Secondary Rainbows

1. ISNS 3371 - Phenomena of Nature Secondary Rainbows

2. ISNS 3371 - Phenomena of Nature The angle at which the red light leaves the raindrop measured from the anti-solar point for the double reflection/secondary rainbow is 51° as compared with 42° for the single reflection/primary rainbow. So the secondary rainbow encircles the primary rainbow at about 10° farther from the anti-solar point (with reversed colors).

3. ISNS 3371 - Phenomena of Nature The light of the secondary bow is one-tenth the intensity of that of the primary bow, given the same viewing conditions.

4. ISNS 3371 - Phenomena of Nature Polarization Light emitted by the sun, a lamp in the classroom, a candle flame, etc… is unpolarized light - created by electric charges which vibrate in a variety of directions - an electromagnetic wave (transverse) which vibrates in a variety of directions. Helpful to picture unpolarized light as a wave which has an average of half its vibrations in a horizontal plane and half of its vibrations in a vertical plane. Polarized light waves - light waves in which the vibrations occur in a single plane. Polarization - Process of transforming unpolarized light into polarized light. Most common method of polarization uses a Polaroid filter - made of a special material capable of blocking one of the two planes of vibration of an electromagnetic wave. When unpolarized light is transmitted through a Polaroid filter, it emerges with one-half the intensity and with vibrations in a single plane; it emerges as polarized light.

5. ISNS 3371 - Phenomena of Nature Two filters with polarization axes perpendicular to each other will completely block the light. Light is polarized upon passage through the first filter - say, only vertical vibrations were able to pass through. These vertical vibrations are then blocked by the second filter since if its polarization filter is aligned in a horizontal direction. Like picket-fence and standing wave on a rope - vibrates in a single plane. Spaces between the pickets of the fence allow vibrations parallel to the spacings to pass through while blocking vibrations perpendicular to the spacings. Orient two picket fences such that the pickets are both aligned vertically - vertical vibrations will pass through both fences - align pickets of second fence horizontally - the vertical vibrations which pass through the first fence will be blocked by the second fence.

6. ISNS 3371 - Phenomena of Nature Polarization by Reflection Unpolarized light can also undergo polarization by reflection off of nonmetallic surfaces - extent dependent upon the angle at which the light approaches the surface and upon the surface material. Metallic surfaces reflect light with variety of vibrational directions - unpolarized. Nonmetallic surfaces (asphalt, snow, water, paint on a car) reflect light such that there is a large concentration of vibrations in a plane parallel to the reflecting surface. A person viewing objects by means of light reflected off of nonmetallic surfaces will often perceive a glare if the extent of polarization is large. Which pair of glasses is best suited for automobile drivers, fishermen, snow skiers?

7. ISNS 3371 - Phenomena of Nature Adding a third filter with between two filters polarization axis at 45º to the other two will allow light though. How? Remember, unpolarized light vibrates in all different directions. So not just the light with horizontal vibrations passes through the first filter, but all light with a vibrational component in the horizontal direction - in other words, all but the light with vertical vibrations has some component in the horizontal direction that gets through.

8. ISNS 3371 - Phenomena of Nature Before the middle filter, the light is horizontally polarized. The component of horizontally polarized light along 45º gets through the middle filter. The component of that light in the vertical direction then gets though the last filter.

9. ISNS 3371 - Phenomena of Nature When light passes through a transparent material such as plastic, internal (and normally invisible) stresses in the material can rotate the angle of polarization - different colors will be rotated by different amounts.  Place horizontal polarizer below the object, and a vertical one above it - no light will be transmitted unless there are stresses inside the object that rotate the light.  Useful in the design of engineering structures - build a model out of plastic, and view it with crossed polarizers.  Put a force on the model - regions of the model that are stressed the most will show up in color.  This way you can determine which parts of the structure are most likely to break, and the design can be changed (if necessary) to relieve some of that stress.

