1445 Introductory Astronomy I

1. 1445Introductory Astronomy I Chapter 3 Light and Telescopes R. S. Rubins Fall, 2010

2. The Speed of Light 1 • Aristotle (ca. 360 BCE) thought the speed of light to be infinite, while Galileo (ca.1600) found it too fast to measure. • In 1675, the Danish astronomer, Ole Roemer, used Newton’s Laws to predict the eclipses of the moons of Jupiter. His predicted times were early when Jupiter was near conjunction, and late when near opposition. • Believing Newton’s Laws to be correct, he was able to calculate a value for the speed of light, which would have been accurate if the Sun-Jupiter distance had been known precisely at that time. • Now known very precisely, the speed of light c in space has the approximate value, c = 300,000 km/s (= 186,000 mi/s).

3. The Speed of Light 2 Roemer’s method (1675) compares the predicted eclipse times for one of Jupiter’s moons, based on Newton’s Laws, with the measured times at opposition and near conjunction.

4. The Speed of Light 3 The terrestrial method (ca. 1920) measures the time for light to travel the 70 km round trip from Mt. Wilson to Mt. Baldy using the equation c = x/t, where x is 70 km.

5. Reflection of Light The angle of reflection r equals the angle of incidence i.

6. Refraction of Light

7. General Properties of Light • A light rayis a very narrow beam of light. • Reflection is the rebound of a light ray off a surface. • Refractionis the bending of a light ray when passing from one transparent medium to another at an oblique angle. • The denser the medium, the slower the speed of light; thus, the speed of light is slower in glass than in air. • Dispersion is the separation of light into its constituent colors. • The color of light depends on its frequency, and therefore wavelength, since c = f. • Monochromaticlight is light of a single wavelength. • Interference,diffraction andpolarizationare wave properties of light.

8. Dispersion of White Light by a Prism • The upper picture shows the variation of wavelength with color. • The lower picture shows Newton’s experimental proof that the glass changes the direction of a light-beam, but does not affect its color.

9. The Continuous Spectrum

10. Light: Waves or Particles ? There are two basic ways of transferring energy in every-day life, either by particles or by waves. In the 17th century, Newton considered light to be particles, while the Dutch scientist, Huygens, thought it to be waves. In 1801, through the phenomenon of interference, Young showed experimentally that light traveled as waves. Wave properties of light Diffraction is the bending of light behind an aperture or around an obstacle. Interference is the combination of two or more waves of the same type and wavelength which meet at a point in space. Polarization is the restriction of the vibration of a (transverse) wave to a particular direction.

11. Wave Motion • The wavelength λ (in km) is the distance between neighboring points on the wave which have the same phase. • The frequency f (in Hz) is the number of crests passing a given point per second. • The speed of the wave is given by v = f λ. • For light, the speed c = 300,000 km/s.

12. Interference of Two Like Waves Constructive interference occurs when the two waves are in phase, so that their crests coincide. Destructive interference occurs when the two waves are 180o out of phase, so that the crest of one wave coincides with the trough of the other.

13. Diffraction of Light Diffraction, which is the bending of a wave behind apertures and around obstacles, plays an important role in double-slit interference. The light passing through the narrow slit shown in Fig (c) behaves as though it originated at the slit. as happens in double-slit interference.

14. Double Slit Interference 5smaller spacing larger spacing

15. Double Slit Interference 4 • Coming from the same source S0, the light passing through slits slits S1 and S2 is coherent, a requirement for interference. • The interference of the diffracted waves from S1 and S2produces a set of interference fringes.

16. Diffraction Grating 1 • A diffraction grating, which consists of thousands of equally spaced fine lines ruled on a small rectangular plastic slide, is used to give very sharp interference maxima. • The figure shows how the spectra are sharpened when the number of slits is increased from 2 in Fig.(a) to 6 in Fig.(b).

17. Grating Spectrometer • The m = 0 spectrum is observed when the telescope is lined up with the collimator (θ = 0). • The m = ±1 spectra are observed by varying the angle θ in both directions. • For the m = ±1 spectrum, the intensity maxima are given by λ= d sinθ.

18. Dispersion by a Diffraction Grating Emission line-spectrum • The m=0 spectrum is not deviated. • The diffracted spectra are denoted m =1 and m = 2. • In the diffracted spectra, the red end (longer wavelengths) is more “deviated” from the m=0 line than the blue. Continuous spectrum

19. Emission Line-Spectra of some Elements

20. Why The Sky is Blue • Sunlight contains all the colors of the rainbow. • The molecules of the Earth’s atmosphere scatter the incoming molecules in all directions. The blue (short wavelength) end of the spectrum is scattered more than the red (long wavelength) end. Thus, the sky looks blue, while the Sun appears yellow, which corresponds to white light minus the scattered blue. • At sunrise or sunset, the Sun’s rays take a longer path through the atmosphere, so that more of the sunlight is scattered, making the Sun appear orange or red.

