Chapter 6 Optics and Telescopes Telescopes, and the detectors to go with them, are important in ASTR 1100, so the important points are covered here. 1. Telescopes are simply extensions of the eye. They gather more light than the eye does because of their large apertures. Magnification is a consequence of different focal lengths for the telescope lens/mirror and eyepiece. 2. More important are the devices used by astronomers to image the sky as well as spectra of astronomical objects. The human eye just won’t do !

Telescopes take advantage of the optical properties of lenses or mirrors, i.e. refraction or reflection.

The bending of a beam of light by refraction in glass. Properly figured surfaces on a convex lens bring the light beam to a focus.

Telescopes can be thought of as “light buckets.” They gather light in proportion to their collecting aperture surface area, D 2, be it lens, mirror, radio dish, or an array of hexagonal mirrors. Thus, a 16-inch telescope has four times the light gathering power as a 8-inch telescope.

Light from distant objects enters telescopes in a plane parallel beam.

Basic Optical Principles: Each point in a distant object is the source of a spherically expanding wave front, but the light arrives as the telescope as plane parallel wave fronts, lightly distorted by Earth’s atmosphere. An ideal telescope would focus the incident wave fronts to a single point, the focus, irrespective of wavelength and position on the wave front.

A prism (upper right) shows how it is possible to deflect a beam of light, albeit with some dispersion resulting from the wavelength dependence of n λ. A thin lens (lower right) can be thought of as simply a series of small prism segments deflecting the light to a single point, the focus, a distance f from the lens. A convex lens (a) focuses light in a converging beam, while a concave lens (b) defocuses light in a diverging beam.

A simple refracting telescope consisting of two lenses: a primary lens and an eyepiece lens. The resulting magnification is given by the ratio of the focal lengths:

e.g. old Burke-Gaffney telescope. Original effective focal length of the 0.4m telescope was f(telescope) = 4780 mm. When used with an eyepiece labelled as having a focal length of 40 mm, In other words, that combination produced a magnification of 119½ power (119½  ).

DAO Director Jim Hesser modelling Galileo’s telescope.

Examples:

Chromatic aberration occurring in glass optics is a serious problem for refracting telescopes, which is why reflectors are superior.

The advantages/disadvantages of telescope types. Refracting telescopes: (i) suffer from chromatic aberration that requires a doublet main lens rather than a single lens, (ii) four surfaces need to be figured, (iii) beyond ~40 inches, a lens sags under its own weight. Reflecting telescopes: (i) spherical mirrors suffer from spherical aberration, parabolic mirrors do not, (ii) parabolic mirrors suffer from “coma,” that requires special shaping of the mirrors, (iii) mirrors need only be figured on one side, (iv) mirrors can always be supported from the back, (v) the material of mirrors need not be transparent since it will be aluminized, (vi) composite mirrors can be built to do the job of one large mirror.

A mirror system focuses light without suffering from chromatic aberration.

A modern view of the Plaskett Telescope.

Reflecting telescopes also suffer from light aberration.

Telescope resolution is established by the diameter of the collecting aperture, the larger the better, except for the effects of atmospheric seeing. The diffraction image of a star is surrounded by the “Airy disk” in excellent seeing.

Larger Size = Better Resolution, θ Up to a point. Atmospheric seeing is the limit for ground- based telescopes. For θ in radians, For θ in arcseconds,

These devices are also telescopes.

Image Scale of a Telescope. The image scale of a telescope links the angular separation of objects in the sky to their linear separation on an image obtained with the telescope. As illustrated below using the “chief ray” from an object passing through the centre of the lens, by geometry: The image scale is therefore defined as: For θ in arcseconds rather than radians, and y in mm:

Example. The ST8 CCD camera at the old BGO operated at an effective telescope focal length of f = 4924 mm. The image scale for the CCD camera was therefore: It seems, at first sight, that one could achieve arbitrarily large separations between image points merely by increasing “f.” But images of Jupiter (θ = 49".7 near opposition) have a size, X, given by: The value corresponds to ~66 18-micron pixels on the ST8, for 2  2 binning. In other words, the size of the detector elements governs the resolution.

Earth’s atmosphere is opaque to gamma rays, X-rays, ultraviolet light, some infrared light, microwaves, and long wavelength radio waves, so observations in these spectral regions can only be done from space.

Chandra X-Ray Orbiting Telescope

Compton Gamma-Ray Observatory

COBE Satellite

Hubble Space Telescope (from Shuttle)

Many modern telescope mirrors are equipped with adaptive optics.

Adaptive optics “off.”

Adaptive optics “on.”

James Webb telescope mirror test.

Keck telescope “mirror,” full scale.

A CCD chip (used for imaging).

The inner workings of a CCD camera.

CCD images of the same field: negative image in B&W (left) and colour image (right).

A photographic image of the same field for comparison.

Telescope spectrographs (used to image spectra of stars and galaxies) must include a prism or grating.

Spectrograph on the DAO Plaskett Telescope.

Modern observing is done from “warm” rooms equipped with computers to control telescope and imaging devices.

Telescopes are housed in domed structures to protect them from the elements. DAO Plaskett Telescope Dome.

DAO 1.2-meter Telescope Dome.

Victoria, B.C., from Little Saanich Mountain (DAO).

Mount Baker from the DAO.

Astronomical Terminology Refractor. A telescope that uses lenses to focus light. Reflector. A telescope that uses mirrors to focus light. Light Gathering Power. A measure of the collecting area of a telescope’s primary element. Atmospheric Window. A region of the electromagnetic spectrum in which Earth’s atmosphere is transparent. Optical Telescope. A telescope designed to gather light in the optical band. Radio Telescope. A telescope designed to gather light at radio wavelengths. Seeing. The fluctuating effect on telescope images caused by turbulent bubbles in Earth’s atmosphere randomly deflecting light paths from the source. CCD = Charge-Coupled Device. An ultrathin wafer of silicon divided into a 2-dimensional array of picture elements (pixels) that collect electrons produced by light falling on the element.

Sample Questions 1. “Twinkle, twinkle, little star. How I wonder what you are.” Explain why stars twinkle. Answer: From ground-level we observe stars through Earth’s atmosphere, where convection and air density differences create small bubbles of air that generate random scattering of the starlight and produce “seeing,” the irregular wobbling and intermittent size changes in star images that we call twinkling.

2. Why are the world’s largest telescopes located on high mountains?

Answer. Earth’s atmosphere is very detrimental to astronomical observations. Thermal currents in the atmosphere make seeing blurry, water vapour absorbs infrared frequencies, and light pollution at the surface limits deep sky observing. Placing telescopes on mountaintops reduces thermal currents and situates telescopes above 90% of the water vapour and well above urban light pollution.