Illustrated Physics
physics, drawn
Concept

Telescope — where it appears

An instrument that collects light with a large lens or mirror and forms an image of distant objects. Its aperture sets both how much light it gathers and, through diffraction, the finest detail it can resolve, about the wavelength divided by the aperture's diameter.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

How bright a nebula looks through a 200 mm telescope. The surface brightness of the image of an extended object — a nebula, a galaxy, the Moon — through a lossless 200 mm telescope, as a fraction of its brightness to the naked eye, against magnification on a logarithmic axis, for eye pupils of 7 and 5 mm. It is never above one. For a 7 mm pupil it is one up to a magnification of 28.6, where the exit pupil equals the eye's; below that magnification the exit pupil is wider than the eye's and part of the collected light falls on the iris; above it the image dims as the square of the exit pupil: 0.327 at 50×, 0.082 at 100×, 0.020 at 200×. The telescope makes the nebula larger, not brighter; at the magnification where its exit pupil matches the eye's it makes it as large as it can while keeping it as bright as it is.

The nebula no telescope can brighten

A telescope eight metres across gathers a million times more light than the eye, and a star seen through it is a million times brighter. The Orion nebula seen through it is not brighter at all. It is bigger, and spread over a bigger patch of the retina, and the two exactly cancel: no instrument made of lenses and mirrors can show an extended object brighter than the naked eye sees it. What a telescope does is decided by the small disc of light behind its eyepiece, the exit pupil, and by whether that disc is larger or smaller than the pupil of the eye looking through it.

optics · Etendue The spikes a star wears are the vanes that hold the mirror. The image of a single star — the squared Fourier transform of the pupil — for a telescope aperture with a central obstruction of 0.3 of its diameter and no vanes, four vanes in a cross, and three vanes at 120°, each vane 2 per cent of the aperture's diameter wide; shown on a logarithmic brightness scale over six decades, each panel spanning ±30 times the angle λ/D. The small pictures are the pupils. With no vanes the star is an Airy core and rings. Each vane adds a streak at right angles to itself, through the core, in both directions: the cross of four vanes, which is two straight bars, gives four spikes, and the three vanes, which are not opposite one another, give six — each vane's two spikes pointing in directions no other vane's do.

The spikes a bright star wears

Photographs of bright stars show them with spikes — four in most telescope pictures, eight in the James Webb Space Telescope's, none at all in some amateur images. The spikes are not in the sky and not in the camera. They are the shadows of whatever holds the telescope's secondary mirror, transformed by diffraction into streaks at right angles to themselves, and they can be counted, predicted and removed by reading a telescope's pupil the way diffraction reads it: as a pattern whose Fourier transform is the star's image.

optics · Diffraction

Named alongside it

The objects these essays reach for when they reach for this one.

Airy discBabinet principleDiffractionEtendueExit pupilFourier transformHuman eyeMagnificationPoint sourcePoint-spread functionPupil functionRadiance

All concepts