in <3A7092D8.7B3FE2F2@psu.edu> Paul Daniel Jones wrote:

>ARGH!!!  I am trying to make a lens which will generate parallel beams
>of light with a spotlight put at it's focal point. I have tried using
>some formulae from my physics book, but just can't get it. Is there
>anybody out there who could help me?

Don't use a spotlight.

light_source {<9, 0, 0> rgb 1}  

#declare Lens = difference {  // f=5 units
   sphere{0,2.5}
   box{<0,-3,-3>,<3,3,3>}
   texture{T_Glass1}
   interior{ior 1.5}
}   

object {  //condensor, mak parallel beam
   Lens
   photons {
      photons_pass_through
   }
   translate <4,0,0>
}



Ingo

-- 
Photography: http://members.home.nl/ingoogni/
Pov-Ray    : http://members.home.nl/seed7/

Post a reply to this message

A beam from the focus going directly horizontal should be reflected directly
upward, which means that the parabola at that point has a slope of 1 or -1.
Since the beam is horizontal, it gives us the y-coordinate of the focus.
So...

d/dx (a*x^2+b*x+c) = 2*a*x+b
2*a*x+b = 1    ==>   x = (1-b)/(2*a)
y = a*x^2+b*x+c   ==>   y = (4*a*c-b^2+1)/(4*a)

Similarly with the x-coordinate:

2*a*x+b = 0    ==>   x = -b/(2*a)

So, unless I made a mistake, the focus should be at <-b/(2*a),
(4*a*c-b^2+1)/(4*a)>


David Fontaine wrote:

> You want a parabolic mirror with a light at its focus, like in a
> flashlight. I don't know how to find the focus of a parabola though, Warp
> or somebody?

Post a reply to this message

Being one of those physicists, I can tell you that an ordinary
spherical glass lens lens *will not* actually produce a parallel beam. 
Spherical lenses are actually just an approximation.  This might
surprise you, but it's true. 

	If you really want a parallel beam, use a reflective parabola like
David Fontaine suggested.

	Ben
	<><

Post a reply to this message

Ben Birdsey wrote:

>         Being one of those physicists, I can tell you that an ordinary
> spherical glass lens lens *will not* actually produce a parallel beam.
> Spherical lenses are actually just an approximation.  This might
> surprise you, but it's true.

Theoretically there should be some sort of lens that makes parallel beams. But
my guess is it is not made of intersected spheres...

--
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/

Post a reply to this message

There are so-called aspheric lenses which will focus light better, but
only light that is exactly on the optical axis.

	But I recently read an article about a gradient index sphere that
should focus light coming from any direction.  The trick here is that
the lens has a different index of refraction at its center than at its
edge.  Very interesting, but pretty hard to model in POV.

	Ben
	<><

Post a reply to this message

Kevin Wampler wrote:

> A beam from the focus going directly horizontal should be reflected directly
> upward, which means that the parabola at that point has a slope of 1 or -1.
> Since the beam is horizontal, it gives us the y-coordinate of the focus.
> So...
>
> d/dx (a*x^2+b*x+c) = 2*a*x+b
> 2*a*x+b = 1    ==>   x = (1-b)/(2*a)
> y = a*x^2+b*x+c   ==>   y = (4*a*c-b^2+1)/(4*a)
>
> Similarly with the x-coordinate:
>
> 2*a*x+b = 0    ==>   x = -b/(2*a)
>
> So, unless I made a mistake, the focus should be at <-b/(2*a),
> (4*a*c-b^2+1)/(4*a)>
>
> David Fontaine wrote:
>
> > You want a parabolic mirror with a light at its focus, like in a
> > flashlight. I don't know how to find the focus of a parabola though, Warp
> > or somebody?

But if you use a parabola and a point light to make a parallel light, only the
light that bounces off the parabola is parallel, you have to block the rest of
the light somehow.

Dan Johnson

Post a reply to this message

Ben Birdsey wrote:

>         Being one of those physicists, I can tell you that an ordinary
> spherical glass lens lens *will not* actually produce a parallel beam.
> Spherical lenses are actually just an approximation.  This might
> surprise you, but it's true.
>
>         If you really want a parallel beam, use a reflective parabola like
> David Fontaine suggested.
>
>         Ben
>         <><

Spherical aberration is one of the reasons people didn't trust Gallileo's
telescopes.  Philosophers liked to work with pure shapes, so it was commonly
known that glass distorts the truth.  I think the answer might be in a book
down the hall on optics, but I don't feel like looking, because my experience
tells me that even when you know you have seen the answer before, you can't
find it again without looking for a least a few hours.

Post a reply to this message

Dan Johnson wrote:

> But if you use a parabola and a point light to make a parallel light, only the
> light that bounces off the parabola is parallel, you have to block the rest of
> the light somehow.

conical spotlight

--
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/

Post a reply to this message

David Fontaine wrote:

> Dan Johnson wrote:
>
> > But if you use a parabola and a point light to make a parallel light, only the
> > light that bounces off the parabola is parallel, you have to block the rest of
> > the light somehow.
>
> conical spotlight
>
> --
> David Fontaine  <dav### [at] faricynet>  ICQ 55354965
> My raytracing gallery:  http://davidf.faricy.net/

Looked in documentation don't see it.  Unless you mean the spotlight source, but
that has an umbra, and penumbra.  I don't know how to make that light source act
like a perfect cone light.

Dan Johnson

Post a reply to this message

Dan Johnson wrote:
> 
> Looked in documentation don't see it.  Unless you mean the spotlight source, but
> that has an umbra, and penumbra.  I don't know how to make that light source act
> like a perfect cone light.
> 

The penumbra can be eliminated by setting the "falloff" and "radius" parameters
to an equal value. This should give what I'd call a "perfect cone light".
I'm not sure what you mean by it having an umbra. Obviously it will cast
shadows.

-- 
Margus Ramst

Personal e-mail: mar### [at] peakeduee
TAG (Team Assistance Group) e-mail: mar### [at] tagpovrayorg
Home page http://www.hot.ee/margusrt

Post a reply to this message