Telescopes and Optics NHAS Astro 101

Agenda Optics relating to Telescopes, Lenses and Mirrors Types of Telescopes and their advantages Focal Length and Focal Ratio Types of Eyepieces and their advantages Magnification and Apparent Field of View Types of Astronomical Mounts and their uses Types of Finders and their uses Filters and their uses

Lenses and Mirrors

Properties of Light Law of Reflection - Angle of Incidence = Angle of reflection Law of Refraction -Light beam is bent towards the normal when passing into a medium of higher Index of Refraction. Light beam is bent away from the normal when passing into a medium of lower Index of Refraction. Index of Refraction - Inverse square law - Light intensity diminishes with square of distance from source.

Normal Law of Reflection   Angle of incidence (  ) = angle of reflection (  ) The normal is the ray path perpendicular to the mirror’s surface.

Center of curvature - the center of the circle of which the mirror represents a small arc Principal axis - a radius drawn to the mirror surface from the center of curvature of the mirror - normal to mirror surface Focus - the point where light rays parallel to principal axis converge; the focus is always found on the inner part of the "circle" of which the mirror is a small arc; the focus of a mirror is one-half the radius Vertex - the point where the mirror crosses the principal axis Focal length - the distance from the focus to the vertex of the mirror Geometry of a Concave Mirror Focus Principal axis Vertex Focal length

Index of Refraction As light passes from one medium (e.g., air) to another (e.g., glass, water, plexiglass, etc…), the speed of light changes. This causes to light to be “bent” or refracted. The amount of refraction is called the index of refraction.

Imagine that the axles of a car represent wave fronts. If the car crosses from a smooth to a rough surface at an angle, one tire of the axle will slow down first while the other continues at normal speed. With one tire traveling faster the other, the car will turn in the direction of the slow tire. This is how refraction works. Refraction

AIR GLASS / WATER Slower Propagating Speed NORMAL

AIR GLASS / WATER Slower Propagating Speed Car ( Sand / Gravel )

AIR GLASS / WATER Slower Propagating Speed Car ( Sand / Gravel )

AIR GLASS / WATER Slower Propagating Speed NORMAL LIGHT BENDING TOWARDS THE NORMAL LIGHT RAY

n2 AIR GLASS / WATER Slower Propagating Speed NORMAL LIGHT BENDING TOWARDS THE NORMAL n1 Snell's Law ( Next Slide )

GLASS / WATER Car AIR Slower Propagating Speed ( Sand / Gravel )

GLASS / WATER Car AIR Slower Propagating Speed ( Sand / Gravel )

GLASS / WATER Car AIR Slower Propagating Speed ( Sand / Gravel )

AIR Slower Propagating Speed GLASS / WATER NORMAL AGAIN, LIGHT BENDS TOWARDS THE NORMAL upon entering a region with slower speed. LIGHT RAY

Slower Propagating Speed GLASS /WATER Car AIR ( Sand / Gravel )

Slower Propagating Speed GLASS /WATER Car AIR ( Sand / Gravel )

Slower Propagating Speed GLASS /WATER Car AIR ( Sand / Gravel )

NOW LIGHT BENDS AWAY FROM THE NORMAL Slower Propagating Speed GLASS /WATER AIR LIGHT RAY NORMAL Snell's Law

Optical axis - axis normal to both sides of lens - light is not refracted along the optical axis Focus - the point where light rays parallel to optical axis converge; the focus is always found on the opposite side of the lens from the object Focal length - the distance from the focus to the centerline of the lens Geometry of a Converging (Convex) Lens Optical axis Focus Focal length

Lens and Mirror Aberrations SPHERICAL (lens and mirror) Light passing through different parts of a lens or reflected from different parts of a mirror comes to focus at different distances from the lens. Result: fuzzy image CHROMATIC (lens only) Objective lens acts like a prism. Light of different wavelengths (colors) comes to focus at different distances from the lens. Result: fuzzy image

Simple lenses suffer form the fact that light rays entering different parts of the lens have slightly difference focal lengths. This defect is corrected with the addition of a second lens. One focal point for all light rays The problem The solution Spherical Aberration in Lenses

Simple concave mirrors suffer from the fact that light rays reflected from different locations on the mirror have slightly different locations on the mirror have slightly different focal lengths. This defect is corrected by making sure the concave surface of the mirror is parabolic The Problem The Solution All light rays converge at a single point Spherical Aberration in Mirrors

Focal point for blue light Focal point for red light Focal point for all light The problem The solution Simple lenses suffer from the fact that different colors of light have slightly different focal lengths. This defect is corrected by adding a second lens Chromatic Aberration in Lenses

