelengths are given. Again, a minimum thickness is asked for where destructive/constructive interference occurs for both wavelengths.

My question ishow do I use both wavelengths to find a common thickness at where interference is occuring?

I'm guessing if my questions in 1) were answered, I'd be able to figure 2) out on my own.

So those are my main concerns for now, and I thank all in advance who try their best to help me clarify these points!!!

Thank you!

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# Homework Help: Thin Film Interference Help?

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