TU Astronomy & the Diameter of The Telescope Question

Lab 3 (Telescopes) Introduction Although eyeglass-makers had been experimenting with lenses well before the year 1600, the first mention of a telescope appears in a letter written in 1608 by Hans Lippershey, a Dutch spectacle maker, seeking a patent for a telescope. The patent was denied because of easy telescope duplication and difficulty in patent enforcement. The instrument spread rapidly. Galileo heard of it in the early 1600s and quickly made improvements in lens grinding that increased the magnification from a relatively low value of 2 to as much as 30. With these more powerful telescopes, he observed the Milky Way, the mountains on the Moon, the phases of Venus, and the moons of Jupiter. These early telescopes were a type of ‘opera glass,’ producing erect or ‘right side up’ images but having limited magnification. When Johannes Kepler, a German mathematician and astronomer working in Prague under Tycho Brahe, heard of Galileo’s discoveries, he perfected a different form of telescope using a concave eyepiece. Although Kepler’s design inverts the image, it is much more powerful than the Galilean type. Galilean Design Keplerian Design Perhaps no scientific instrument is as closely associated with a particular field of study as the telescope is to astronomy. Yet arguably, the telescope is also one of the most misunderstood of scientific instruments, so closely associated is the telescope with the word “magnification”. First and foremost, an astronomical telescope is a “light bucket” designed to collect light. A celestial object, such as a star, emits light in all directions. After traveling for thousands of years across billions of kilometres, a tiny portion of that light rains down on the hemisphere of the Earth facing that star. Almost all of that light does nothing more than be absorbed by the atmosphere or the ground. An infinitesimal portion of the star’s light strikes the lens or mirror of a telescope and is directed into an eye, or onto a piece of film, or through a spectrograph. The bigger the diameter of the lens or mirror, the more light that is guided to the detector, and the more knowledge that is gained about the Universe. This is the basic fact that underlies astronomers’ never-ending quest for telescopes of larger diameter aperature. 1 Considered broadly, telescopes are all around you in optical devices of other names – cameras, eyes, binoculars, eyeglasses, and more. The details of the optics in each of these telescopes dictates how effectively the collected light is used. The simplest variety of telescope uses a single lens. The image is formed at the “focus” of the telescope, which is simply the focal plane of the lens. A piece of film or – more commonly these days – an electronic detector known as a “charged-coupled device,” or “CCD” is placed in the focal plane, and a picture is taken. The first telescopes ever used to study the heavens, those built by Galileo in 1610, were 2-lens telescopes. Telescopes that use lenses are called “refractors” (refracting means to bend light). In a refracting telescope, the first lens (the one the starlight hits first) is called the objective lens. The second lens (the one in front of your eyeball) is called the eyepiece. An easy way to remember this is that the objective lens is nearest to the object, which the eyepiece lens is nearest to your eye. The objective lens in a telescope is always much bigger than the eyepiece lens. Many modern telescopes use mirrors instead of lenses to redirect light, in part because they are easier to manufacture in large sizes. Telescopes that use mirrors are called “reflectors” because they reflect light coming through the aperature towards an eyepiece or camera. Simple Reflecting Telescope The objective lens or mirror in a telescope is a permanent (non-removable) feature of the telescope. The most important thing about the objective is its diameter. The larger the diameter, the more light the telescope can collect and focus, and the brighter the images it produces. The light-collecting capacity of a telescope also enables faint stars to be seen through a telescope that cannot be seen with the unaided eye. The other important feature of the objective is its focal length. The longer the focal length, the larger the image formed in the focal plane. 2 Magnification The eyepiece lens in a telescope acts like a magnifying glass, magnifying the image in the focal plane so that the observer can see its detailed features. Eyepieces are typically interchangeable on a telescope. Interestingly, the smaller the focal length of the eyepiece (the more curved it is), the more magnification it provides. The telescope magnification formula is: m = fo fe (1) Here, (m) is the magnification, (fo ) is the focal length of objective, and (fe ) is the focal length of eyepiece. For this formula, the focal lengths of both objective and eyepiece are expressed in the same units (typically mm). Beware however that this doesn’t always mean a small focal length eyepiece is better! The larger the magnification, the smaller the patch of sky (“field of view”) you will get to see through the telescope. To get a large “field of view” (to see a bigger patch of the sky) you need to use low magnification. Moreover, because the Earth’s atmosphere is turbulent, which blurs out the images of stars, there are limits to how much you can magnify a star image before it just looks like a big fuzzy blob. Diffraction Limit The minimum angular separation of two sources that can be distinguished by a telescope depends on the wavelength of the light being observed and the diameter of the telescope. This angle is called the Diffraction Limit. It is given by: 1 D Where, (λ) is the wavelength of the light and (D) is the diameter of the telescope. In the approximation of small angles, this angle is approximately equal to the ratio: θ = 1.22 λ s d Here, (s) is the separation distance between two objects and (d) is the distance between the telescope and the object. Thus we get: θ≈ s ≈ 1.22 λ d D (2) What this says is that two objects on the sky that are a distance (d) from Earth that closer together than (s) will look like a single point of light if viewed by a telescope with an aperature diameter of (D) or less. Left: Resolved Sources, Right: Unresolved Sources 3 Procedure Part 1: Telescope Diagrams After finding images online, sketch an internal diagram (include labels) of the following types of telescopes: 1. Newtonian Reflecting Telescope 2. Cassegrain Telescope Part 2: Diffraction Limit and Magnification Determine the size of the telescope (D) needed to resolve the following objects. (Assume that the wavelength of light is (λ = 500 nm). 1. s = 100 m, d = 1 km 2. s = 100 m, d = 3.5 ×105 km (Distance to the Moon) 3. s = 1 km, d = 1.5 ×108 km (Distance to the Sun) Determine the magnification of the following pairs of objective and eyepiece lenses: 1. fo = 30 mm, fe = 15 mm 2. fo = 105 mm, fe = 22 mm 3. fo = 270 mm, fe = 33 mm Part 3: Scientific Telescopes Use the internet to find information about a major research telescope of your choosing. If you don’t have a particular telescope in mind, this Wikipedia page is a good place to start: https://en.wikipedia.org/wiki/Lists of telescopes You can choose a telescope of any wavelength range (radio to gamma rays), any location (whichever continent to space-based) and it can be a currently active telescope or a historical telescope. Choose something that you find interesting! Note. Please use your own words when relaying information about the telescope you choose. Please DO NOT copy and paste information! That falls under Academic Dishonesty and you will receive a zero for this lab. Please use complete sentences when answering the following questions: 1. What telescope did you choose? 2. Where is the telescope located? 3. What wavelength(s) does the telescope observe? Note. This answer could be a wavelength range or a wavelength category (ex. visible/optical, infrared, X-rays, etc). 4. What are some interesting facts/information about your telescope? This could include things like historical events or important discoveries made by the telescope, instruments on the telescope that do different things, interesting things about who the telescope is named after, were you able to find any cool images taken by the telescope and what were they, etc. Your answer needs to be a minimum of 50 words. 4