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Science Forum Index » Optics Forum » Image of a straight line in a convex cylindrical mirror
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| Narasimham G.L. |
 Posted: Sat Nov 08, 2003 11:59 pm |
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What is the reflection in a cylindrical mirror x^2+y^2 = a^2 of a
straight line y+b = 0 as seen from a viewpoint (0,-c,h) ( a < b << c)
? Is it a catenary ? If not, what is it? |
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| Sam Wormley |
| Posted: Sun Nov 09, 2003 8:07 am |
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"Narasimham G.L." wrote:
Quote:
What is the reflection in a cylindrical mirror x^2+y^2 = a^2 of a
straight line y+b = 0 as seen from a viewpoint (0,-c,h) ( a < b << c)
? Is it a catenary ? If not, what is it?
What have you done so far? |
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| mg |
| Posted: Sun Nov 09, 2003 6:35 pm |
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When is the homework due?
"Narasimham G.L." <mathma18@hotmail.com> wrote in message
news:676dc11a.0311082059.553f3924@posting.google.com...
Quote: What is the reflection in a cylindrical mirror x^2+y^2 = a^2 of a
straight line y+b = 0 as seen from a viewpoint (0,-c,h) ( a < b << c)
? Is it a catenary ? If not, what is it? |
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| Narasimham G.L. |
| Posted: Sun Nov 09, 2003 10:27 pm |
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"mg" <nospam@no.com> wrote in message news:<7bArb.79217$ZC4.3003@twister.nyroc.rr.com>...
Quote: When is the homework due?
 this is my curiosity about curvarture of lines when the virtual
image is distorted in reflection.
I observed clear images of square lines of floor mosaic in a polished
cylindrical flowerpot in Twelve Oak Mall, Detroit. What is commonly
known is the optics: image-object distances are connected by standard
formula (u-f)(v-f)=f^2 where f=a/2 or focal length, u,v are object &
image distances etc. in reflection. I did not do much of image / ray
tracing in 3D before .
I believed that cos(slope angle) in the x-z projection is inversely
proportional to z-coordinate, as it is for a catenary z=A cosh(x/A).
I asked this question expecting that there could be elementary
geometrical operations with straight lines, cylinders, reflection &c.
My imagination surrounded vague thoughts about geodesic deviation, but
I right now I would thank in advance for any ensuing pointers and
clarifications. |
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| mg |
| Posted: Mon Nov 10, 2003 9:45 pm |
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In 3D, y+b=0 is a plane. Right? Are you looking for its reflection, or
reflection of a line?
"Narasimham G.L." <mathma18@hotmail.com> wrote in message
news:676dc11a.0311082059.553f3924@posting.google.com...
Quote: What is the reflection in a cylindrical mirror x^2+y^2 = a^2 of a
straight line y+b = 0 as seen from a viewpoint (0,-c,h) ( a < b << c)
? Is it a catenary ? If not, what is it? |
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| Detector195 |
| Posted: Tue Nov 11, 2003 10:11 pm |
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"mg" <nospam@no.com> wrote in message news:<A3Yrb.88443$ZC4.55356@twister.nyroc.rr.com>...
Quote: In 3D, y+b=0 is a plane. Right? Are you looking for its reflection, or
reflection of a line?
"Narasimham G.L." <mathma18@hotmail.com> wrote in message
news:676dc11a.0311082059.553f3924@posting.google.com...
What is the reflection in a cylindrical mirror x^2+y^2 = a^2 of a
straight line y+b = 0 as seen from a viewpoint (0,-c,h) ( a < b << c)
? Is it a catenary ? If not, what is it?
It's probably safe to assume, since this is a line on the floor of the
mall, that the equation is y+b = 0 and z = 0. Now that it's been a few
days, can I give a hint? The symmetry of the problem -- what
coordinate system should you be using? |
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| Narasimham G.L. |
| Posted: Wed Nov 12, 2003 11:08 pm |
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"mg" <nospam@no.com> wrote in message news:<A3Yrb.88443$ZC4.55356@twister.nyroc.rr.com>...
Quote: In 3D, y+b=0 is a plane. Right? Are you looking for its reflection, or
reflection of a line?
Looking for the reflection of line y+b=0,z=0, omitted typo. |
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| Narasimham G.L. |
| Posted: Wed Nov 12, 2003 11:15 pm |
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Detector195@yahoo.com (Detector195) wrote in message news:<6213f73a.0311111911.662464ad@posting.google.com>...
Quote: "mg" <nospam@no.com> wrote in message news:<A3Yrb.88443$ZC4.55356@twister.nyroc.rr.com>...
In 3D, y+b=0 is a plane. Right? Are you looking for its reflection, or
reflection of a line?
"Narasimham G.L." <mathma18@hotmail.com> wrote in message
news:676dc11a.0311082059.553f3924@posting.google.com...
What is the reflection in a cylindrical mirror x^2+y^2 = a^2 of a
straight line y+b = 0 as seen from a viewpoint (0,-c,h) ( a < b << c)
? Is it a catenary ? If not, what is it?
It's probably safe to assume, since this is a line on the floor of the
mall, that the equation is y+b = 0 and z = 0. Now that it's been a few
days, can I give a hint? The symmetry of the problem -- what
coordinate system should you be using?
Looking for the reflection of line y+b=0,z=0, an omitted typo. Should
be using polar/cylindrical (r-th-z) coordinates for convenience of
symmetry. |
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