1. Types of Optical Telescopes
PHYS Astronomy
Types of Optical Telescopes

2. PHYS Astronomy
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.

3. PHYS Astronomy
The largest refracting telescope in the world is the at the University of Chicago’s Yerkes Observatory - it is 40 inches in diameter and 63 feet long.

4. PHYS Astronomy
Reflecting Telescope
The primary mirror focuses light at the prime focus. A camera or another mirror that reflects the light into an eyepiece is placed at the prime focus.

5. Types of Reflecting Telescopes
PHYS Astronomy
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.

6. PHYS Astronomy
The Keck Telescopes
Keck telescopes on Mauna Kea in Hawaii. 36 hexagonal mirrors function as single 10-meter mirror.
Largest in the world is the Gran Telescopio Canarias in the Canary Islands which began operations in May 2009 – 10.4 m. The European Extremely Large Telescope (E-ELT) is planned to have first light in The E-ELT will measure close to 40 meters in diameter

7. The Hubble Space Telescope
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The Hubble Space Telescope
The Hubble Space Telescope is 43.5 ft long and weighs 24,500 lbs. Its primary mirror is 2.4 m (7 ft 10.5 in) in diameter.

8. Focus Optical axis Focal length
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Focus
Optical axis
Focal length
Remember: the focus is the point where light rays parallel to optical axis converge and the focal length is the distance from the focus to the centerline of the lens

9. Geometry of a Simple Lens
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Geometry of a Simple Lens
Focal Plane l1 l2 f o i
The focal plane is where incoming light from one direction and distance (object distance o greater than focal length) is focused.
Using the Gaussian form of the lens equation, a negative sign is used on the linear magnification equation as a reminder that all real images are inverted
Lens formula
Linear Magnification

10. The image formed by a single lens is inverted.
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The image formed by a single lens is inverted.

11. PHYS Astronomy
Focal Plane
Focal length

12. The Eye
PHYS Astronomy
The eye consists of pupil that allows light into the eye - it controls the amount of light allowed in through the lens - acts like a simple glass lens which focuses the light on the retina - which consists of light sensitive cells that send signals to the brain via the optic nerve. An eye with perfect vision has its focus on the retina when the muscles controlling the shape of the lens are completely relaxed - when viewing an object far away - essentially at infinity. Farsightedness/Nearsightedness - focus behind/in front of the retina

13. PHYS Astronomy
When viewing an object not at infinity, the eye muscles contract and change the shape of the lens so that the focal plane is at the retina (in an eye with perfect vision). The image is inverted as with a single lens - the brain interprets the image and rights it.

14. Geometry is similar for a concave mirror - image is inverted.
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Geometry is similar for a concave mirror - image is inverted.

15. Geometry of a Concave Mirror
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Geometry of a Concave Mirror
Focal plane
Vertex
Focal length

16. Refracting/Reflecting Telescopes
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Refracting/Reflecting Telescopes
Refracting Telescope: Lens focuses light onto the focal plane
Focal length
Reflecting Telescope: Concave Mirror focuses light onto the focal plane
Focal length
Almost all modern telescopes are reflecting telescopes.

17. PHYS Astronomy
Secondary Optics
In reflecting telescopes: Secondary mirror, to re-direct light path towards back or side of incoming light path.
Eyepiece: To view and enlarge the small image produced in the focal plane of the primary optics.

18. Magnification Using Two Lenses - Refracting Telescope
PHYS Astronomy
Magnification Using Two Lenses - Refracting Telescope
f1 = 0.5 m
f2 = 0.1 m
f1 = 0.5 m
f2 = 0.3 m
Refracting telescope - consists of two lenses - the objective and the eyepiece (ocular). Incident light rays (from the left) are refracted by the objective and the eyepiece and reach the eye of the person looking through the telescope (to the right of the eyepiece). If the focal length of the objective (f1) is bigger than the focal length of the eyepiece (f1), the refracting astronomical telescope produces an enlarged, inverted image:
magnification = f1 /f2
Similar for a reflecting telescope.

19. Refracting vs Reflecting Telescopes
PHYS-3380 Astronomy
Refracting vs Reflecting Telescopes
Four primary reasons reflecting telescopes are primary astronomical tools used for research:
Lens of refracting telescope very heavy - must be placed at end of telescope - difficult to stabilize and prevent from deforming
Light losses from passing through thick glass of refracting lens
Lens must be very high quality and perfectly shaped on both sides
Refracting lenses subject to chromatic aberration

20. Lens and Mirror Aberrations
PHYS-3380 Astronomy
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.

21. Chromatic Aberration in Lenses
PHYS-3380 Astronomy
Chromatic Aberration in Lenses
Focal point for blue light
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
Focal point for red light
The problem
Focal point for all light
The solution

22. Spherical Aberration in Lenses
PHYS-3380 Astronomy
Spherical Aberration in Lenses
Simple lenses suffer from the fact that light rays entering different parts of the lens have slightly difference focal lengths. As with chromatic aberration, this defect is corrected with the addition of a second lens.
The problem
One focal point for all light rays
The solution

23. Spherical Aberration in Mirrors
PHYS-3380 Astronomy
Spherical Aberration in Mirrors
The Problem
Simple concave mirrors suffer from the fact that light rays reflected from 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 Solution
All light rays converge
at a single point

24. PHYS-3380 Astronomy
Reflecting Telescope
The primary mirror focuses light at the prime focus. A camera or another mirror that reflects the light into an eyepiece is placed at the prime focus.

