Optics Read Your Textbook: Foundations of Astronomy –Chapter 6, 7 Homework Problems Chapter 6 –Review Questions: 1,2 5-7 –Review Problems: 1-3, 8 –Web Inquiries: 2 Homework Problems Chapter 7 –Review Questions:1, 2, 4, 5, 7, –Review Problems: 1-4, 9 –Web Inquiries: 1

Light Gathering Power Telescope diameter (D) Light Gathering Power (LGP) is proportional to area. LGP =  (D/2) 2 D = diameter Light Gathering Power

Telescope diameter (D) Light Gathering Power (LGP) is proportional to area. LGP =  (D/2) 2 D = diameter A 16 inch telescope has 4 X the LGP of an 8 inch. LGP 16 inch =  (16/2) 2 LGP 16 /LGP 8 = 4 LGP 8 inch =  (8/2) 2 A 16 inch telescope has 2800 X the LGP of the eye. LGP 16 inch/LGP eye (0.3inch) = (16/0.3) 2 = 2844 Light Gathering Power

More Light

Types of Waves Compression wave oscillations are in the direction of motion Transverse Wave oscillations are transverse to the direction of motion

Wave Parameters Wavelength ( ) length Amplitude (A) height Frequency (f) repetition

Amplitude: Size of wave (perpendicular to direction of propagation) Proportional to Intensity(Sound loudness, Light brightness) Wavelength:  Size of wave (in the direction of propagation) Frequency: Number of waves passing a fixed position per second f (cycles/second, Hertz) Wave Speed: v =  f Frequency increases Frequency decreases Energy increases Energy decreases Wavelength decreases Wavelength increases

An Electromagnetic Wave (a.k.a. Light) Light travels at a velocity c =  f (3x10 8 m/s)

E-M Frequency and Wavelength

Electromagnetic Spectrum

Electromagnetic Spectrum Uses

The Visible Spectrum COLORFREQUENCY (10-14 Hz)WAVELENGTH (nm) R O Y G B V

Radio (Light) Wave 94.1 THE POINT, broadcasts at a frequency of 94.1 MHz (10 6 Hz). What is the wavelength of its carrier wave? A radio wave is a light wave, c =  f

Radio (Light) Wave 94.1 THE POINT, broadcasts at a frequency of 94.1 MHz (10 6 Hz). What is the wavelength of its carrier wave? A radio wave is a light wave, c =  f = 3 x 10 8 /94.1 x 10 6 = 3.2 meters

Doppler Effect Change in frequency of a wave due to relative motion between source and observer. A sound wave frequency change is noticed as a change in pitch.

Doppler Effect for Sound Change in frequency of a wave due to relative motion between source and observer.

Line of Sight Only sensitive to motion between source and observer ALONG the line of sight.

Radial Velocity Convention  True Velocity  Radial  Line of Sight Component Observer No Doppler Shift Transverse motion Radial Velocity > 0 Moving Away Radial Velocity < 0 Moving Toward

Doppler Effect Light

Doppler Effect for Light Waves Change in frequency of a wave due to relative motion between source and observer. c =  f speed of light = wavelength x frequency c = 3 x 10 8 m/s E = hf = hc/  energy of a light wave, a photon of frequency (f) or wavelength (  h = planck’s constant 6.63 x J-sec A light wave change in frequency is noticed as a change in “color”.

Wavelength Doppler Shift  0 = at rest (laboratory) wavelength = measured (observed) wavelength  =  0 = difference between measured and laboratory wavelength v r / c =  0 v r = (  0 ) c radial velocity

Solar Spectrum Solar Radiation Output The sun looks “yellow”

Wien's law relates the temperature T of an object to the wavelength maximum at which it emits the most radiation. Mathematically, if we measure T in kelvins and the wavelength maximum ( ) in nanometers, we find that* max = 3,000,000/T *3,000,000 is an approximation of the true value 2,900,000 (just like m/s approximates the speed of light Wien’s Law

max = 3,000,000/T T surface = 5800 K (solar surface temperature) max = 3,000,000 / 5800 K = 517 nm (Yellow-Green) The atmosphere scatters most of the blue light making the sun appear more yellow and the sky blue Approximate Solar Peak

Light Waves Light is a wave that propagates at speed c. –c = 3 x 10 8 m/s in a vacuum –velocity is slower in other media Like sound waves and other waves, light should exhibit the same properties seen for other waves. These are diffraction, reflection, and interference. In addition, light waves also exhibit refraction, dispersion and polarization.

Diffraction of Water Waves Diffraction: Waves ability to bend around corners

Ray Trace A ray trace is meant to represent the direction of propagation for a set of parallel waves called a “wave front.”

Diffraction

Constructive Interference Waves combine without any phase difference When they oscillate together (“in phase”)

Wave Addition Amplitude ~ Intensity

Destructive Interference Waves combine differing by multiples of 1/2 wavelength They oscillate “out-of-phase”

Wave Subtraction

Two Slit Destructive Interference Path Length Difference = multiples of 1/2

Two Slit Interference

Slits are closer together, path length differences change

Light or Dark? Path Length Differences = , Waves arrive in phase Path Length Differences = 1/2, Waves arrive out of phase

Light or Dark? Light from the slits arrives at A. Path Length from slit 1 is 10,300 nm and from slit 2 is 10,300 nm for a difference of 0 nm. There is no path length difference so the waves from the two slits arrive at A oscillating in phase. They add constructively and produce a brighter area.

