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We look at thin film interference.


Thin films

Suppose there is a very thin film of dielectric and light is incident on it normally. Lets consider single reflections. (We make the small angle ofincidence approximation)

We will assume n 3 > n 2 > n 1 . The physical path length difference of the reflected light is Δ r = 2 d . We will get maxima in the interference when: Δ r = 2 d = m λ 2    m = 1 , 2 , 3 where λ 2 is the wavelength in the film. Now λ i ν i = c / n i . In our example we have ν 1 = ν 2 = ν 3 , that is the frequency does not change moving between the media. So we have λ 1 n 1 = λ 2 n 2 = λ 3 n 3 . Thus constructive interference will happen when λ 2 = λ 1 n 1 n 2 2 d = m λ 2 m = 1 , 2 , 3 . . 2 d = m λ 1 n 1 n 2 2 d = m λ a i r n a i r n f i l m 2 d = m λ 1 1 n f i l m ( 2 d ) n f i l m = m λ a i r m = 1 , 2 , 3 where n f i l m = n 2 . Destructive interference will happen when ( 2 d ) n f i l m = m λ a i r / 2 m = 1 , 3 , 5

When destructive interference occurs then that value of λ is not reflected. Note that this is a function of both d and λ . The next effect is that different colours of light get reflected at differentthicknesses of the film. This is why soap films or oil films on water give rainbow effects.

Note I have assumed that n 3 > n f i l m > n a i r in the above, where n 3 is the material that the film sits upon.

Consider an interface between two materials with indices of refraction n 1 and n 2 . If n 2 > n 1 . Then lets examine what happens to the phase of an electromagnetic wave uponreflection. For a transverse electric field, there is a phase change of π . For the transverse magnetic field (or E ) there is not, if the light ray is close to the normal. However if n 1 > n 2 then and the situation is reversed and the transverse electric field does not undergo a phase change and the transverse magnetic field does. In the exampleabove, their will be no relative phase change between the rays in either case. Either both will change by π or neither will change, depending on the orientation of the E field.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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Damian Reply
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
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for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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Source:  OpenStax, Waves and optics. OpenStax CNX. Nov 17, 2005 Download for free at http://cnx.org/content/col10279/1.33
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