21. The Electromagnetic Spectrum 1

22. The Electromagnetic Spectrum 2

23. Photons All EM radiation travels through space at the speed c. While EM waves travel through space as waves, their interaction with matter is as tiny packets of energy, known as photons (Einstein, 1905). The energy E of a photon is given by E = hf = hc/λ, where h is Planck’s constant. In practical units, the energy of a photon is given by E = 1240/λ, where E is in eV (electron-volts) and λ is in nm. Photons longer λ of have lower energies, and vice-versa. Example:a photon of wavelength 310 nm has energy E = 1240/310 = 4.0 eV. 23

24. Transparency of Earth’s Atmosphere Only visible light and radiowaves reach the ground at all their wavelengths, while all infrared rays reach high mountains.

25. Refraction by a Converging Lens • A converging (or convex) lens focuses light entering the lens parallel to the axis at the focal point F. Off-axis rays focus at a point in the focal plane.

26. Focusing Light with a Converging Lens

27. Chromatic Aberration 1 • Chromatic aberrationin a lens causes blue end of the visible spectrum to have a shorter focal length than the red. • Chromatic aberration does not occur in mirrors.

28. Chromatic Aberration 2 An achromatic combination lens made with two different types of glass can greatly reduce chromatic aberration by correcting for two colors.

29. Spherical Aberration in a Lens Spherical aberration refers to the fact that the outermost rays striking a spherical lens or mirror come to focus earlier than the central rays.

30. Spherical Aberration in a Mirror Spherical aberration occurs in a concave mirror with a spherical reflecting surface, as shown below.

31. Parabolic Mirror Spherical abberation does not occur in a mirror with a parabolic reflecting surface.

32. Parallel Rays from a Distant Object

33. Astronomical Telescope 1 • The magnification is given by M = – fo/fe , where fo and fe are the focal lengths of objective and eyepiece. • The length of the instrument is L = fo + fe.

34. Astronomical Telescope 2 The final image seen by an observer looking through the eyepiece is inverted.

35. World’s Largest Refracting Telescope Built in the late 1800s, the telescope at the Yerkes Observatory, near Chicago, has an objective of diameter 40 inches.

36. Astronomical Telescope 3 • Large objectives use parabolicmirrors because i. neither spherical aberration nor chromatic aberration occur; ii. they weigh much less than large glass lenses; iii. Unlike glass lenses, metal mirrors are structurally stable.

37. Effect of Twinkling: Star-Field from the Ground

38. Effect of Twinkling: View from the HST

39. Active Optics 1 • Active optics began to be used in the 1980s to counteract distortions of the telescope’s primary mirror. • Earlier mirrors were made very thick, so that they would keep their shape as the telescopes were moved across the sky: this limited their diameters to about 6 m. • Later telescopes, were deliberately made too thin for them to keep the correct shape; instead, a set of actuators behindthe mirror kept the shape optimal. • In some cases, the mirror was segmented into many small mirrors, which eliminated most of the gravitational distortion occurring in large, thick mirrors. • Active optics is used in the larger telescopes built in the last decade, such as the 8m Keck telescopes in Hawaii.

40. Active Optics 2 Proposed OWL 100m Reflecting Telescope

41. Adaptive Optics 1 • Active optics cannot compensate for atmospheric changes which occur at millisecond time-scales. • Adaptive optics (AO) is a technique used to compensate for rapidly changing optical distortion, which occurs in ground-based telescopes through atmospheric turbulence. • The small rapid shifts in the position of a star’s image both blur the image and produce the ‘twinkling” of stars. • Adaptive optics works by measuring the distortions in a wavefront , and compensating for them with a deformable mirror (or liquid crystal display). • The mirror is adjusted so that a reference star (or artificial image, produced by a laser beam) is kept in sharp focus.

42. Adaptive Optics 2 • The Cat’s Eye Nebula, taken from the same ground-based telescope, is shown without (left) and with (right) adaptive optics. With adaptive optics, the proposed ground-based 100 m OWL (overwhelmingly large) telescope would have a resolving power 40 times better than the HST.

43. Adaptive Optics 3 • Left: atmospheric distortion makes the ground-based image of a double star look like a single star. • Right: adaptive optics allows the two stars to be clearly distnguished.

44. Radio Telescopes 1 Prior to 1930, all astronomy was done with visible light. The largest single radio telescope dish in the world, in Arecibo, Puerto Rico, is 300 m in diameter, but its resolution is appreciably less than that of a large optical telescope. Very high resolution radio telescopes link individualtelescopes through a process known as interferometry. The Very Large Array (VLA), situated near Socorro, NM, contains 27 concave reflecting dishes, each 26 m in diameter, arranged along three arms. The Very Long Baseline Array (VLBA), uses radio telescopes thousands of miles apart, from Hawaii to New Hampshire. • The downsides of such systems are their poor light-gathering ability (sensitivity) and their small fields-of-view.

45. Keck Reflecting Telescopes, Hawaii While each telescope singly is equivalent to a 10 m reflecting telescope, when linked together they are equivalent to a single 85 m telescope.

46. VLA 1

47. VLA 2

48. Radio Telescopes 2 The new Green Bank Telescope (GBT) in West Virginia has a dish about 100 m in diameter, and is the world’s largest rotatable radio telescope.

49. Optical and Radio Photos of Saturn • To be displayed as a photo, the radio signal must be shown in “false” color. • The most intense radio emission is red, followed by yellow and blue, while black means that there is no measurable signal.

50. Radio Telescope at Cambridge U. With this detector strung together with 120 miles of wire and cable, Jocelyn Bell in 1967 discovered the pulsar.