Math Is Fun Forum

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)

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

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: physics/math problem

awww. doesnt work ah well, atleast i tried

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

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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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The Beginning Of All Things To End.
The End Of All Things To Come.

Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: physics/math problem

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

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: physics/math problem

Yeah, neat animation, luca, as always

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

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

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