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#1 2007-02-11 09:18:44

Kurre
Member
Registered: 2006-07-18
Posts: 280

physics/math problem

here is a math/physics problem or exercise that i made:p

You have a disc made of glass formed as shown in the picture. The edge of the disc is described by the function 4 - x².
a light beam is launched straight down at the point (x,f(x)) where it is refracted and hits the X-axle.

Your task is to describe how the distance a depends on the distance x, in other words the function a(x) smile

the law of refraction is:


where V1 is the angle of incidence, V2 the angle of refraction and N1 is the refractive index for air (1) and N2 is the refractive index for glass (1,52)


i will post my solution later smile

View Image: maopt_upg.JPG

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#2 2007-02-12 08:48:34

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: physics/math problem


awww. doesnt work yikes ah well, atleast i tried

Last edited by luca-deltodesco (2007-02-12 08:48:46)


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#3 2007-02-12 08:52:03

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: physics/math problem

actually. when refraction occurs, the refracted ray is in the opposing side of the normal, so r is negative to what i have above, and plugging that in, it does seem to work.

http://denvish.net/ulf/1171313711_grah.php

Last edited by luca-deltodesco (2007-02-12 08:55:21)


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#4 2007-02-12 09:31:53

Kurre
Member
Registered: 2006-07-18
Posts: 280

Re: physics/math problem

nicely done, and cool "animation" smile
i think I got the same graph as you, altough my function is way different from your..interesting smile

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#5 2007-02-12 12:29:02

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: physics/math problem

Yeah, neat animation, luca, as always smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#6 2007-02-16 05:34:16

Kurre
Member
Registered: 2006-07-18
Posts: 280

Re: physics/math problem

Here is my solution:

the derivative of the function will be the same as -tan for the corner in the tangent, since


(its negative since the curve is going down)
V being the angle in the corner of the triangle that the function for the tangent in (x,f(x)) creates.
V will be the same as the angle of incidence
(see picture)

B=angle of refraction


i think it works, it is maybe possible to short it down

View Image: maopt_upg2.JPG

Last edited by Kurre (2007-02-16 06:39:08)

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