Coma Affects Fast Mirrors with deeply curved reflecting surface Causes elongation in one axis if the object is not near the center of the FOV Faster the Mirror the more of an issue. Its Not a mistake in workmanship This off-axis distortion is called coma, named after the term for a comet’s head

Types of Optical Telescopes

Basic Telescope Designs Refractor Uses a lens to gather the light to a point Most rugged design - easy to care for Gives the sharpest views - especially of planets and the moon Most expensive for any given aperture Usually the tube is quite long, although short tube designs are now available Inexpensive models suffer from chromatic aberration – achromatic vs. apochromatic

Basic Telescope Designs Reflector Uses a mirror to gather the light to a point Open tube collects dust, mirror eventually tarnishes Requires periodic alignment (collimating) of the mirrors Least expensive for any given aperture Available in both long and short tube design Generally no chromatic aberration Most “bang for the buck”

Basic Telescope Designs Compound Schmidt-Cassegrain, Maksutov Uses mirror and lens to gather the light to a point Sharp views, Maksutov are almost as good as refractors Closed tube protects optics Moderate cost for any given aperture Tube is shortest for any given aperture Most portable for any given aperture

Refracting Telescope Uses lens to focus light from distant object - the eyepiece contains a small lens that brings the collected light to a focus and magnifies it for an observer looking through it. Focal Ratio= FL/Obj Diam FL= Focal Length Obj Diam

Types of Reflecting Telescopes Each design incorporates a small mirror just in front of the prime focus to reflect the light to a convenient location for viewing.

Focal Length and Focal Ratio Focal Ratio= Focal Length/Objective Diam Faster = Shorter= is smaller ratio Shorter Focal Ratio Optics (F6 and below) Wider Fields of View More Compact More Expensive or More Distorted –Optics must be close to perfect –Fast Optics are difficult to make

Telescope Specs 100mm F7 Refractor 100mm F10 Refractor 200mm F10 Schmidt Cass 400mm F4.5 Newtonian 16 inch F4.5 Newtonian

The Powers of a Telescope Light Gathering Power Light Gathering Power : Astronomers prefer *large* telescopes. A large telescope can intercept and focus more starlight than does a small telescope. A larger telescope will produce brighter images and will be able to detect fainter objects. Resolving Power Resolving Power : A large telescope also increases the sharpness of the image and the extent to which fine details can be distinguished. Magnification Magnification : The magnifying power is the ability of the telescope to make the image appear large in the field of view.

Three Fundamental Properties of a Telescope Light-Collecting Area think of the telescope as a “photon bucket” The amount of light that can be collected is dependent on the mirror area A =  (D/2) 2 Resolution smallest angle which can be seen  = 1.22 / D The angular resolution of a reflecting telescope is dependent on the diameter of the primary (D) and the wavelength of the light being viewed ( ) These properties are much more important than magnification which is produced by placing another lens - the eyepiece - at the mirror focus.

Light Gathering Ability: Size Does Matter 1. Light-gathering power: Depends on the surface area A of the primary lens / mirror, proportional to diameter squared: A =  (D/2) 2 D

Angular Resolution The ability to separate two objects. The angle between two objects decreases as your distance to them increases. The smallest angle at which you can distinguish two objects is your angular resolution.

Eyepieces Used to magnify the image at the focal plane for viewing by the naked eye Your image will only be as good as the weakest chain in your optical system Many Different designs –All specified with an Eyepiece FL and an AFOV

Types of Eyepieces Old designs (limited use) –Huyghenian, Ramsden, Kellner, Erfle –Low Cost, with distortion Gold Standards, (52deg AFOV) –Plossl, Orthoscopics –Med Cost, without distortion Widefields, ( up to 82deg AFOV) –Naglers, Panoptics, Radians, Swans –High Cost: Distortion Free AFOV correlates to Cost –More money vs more distortion

Magnifying Power Magnifying Power = ability of the telescope to make the image appear bigger. The magnification depends on the ratio of focal lengths of the primary mirror/lens (F s ) and the eyepiece (F e ): M = F s /F e A larger magnification does not improve the resolving power of the telescope! Rule of Thumb- Maximum useful Mag is 50x per inch of Objective diameter under ideal seeing - 20x to 30x per inch of Objective is more common in NE

Field of View: FOV Each eyepiece design has a specified Apparent Field of View, AFOV AFOV/ Magnification = effective FOV –Expressed in angular degrees Ex… A 25mm Plossl with 52deg FOV is being used on a refractor with a 1000mm FL. What is the magnification and FOV: 1000mm FL/25mm Ocular= 40x mag 52deg AFOV / 40 Mag = 1.3 deg effective FOV