10. ISNS 3371 - Phenomena of Nature Lenses and Mirrors (and applications to astronomy)

11. ISNS 3371 - Phenomena of Nature Geometry of a Concave Mirror Focus Principal axis Vertex Focal length 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

12. ISNS 3371 - Phenomena of Nature Geometry of a Converging (Convex) Lens Focus Optical axis Focal length 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

13. ISNS 3371 - Phenomena of Nature Image Magnification Using a Simple Lens Focal Plane L1 L2 D1 D2 L1 D1 _ _ = L2 D2

14. ISNS 3371 - Phenomena of Nature The image formed by a single lens is inverted.

15. ISNS 3371 - Phenomena of Nature The Eye 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.

16. ISNS 3371 - Phenomena of Nature 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.

17. ISNS 3371 - Phenomena of Nature Types of Optical Telescopes

18. ISNS 3371 - Phenomena of Nature 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

19. ISNS 3371 - Phenomena of Nature 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.

20. ISNS 3371 - Phenomena of Nature 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.

21. ISNS 3371 - Phenomena of Nature 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.

22. ISNS 3371 - Phenomena of Nature 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.

23. ISNS 3371 - Phenomena of Nature The Keck Telescopes Largest in the world - on Mauna Kea in Hawaii. 36 hexagonal mirrors function as single 10-meter mirror.

24. ISNS 3371 - Phenomena of Nature 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.

25. ISNS 3371 - Phenomena of Nature Refracting vs Reflecting Telescopes 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 - must be very high quality and perfectly shaped on both sides Refracting lenses subject to chromatic aberration

26. ISNS 3371 - Phenomena of Nature 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

27. ISNS 3371 - Phenomena of Nature 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

28. ISNS 3371 - Phenomena of Nature 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

29. ISNS 3371 - Phenomena of Nature 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 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

30. ISNS 3371 - Phenomena of Nature 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

31. ISNS 3371 - Phenomena of Nature Uses of Telescopes • Imaging • use a camera to take pictures (images) • Photometry  measure total amount of light from an object • Spectroscopy • use a spectrograph to separate the light into its different • wavelengths (colors) • Timing • measure how the amount of light changes with time (sometimes in a fraction of a second)

32. ISNS 3371 - Phenomena of Nature In astronomy, filters are usually placed in front of a camera to allow only certain colors to be imaged Single color images are superimposed to form true color images. Imaging

33. ISNS 3371 - Phenomena of Nature Nonvisible Light • Most light is invisible to the human eye - gamma rays, x-rays, ultraviolet, infrared, radio waves. • Special detectors/receivers can record such light - each type of light can provide information not available from other types. • Digital images are reconstructed using false-color coding so that we can see this light. Chandra X-ray image of the Center of the Milky Way Galaxy

34. The Crab Nebula ISNS 3371 - Phenomena of Nature Visible Infrared X-rays Radio Waves

35. ISNS 3371 - Phenomena of Nature Atmospheric Effects Earth’s atmosphere causes problems for astronomers on the ground: • Bad weather makes it impossible to observe the night sky. • Man-made light is reflected by the atmosphere, thus making the night sky brighter. • this is called light pollution • The atmosphere absorbs light - dependent on wavelength • Air turbulence in the atmosphere distorts light. • That is why the stars appear to “twinkle”. • Angular resolution is degraded.

36. ISNS 3371 - Phenomena of Nature Atmospheric Absorption of Light • Earth’s atmosphere absorbs most types of light. • good thing it does, or we would be dead! • Only visible, radio, and certain IR and UV light make it through to the ground. To observe the other wavelengths, we must put our telescopes in space!

37. ISNS 3371 - Phenomena of Nature Space Astronomy

38. ISNS 3371 - Phenomena of Nature Space Based Telescopes FUSE (Far UV) Chandra X-ray Obs. Hubble Space Telescope Compton Gamma Ray Obs. Spitzer Space Telescope (IR)

39. ISNS 3371 - Phenomena of Nature Radio Telescopes • The wavelengths of radio waves are long. • So the dishes which reflect them must be very large to achieve any reasonable angular resolution. 305-meter radio telescope at Arecibo, Puerto Rico