Re: calculating focal length of extender?

On Nov 20, 11:58 pm, Robert <renen...@xxxxxxxxxxx> wrote:
Hello -- I am hoping someone here can help me. I have what looks like
simple optical problem but lack ray-tracing software or enough
knowledge of optics to solve it.

I have a telescope whose focal plane is 1/2" outside of the most
retracted position of the focuser tube. I need more room to attach
some instrumentation (a spectrophotometer), so I would like the focal
plane to be further outside the tube. I think I can do this by adding
a concave lens ahead of the focal plane, so that it causes the
converging cone of image light from a point source subject (a star,
say) to converge less strongly, and hence come to a focus further
outside the tube.

I can calculate the angle "a" of the converging cone of light (knowing
the size of the telescope mirror and its focal length). I also know
the distance "d" that I want to move the focal plane. Is there a
formula I can use to calculate the required focal length for the
concave lens I need to do the job?

Thanks for any advice or references,
Robert

While adding a simple lens may introduce unwanted aberrations, yes it
is possible to do the calculation with the thin-lens-formula.

If:
d = distance to move the focal plane,
L = distance from lens to current focal plane,
f = focal length of the lens (= a negative number for concave a
concave lens)
and
i = L+d = distance from lens to new focal plane

Then calculate the focal length using:
1/f = -1/L + 1/i

Again, you should get a negative value for f, indicating a concave
lens.

Note: the lens diameter should be more than
minimum diameter = 2 * L * tan(a/2)
in order to transmit all of the incident light.
(As an approximation to this expression, you could also divide L by
the f-number (f/#) of the telescope's primary, and take that as the
minimum lens diameter.

If you use a plano-concave lens (one side flat, one side concave),
then put the curved side toward your photometer to minimize
aberrations.

Regards,

Mark
.

Relevant Pages

  • Re: Whats "focus"
    ... I know that the focal legnth is the distance between the sensor (or ... film) and the bottom of the lens (so the first piece of glass), ... to the focal plane, and way less than 40mm to the focal plane.) ...
    (rec.photo.digital)
  • Re: Admit it; Youd like a Nikon FE-2 with a digital back
    ... is a defined distance between the camera's lens interface, the mount, and the focal plane. ... For any particular camera body there is a defined distance between the focal plane and the shutter. ... The former defines where the sensor needs to be, the latter defines how much clearance there is to mount additional physical components. ...
    (rec.photo.digital)
  • Re: Rambling load all right
    ... a telecentric lens maps objects of the same ... If you draw out a simple lens then all of the principle rays to every point between the object and its image on the focal plane passes through the centre of the lens. ... However, since telecentricity means that the principle ray to every point in the image is perpendicular to the focal plane, there is an argument that it is ideal in digital sensors to ensure that the amount of leakage from one filter to adjacent ...
    (rec.photo.digital)
  • Re: Rambling load all right
    ... If a lens is fully telecentric, wouldn't that mean that a one foot ... > principle ray is the central ray in the bundle) to every point between ... > the object and its image on the focal plane passes through the centre of ... However, since telecentricity means ...
    (rec.photo.digital)
  • Re: Rambling load all right
    ... >>that was let's say 2 feet from the lens and a one foot ruler that was ... > group at the back which bends all of the ray bundles back towards the ... > ray bundles still all come to a focus at the focal plane, ... the edge of the frame will ...
    (rec.photo.digital)