Light or Dark? Light from the slits arrives at E. Path Length from slit 1 is 10,800 nm and from slit 2 is 11,800 nm for a difference of 1000 nm. This path length difference is exactly two wavelengths so the waves from the two slits arrive at E oscillating in phase. They add constructively and produce a brighter area.

Light or Dark? Light from the slits arrives at B. Path Length from slit 1 is 10,450 nm and from slit 2 is 10,200 nm for a difference of 250 nm. This path length difference is exactly 1/2 a wavelength so the waves from the two slits arrive at B oscillating out of phase. They add destructively and produce a dark area.

Newton’s Rings

Resolution

Resolving Power Telescope diameter = D (cm) Resolution =  (arcminutes)  = 11.6/D Larger D = smaller angular sizes resolved

Increasing Resolving Power

Magnification Telescope diameter (D) Focal Length (f) f/# The focal length is # times the objective diameter Magnification = focal length of objective/ focal length of eyepiece

f-number (f/#) The f/# refers to the ratio of the focal length to the diameter. An f/10 optical system would have a focal length 10 X bigger than its diameter. The f/10 celestron C8 has a focal length of 80 inches. (8 inch aperture times 10) Our 16 inch telescope in the newtonian f/4 configuration has a focal length of 64 inches (16 x 4).

Magnification Magnification depends on the ratio of the focal lengths for the primary aperture to the eyepiece. M = focal length of objective / focal length of eyepiece = f o /f e Therefore for the same eyepiece, in general, the telescope with the longest focal length can achieve the greater magnification.

Magnification Isn’t Everything Magnifying something spreads the light out into a larger and larger area. An object is only so bright and magnifying an image too much causes it to become so diffuse that it ceases to be visible. Magnifying power for a telescope is not what you are looking for. Besides, increased magnification can be achieved by changing eyepieces. What do you want in a telescope?

Telescope diameter = D (cm) Resolution =  (arcminutes)  = 11.6/D Larger D = smaller angular sizes resolved Resolving Power

The Principle of Reflection The Angle of Incidence = The Angle of Reflection

Reflection

Optical Mirrors

Reflection

Telescope Configurations

Imaging

Interactive Demonstrations On The WEB Simple Geometric Optics Wave Addition l Two-slit Interference Doppler Shift

Refraction Refraction: The bending of light upon entering a medium with with a different density. A light wave will speed up or slow down in response to a changing medium.

Refraction is Dispersive Light of different frequencies is refracted by different amounts

Beach Party Pavement Sand

Beach Party Pavement Sand

Beach Party Pavement Sand

Beach Party Pavement Sand

Beach Party Pavement Sand

Refraction Light waves, like people wave fronts can slow down also.

Bending Because of Velocity Principle of Refraction: A light wave will slow down upon entering a denser medium. The refracted light will be bent toward the normal to the surface in this case. A light wave will speed up upon entering a less dense medium. The refracted light will be bent away from the normal to the surface in this case.

Refraction Velocity slows down and is bent toward the normal to the surface, then speeds up upon exiting the glass and is bent away. Air Glass

Index of Refraction To characterize the change in velocity of a light wave in a transparence medium, we use the index of refraction (n). It is the ratio of the speed of light in a vacuum (c) compared to the speed of light in the medium (v). n = c / v Note: since c = 3x10 8 m/s is the speed limit for light, v for any other medium is less than c. Therefore, the index of refraction is always > 1.0

Indices of Refraction transparent mediumindex of refraction vacuum air water 1.33 ice 1.31 salt 1.54 Pyrex glass 1.50 quartz 1.46 glycerine 1.47 acrylic 1.70 diamond 1.24

Light Speed What is the speed of light waves traveling through acrylic? n acrylic = c / v

Light Speed What is the speed of light waves traveling through acrylic? V = 3x10 8 /1.7 = 1.76x10 8 m/s n acrylic = c / v 1.7 = 3x10 8 /v

Light Speed What is the index of refraction for a substance in which the speed of light is only 2.0x10 8 m/s? This substance is, or most resembles….glass. Glass has an index of refraction of 1.50 n unknown = c / v = 3x10 8 /2x10 8 = 1.5

Refracting and Reflecting Telescopes

Lenses

Refraction

The Beauty of Dispersion and Refraction

Rainbows

Chromatic Aberration

Formation of Images

Hubble Space Telescope

Hubble’s Innards

Repairs and Instrument Upgrades

New Instruments

Hubble Images a-Ground based image b-Hubble before repair image c-Hubble before repair (image processing) image d-Hubble fixed image

Instrumentation

CCD Cameras

Lasers

Clock Drive Last but NOT least. You and telescopes are on the moving observatory we call earth. A clock drive is required to counter earth’s rotation and provide tracking for telescopes and cameras.