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Old 01-04-2009, 09:29 PM #1
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Default All members please read, optics info...

;D ;D ;D A little physics... ;D ;D ;D

Seeing as there are often many questions about optics and why things act the way they do, I thought I would write up this.

Starting out at basics.


Electromagnetic waves:

Electromangetic waves consist of an oscillating electrical field and magnetic field at right angles to eachother. These waves vary based on frequency and wavelength. This relationship can be defined as

C=FW

Where C is the speed of light in a medium, F is the frequency of the wave, and W is wavelength.


Index of Refraction

C, the speed of light measured in a vaccum is 299,792,458 meters per second. This speed changed based on the density of the medium the wave is traveling through. The speed in a meduim can be found using it's index of refraction. Index of refraction is the ratio between the speed of light in a vaccum and the speed of light in a medium. This equasion is defined as:

Index of refraction = speed of light in a vacuum / speed of light in medium

A good way to think of Index of refraction is the viscosity of liquid. If you toss a stone into a pond, when the stone hits the water, it will slow down. Same with light, if you send light from air to glass, it will slow down.


Snell's Law

If you have ever put a straw in a glass of water, it appears to bend where it meets the surface. This change in angle can be explained with Snell's law.

Snells law states

First medium Index of Refraction(sine of angle of incidence)= second medium index of refraction (sine of angle of refraction)

That being said, I think it is time for a graphic:



In this picture, Angle 1 is the angle of incidence, angle 2 is the angle of refraction, N1 is the refractive index of the first material, and N2 is the refractive index of the second medium.


Lens Equasion

The lens equasion can be used to find locations of the image and objects in lenses. The object is the source of the light. Remember to keep your units in perspective. If you use 10cm for one measure, you can't use 1m for the other, you would have to use 100cm.

The lens equasion is pretty simple, it states

_______1________ + ________1_________ = ________1_______
* * Object Distance * * * Image Distance * * * * *Focal Length

The magnification of a lens can also be found using this equasion:

Magnification = Image Height
* * * * * * * * * * Object Height

Or, if you have different information you can use


Magnification = Image Distance
* * * * * * * *Object Distance


Total Internal Reflection

This is why prisms work, why that clear lens in your flashlight works, why fiber optic cables work, etc...

Total internal reflection is a phenomena that happens when a beam of light is traveling from a medium with a high index of refraction to one with a lower index of refraction. The critical angle is the angle at which the light will no longer leave the medium, but rather reflect off the transition area.

The critical angle can be defined as:

[img]http://upload.wikimedia.org/math/7/f/9/7f91dcc3a57bdde7b3b81318c379379f.png[img]

Where the critical angle is equal to the inverse sine of the higher index of refraction devided by the lower index of refraction.

The result of total internal reflection looks like this:





This is all I have at the moment, I will continue to update this post with more information.


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Old 01-30-2009, 09:23 PM #2
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Default Re: All members please read, optics info...

equasion = equation

Great post!! In your equation C=FW, the wavelength and frequency are in what units? Nanometers, THz?
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Old 01-30-2009, 11:58 PM #3
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Default Re: All members please read, optics info...

^Just use meters and Hz to keep it in nice, roung SI units. *Hz = s^(-1), so m * s^(-1) = m/s = nice units for speed. *And with SI, as long as you keep everything consistently on the same "level" (m, s, kg, J, etc), then your answers will typically come out in a nice unit as well. *

For instance, if you keep speed in m/s, wavelength in m, keep your f & w straight (frequency in Hz and rad, just a factor of 2pi between them), use Planck's constant in J*s, your photon energy will come out right every time. *Then, you can convert to a unit that you want. *If you start worrying about "this is in nm, but this it in GHz, but I only remember h in eV*s", then you'll end up with screwy results that are tougher to translate to the unit you want.

And, as long as you stay in SI, you can always do cool stuff like this (this is from an actual HW problem a couple weeks ago, just checking to make sure my units came out right; I've had a couple even more complicated, but I haven't gotten those back graded yet so I don't remember how they came out):

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Old 01-31-2009, 12:24 AM #4
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Default Re: All members please read, optics info...

Quote:
Originally Posted by pullbangdead
^Just use meters and Hz to keep it in nice, roung SI units. *Hz = s^(-1), so m * s^(-1) = m/s = nice units for speed. *And with SI, as long as you keep everything consistently on the same "level" (m, s, kg, J, etc), then your answers will typically come out in a nice unit as well. *

For instance, if you keep speed in m/s, wavelength in m, keep your f & w straight (frequency in Hz and rad, just a factor of 2pi between them), use Planck's constant in J*s, your photon energy will come out right every time. *Then, you can convert to a unit that you want. *If you start worrying about "this is in nm, but this it in GHz, but I only remember h in eV*s", then you'll end up with screwy results that are tougher to translate to the unit you want.

And, as long as you stay in SI, you can always do cool stuff like this (this is from an actual HW problem a couple weeks ago, just checking to make sure my units came out right; I've had a couple even more complicated, but I haven't gotten those back graded yet so I don't remember how they came out):
Makes perfect sense.. Thanks! It's been awhile since I did any physics-related math outside of the usual basic electronics-related stuff...
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Old 01-31-2009, 12:28 AM #5
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Default Re: All members please read, optics info...

^No problem. Physics-related math is my life right now. My classes right now are the nitty-gritty physics of how materials work - using quantum mechanics to build the framework for the electronic properties of materials, which really the electronic properties are what determine ALL the other properties of materials, all of chemistry, everything. It's all about the electrons.
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Old 01-31-2009, 12:46 AM #6
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Default Re: All members please read, optics info...

Quote:
Originally Posted by pullbangdead
^No problem. *Physics-related math is my life right now. *My classes right now are the nitty-gritty physics of how materials work - using quantum mechanics to build the framework for the electronic properties of materials, which really the electronic properties are what determine ALL the other properties of materials, all of chemistry, everything. *It's all about the electrons. *

It's not often I run into someone who understands that.. What are you studying for?
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Old 01-31-2009, 01:03 AM #7
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Default Re: All members please read, optics info...

I'm a Ph.D student in materials science. This class is the 2nd in the 3-course core/required class sequence on the fundamentals of materials at the graduate level. It really just goes through enough quantum mechanics to prove the solid state theory presented, and so I'm also taking an in-depth quantum mechanics course at the same time.

Yeah, it's cool stuff, those electrons. It's like my wife asked just the other night when talking about some of my coursework, "So once you have the wave equation for the electrons, what does that do? What does it tell you?" And I just had to laugh, "Everything. Literally."
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Old 01-31-2009, 01:53 AM #8
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Default Re: All members please read, optics info...

Shit, if my wife said something like that to me, I think I might pass out.. She's an extremely intelligent person, don't get me wrong, but I'm pretty much stuck holding deeply intellectual scientific conversations with other parties..

Sounds to me like you're into some deep stuff there.. how long till you're done?
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Old 01-31-2009, 02:06 AM #9
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Default Re: All members please read, optics info...

I'm first year, the average for my group is right around 5 years, so I've got a while to go. Not sure exactly how long, some do it in 3-4, some take 6, but either way I'm just getting started. I'll be done with classes after 2 years though, and that's by far the worst part.

It's terrible at times, but it can be fun at times as well.
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Old 01-31-2009, 02:43 AM #10
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Default Re: All members please read, optics info...

^sent you a PM
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