Examples 100mm F7 Refractor, w 32mm Plossl (52deg AFOV) Mag FOV 200mm F10 Schmidt Cass, w 32mm Nagler (82deg AFOV) Mag FOV 400mm F4.5 Newtonian, w 32mm Widefield (66deg AFOV) Mag FOV

Eye relief The distance from the last surface of the eyepiece eye lens (the lens closest to your eye) to where the image is formed. Eye relief should be fairly long for comfortable viewing, – if you must wear eyeglasses, you will need a minimum of 15mm of eye relief to see the entire field of view –Eye relief usually decreases as eyepiece focal lengths get shorter More $$ for more eye relief

Barlow Lens x2 or x3 increase in your mag or a /2 or /3 decrease in your eyepiece FL. Using a x2 barlow you can make a 32mm eyepiece also serve as a 16mm eyepiece. –(But you keep the 32mm eye relief) Slight decrease in image brightness due to extra elements.

Telescope Mounts Altitude-Azimuth (Alt-Az) Simple, easy to use Inexpensive Most portable Equatorial Easy to keep objects in the field of view More difficult to setup Usually heavy Usually driven Dobsonian (Dob) Very easy to use Least expensive ?? Very stable Most important: Stability! Many mounts are motorized, some are computerized!

Finders Why? most telescopes have a 1 to 2 deg FOV at their lowest magnification Types –Reflex Sight: Zero Power dovetail, red dot, telrad (concentric circles) –Magnifying 30mm, 50mm and 70mm Correct view Telescope view

Finder Protocol Use a star map to define area to observe Use the finder to point the scope to the general area Use your eyepiece with the widest effective field to locate your target. Happy Observing

Filters

Filters are designed to block light. This inherently darkens the image, so the scope must be able to pull in enough light to still allow you to see the object you are interested in. Due to this fact, small telescope often do not benefit from filters. The Moon looks better through a filter in any size telescope. The Sun can be viewed directly with the proper filter. Filter Basics Most filters are threaded for attaching to the bottom of eyepieces, the front of diagonals or to the visual back of an SCT telescope.

Conventional solar filters come in two varieties (glass and Mylar film) and allow us to see sunspots on the surface of the sun. Most Mylar filters show the sun as a blue disk. Glass filters generally show the sun in yellow. Baader Solar Film (Mylar) show the sun as a white disk and has the best contrast. H-Alpha filters are expensive, but allow us to view the flares and other features in the Sun’s chromosphere. Solar Filters These conventional solar filters mount on the front of the scope. Never use a solar filter that mounts on the eyepiece!

The Moon is very bright, especially at lower magnifications. This makes it difficult to see fine detail. A standard lunar filter may block 80% or more of all visible light. A polarizing filter uses two polarized elements that can be rotated to vary the amount of light blocked. Moon Filters

Color filters are mostly used for the planets. By blocking certain wavelengths (colors) of light, they help to bring out faint details. To learn what colors work well for which planets, visit the Learning Center at Other than Jupiter and Venus (two very bright objects) color filters will not provide much benefit for scopes smaller than 4.5”. Color Filters

Designed to pass only certain wavelengths of light in order to show faint objects while blocking manmade light and skyglow. Broadband filters allow most light to pass, but block wavelengths commonly produced by exterior lighting. They improve most faint objects. Narrowband filters block much more light, but pass the light emitted by many faint nebulae. Deep Sky Filters Oxygen III (O-III) filters block all but the one specific wavelength common to just a few nebulae (the Veil nebula for example). Hydrogen Beta (H-Beta) filters block all but the one specific wavelength common to just a few nebulae (the Horsehead and California nebula for example). These filters will not provide much benefit for scopes smaller than 6”.

Credits Phillip Anderson, University of Texas Joseph Howard, Info Technology Michael Swanson, US Naval Hospital Okinawa

Appendix

Snell's Law Where: V L1 is the longitudinal wave velocity in material 1. V L2 is the longitudinal wave velocity in material 2. Snell's Law describes the relationship between the angles and the velocities of the waves. Snell's law equates the ratio of material velocities V L1 and V L2 to the ratio of the sine's of incident and refracting angles.

Snell's Law where  1 and  2 are the angles from the normal of the incident and refracted waves, respectively. n 1, n 2 are indices of refraction of the two media respectively. n=(c/v) where : C is the velocity of light and v is the velocity of light in that medium

Reflecting telescopes are primary astronomical tools used for research: 1.Lens of refracting telescope very heavy - must be placed at end of telescope - difficult to stabilize and prevent from deforming 2.Light losses from passing through thick glass of refracting lens - must be very high quality and perfectly shaped on both sides 3.Refracting lenses subject to chromatic aberration Refracting vs Reflecting Telescopes