25. The image from an reflecting telescope is inverted.
PHYS-3380 Astronomy
The image from an reflecting telescope is inverted.
Focus Inversion Animation
The focus is adjusted by changing the secondary mirror position.
Mirror Position and Focus Animation

26. Types of Reflecting Telescopes
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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.

27. - most common form of astronomical telescope
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Cassegrain reflector
- most common form of astronomical telescope
- allows room for large instruments

28. Schmidt-Cassegrain focus most common in small telescopes
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Schmidt-Cassegrain focus most common in small telescopes
- uses catadioptrics - combines optical advantages of both lenses and mirrors
- light enters through a thin aspheric Schmidt correcting lens
- focal length increased by the magnification of the correcting lens
- lens carefully matched to the primary concave mirror to correct for spherical aberration
- too slightly curved to introduce serious chromatic aberration
- shorter physical length
- lighter and more compact
- easy to use

29. PHYS-3380 Astronomy
The Keck Telescopes
On Mauna Kea in Hawaii. 36 hexagonal mirrors function as single 10-meter mirror.
- segmented mirrors
- more economical - segments can be made separately
- weighs less
- cools rapidly
- less distortion from uneven expansion and contraction
- optical shape maintained by computer-driven thrusters

30. Two Fundamental Properties of a Telescope
PHYS-3380 Astronomy
Two Fundamental Properties of a Telescope
Resolution
smallest angle which can be seen
 = 1.22  / D
The angular resolution of a reflecting telescope is dependent on the diameter of the mirror (D) and the wavelength of the light being viewed (). Called Dawes’ Limit
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
These properties are much more important than magnification which is produced by placing another lens - the eyepiece - at the mirror focus. Astronomers do not look through telescopes with their eyes - a light gathering detector (for instance a camera) records the image which can later on be magnified to any desired size.

31. The ability to separate two objects.
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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.

32. Angular Resolution of Car Lights Animation
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Angular Resolution of Car Lights Animation
The maximum angular resolution attainable by the human eye is about one arcminute - in other words two stars will appear distinct if they are separated by more than one arcminute - remember that Tycho Brahe produced the best naked eye star charts ever - had resolution of one arcminute.

33. Angular Resolution amin min Airy disc
PHYS-3380 Astronomy
Airy disc
Resolving power: Wave nature of light
=> The telescope aperture produces fringe rings that set a limit to the resolution of the telescope.
=> Two point sources are just resolved when the principal diffraction maximum of one image coincides with the first minimum of the other. If the distance is greater, the two points are well resolved and if it is smaller, they are regarded as not resolved.
Fully Resolved
amin
Resolving power = minimum angular distance amin between two objects that can be separated.
Just Resolved
amin = 1.22 (/D)
amin is the the angle at which the first minimum occurs
min
For optical wavelengths (assuming =550 nm), this gives
amin = 11.6 arcsec / D[cm]
Unresolved

34. Note on the calculations of resolving power:
PHYS Astronomy
Note on the calculations of resolving power:
The formula amin = 1.22 (/D) gives it in radians. To get it in arc seconds (which all resolutions are given in) you need to multiply by 206,265 “/rad
The book gives slightly different formulas for resolving power:
𝜶 (arc seconds) = 2.06 X 105 (/D)
and
𝜶 (arc seconds)=0.113/D
These ignore the 1.22 factor and uses 206,000 “/rad instead of 206,265 “/rad
I don’t know why the book ignores the 1.22 factor. This really irritates me! Please use the correct number.

35. Mirror Angular Resolution Animation
PHYS-3380 Astronomy
So: the angular resolution/resolving power of a reflecting telescope is dependent on the diameter of its mirror
Mirror Angular Resolution Animation
and the wavelength of the light
Wavelength Effect on Resolution

36. Light Gathering Ability: Size Does Matter
PHYS-3380 Astronomy
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: D
A = (D/2)2

37. Light Collecting Area Animation
PHYS-3380 Astronomy
So: light collecting ability of a reflecting telescope is dependent on the area of the mirror
Light Collecting Area Animation

38. PHYS-3380 Astronomy
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 (Fo) and the eyepiece (Fe):
M = Fo/Fe
A larger magnification does not improve the resolving power of the telescope!

39. PHYS-3380 Astronomy
Interferometry
Recall: Resolving power of a telescope depends on diameter D:
amin = 1.22 /D.
This holds true even if not the entire surface is filled out.
Combine the signals from several smaller telescopes to simulate one big mirror  Interferometry