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The Huygens-Fresnel principle, reflection and refraction

The huygens-fresnel principle

In order to proceed with the discussion we have to define two terms. A wave front is the surface of constant phase. In a plane wave these are planes andin a spherical wave these are spheres. A ray travels perpendicular to the fronts.

Huygens postulated that as a wave propagates through a medium each point on the advancing wavefront acts as a new point source of the wave. This iscorrect physics for the water waves but not for light waves. However the Helmholtz equation for diffraction of EM waves gives a solution identical tothat give by Huygens' principle.

Look at the figure which shows a wavefront AB coming to a surface and is reflected creating the front CD. The point A hits the surface first. The pointB hits a time v t later. During that time a spherical wave is emitted from A and travels a distance v t . In fact this happens for every point along the wavefront. The next figureattempts to show how a number of waves line up along the line DC and that this is perpendicular to the line AD.

From this we see that sin θ i = v t A C and sin θ r = v t A C so θ i = θ r

For refraction a similar thing happens. See figure (geometric optics / Huygens refraction.vsd )

In this case the velocities are different in the two media and so one obtains: sin θ i = v i t A C and sin θ t = v t t A C which then can be rearranged sin θ i v i t = sin θ t v t t or rearranging some more sin θ i sin θ t = v i t v t t or sin θ i sin θ t = n t n i finally n t sin θ t = n i sin θ i which is Snell's law. Now note that normally one uses rays, in which case the anglesare measured w.r.t. the normal to the surface.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
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Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
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?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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