Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #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)

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

Offline

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

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)

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

Offline

## #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)

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

Offline

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

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

Offline

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

MathsIsFun
Registered: 2005-01-21
Posts: 7,664

### Re: physics/math problem

Yeah, neat animation, luca, as always

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

Offline

## #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

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

Offline