English Brass Refracting Telescope - 3D

The Keplerian refractor. A long-focus objective lens of focal length f_o forms a small real image of the sky at its focal plane. The eyepiece (focal length f_e) is pushed out until its own focal plane coincides with that image, so the light leaves almost parallel and a relaxed eye can look at it. Tube length is therefore about f_o + f_e, and the draw tube moves the eyepiece to focus.

The page checks M and the exit pupil against a paraxial (ABCD matrix) trace of a ray through objective, gap f_o + f_e and eyepiece. The image is inverted, as for every Keplerian telescope; the eyepiece view here is drawn the way the eye sees it.

Resolution. A circular aperture D turns every star into an Airy pattern. Its first dark ring is at 1.22 λ/D (the Rayleigh criterion, where two equal stars show a 73.5 % dip between them, verified here by numerically adding two Bessel J₁ patterns). The empirical Dawes limit 116/D(mm) arcsec is what observers measure for double stars. Seeing (turbulence) adds a Gaussian blur of a stated FWHM, so a bigger aperture stops helping once D > about 116 mm / seeing.

Colour error. Glass bends blue light more than red, so a single lens has a different focal length for each colour. With Abbe number V the focal shift between the blue F line (486 nm) and the red C line (656 nm) is about f_o/V. Each colour channel is therefore defocused by a different amount and the geometric blur is d = D · δf / f_o². A Dollond achromat pairs crown and flint glass so that two colours meet; the residual secondary spectrum is modelled as roughly f_o/2000.

The eyepiece view is rendered per colour (650, 550 and 450 nm): stars as true Airy patterns blurred by the Gaussian seeing and defocus, the Moon and Jupiter as extended objects blurred by the same total width. Best focus at the eye is the circle of least colour confusion, found by a search over the focus offset. The sky drifts across the field at 15 arcsec per second of time times cos(declination) (a declination of about 20 degrees is assumed), so a high-power view loses the target within minutes without tracking.

Honest simplifications. Paraxial optics only: no spherical aberration, coma, field curvature or lateral colour; the single-lens dispersion is a one-term Cauchy model calibrated to V, the doublet a quadratic secondary-spectrum curve; the Gaussian blur stands in for the true convolution of the defocus disc; the Moon is drawn four times its real angular size in the 3D sky, Jupiter's satellites are placed schematically, and the planetary and lunar images are procedural pictures, not photographs. Observatory, mount and eyepiece are generic Victorian-style models, not a particular instrument.