14af914a
From: mathma18@gmail.com
On May 18, 8:44 pm, Narasimham Gudipaty wrote:
> On Saturday, May 11, 2013 1:43:15 AM UTC+5:30, Boxman wrote:
> > On 5/9/2013 5:37 PM, Narasimham Gudipaty wrote:
> > > On Thursday, May 9, 2013 6:41:03 PM UTC+5:30, Narasimham Gudipaty wrote:
> > >> On May 7, 6:40 pm, boxman wrote:
> > > ....
> > >> Thanks. So, in fact is it a point to point imaging effected through
>
> > >> a Cartesian aplanatic in the refracting portion? (Am unable to get
>
> > >> to see the book).
>
> > > Or,if used here in non-imaging application then wave-front does not
>
> > > arrive at target in the same phase as at source,right? I am trying to
>
> > > find at least one example anywhere.. as per Descartes' original
> > > expectation.
> > > Regards Narasimham
>
> > I'm not sure I understand your question completely, but I will explain
>
> > what I can to see if it helps.
>
> > If you have a point source F in a medium of refractive index n1, you can
>
> > concentrate the light emitted from that source onto a point G in a
>
> > medium of refractive index n2 using a refractive surface that is a
>
> > cartesian oval. For this case, the optical path length from F to G is a
>
> > constant and is given by n1*t + n2*s = K where t is the length of the
>
> > ray in medium 1, s is the length of the ray in medium 2 and K is a
>
> > constant. Using that relationship, you can derive parametric equations
>
> > for a given set of points that are a function of the angle phi which is
>
> > the angle of the ray to the optical axis passing through the points.
> > The Limacon of Pascal falls out of these equations when you have the
>
> > special case where K^2-f^2*n2^2=0 where f = distance along optical axis
>
> > from cartesian oval to point G (i.e. the focal length) and n2 is less
>
> > than n1.
>
> > Don't know if that helps, but feel free to explain further what you are
>
> > looking for.
>
> Dear Boxman and all others,
To make what I mean is clearer, slightly change it.
> Requesting for your specific comments to clear up it fully. The following
seems to me right.I worked on it.
>Shall much appreciate your responses.
> Which of the following four statements are true? If untrue what should be
correct?
>
> (Spherical aberration free aplanat lens of single material of refractive
index > 1 , say 1.5.
Assume dense medium lens at left / rarer medium (air) at right on
the x-axis for cases 1 & 3,
and dense medium lens at right/ rarer medium (air) at left on the x-
axis for 2 & 4.
Light travels from left to right in the four situations.
( this makes 1 & 3 emerging out of dense medium, 2 & 4 entering into
dense medium).
> 1. Planar wave-front from inside the lens focuses to a point in air F
with shrinking /converging spherical waves. For this to happen, lens shape is
a hyperbola.
>
> 2. Planar wave-front from outside the lens focuses to a point F inside
lens with shrinking /converging spherical waves. For this to happen, lens
shape is an ellipse.
>
> In 1 and 2 above expanding wave-fronts.If taken direction of light is
reversed it gives rise to straight planar beams.
>
> 3. Spherical expanding wave-front issuing from focus F1 inside the lens
focuses to a point F2 in air with shrinking /converging spherical waves. For
this to happen, lens shape is (near to axis portions of) a Cartesian Oval of
dimpled ball type.
>
> 4. Spherical expanding wave-front front issuing from focus F1 from
outside the lens focuses to a point F2 in the lens with shrinking /converging
spherical waves. For this to happen, lens shape is ( near to axis portion of)
a Cartesian Oval egg
type.
>
> In 3 and 4 above F1 and F2 can be swapped if direction of light is reversed.
Regards
Narasimham
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