optics

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, 10-12– Review Problems: 1-4, 9– Web Inquiries: 1

Light Gathering PowerTelescope diameter (D)Light Gathering Power (LGP) is proportional to area.

LGP = (D/2)2 D = diameter

Light Gathering Power

Light Gathering PowerTelescope 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 LGP16/LGP8 = 4LGP 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 Waveoscillations are transverse

to the direction of

motion

Wave ParametersWavelength () 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 decreasesEnergy increases Energy decreases Wavelength decreases Wavelength increases

An Electromagnetic Wave (a.k.a. Light)

Light travels at a velocity c = f (3x108 m/s)

E-M Frequency and Wavelength

Electromagnetic Spectrum

Electromagnetic Spectrum Uses

The Visible Spectrum

COLOR FREQUENCY (10-14 Hz) WAVELENGTH (nm)

• R 4.0-4.8 750-630• O 4.8-5.1 630-590• Y 5.1-5.4 590-560• G 5.4-6.1 560-490• B 6.1-6.7 490-450• V 6.7-7.5 450-400

Radio (Light) Wave

94.1 THE POINT, broadcasts at a frequency of

94.1 MHz (106 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 (106 Hz).

What is the wavelength of its carrier wave?

A radio wave is a light wave, c = f

= 3 x 108/94.1 x 106

= 3.2 meters

Doppler EffectChange 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.

http://pls.atu.edu/physci/physics/people/trantham/applets/doppler/javadoppler.html

Doppler Effect for Sound• Change in frequency of a wave due to relative motion

between source and observer.

Line of SightOnly

sensitive

to motion

between

source and

observer

ALONG

the line of

sight.

Radial Velocity ConventionTrue Velocity

RadialLine of Sight Component

Observer

No Doppler ShiftTransverse motion

Radial Velocity > 0Moving Away

Radial Velocity < 0Moving 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 108 m/s

E = hf = hc/energy of a light wave, a photon

of frequency (f) or wavelength ( h = planck’s constant 6.63 x 10-34 J-sec

A light wave change in frequency is noticed as a change

in “color”.

Wavelength Doppler Shift0 = at rest (laboratory) wavelength

= measured (observed) wavelength

= 0

= difference between measured and laboratory wavelength

vr/c = 0

vr = (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 300000000 m/s approximates the speed of light 299792458.

Wien’s Law

max = 3,000,000/T

Tsurface = 5800 K (solar surface temperature)

max = 3,000,000 / 5800 K

= 517 nm (Yellow-Green)

The atmosphere scatters most of the blue lightmaking 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 108 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 AdditionAmplitude ~ 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

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 Lengthfrom slit 1 is 10,300 nm and from slit 2is 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 Lengthfrom slit 1 is 10,800 nm and from slit 2is 11,800 nm for a difference of 1000 nm.

This path length difference is exactlytwo wavelengths so the waves from the two slitsarrive at E oscillating in phase. They add constructivelyand produce a brighter area.

Light or Dark?

Light from the slits arrives at B. Path Lengthfrom slit 1 is 10,450 nm and from slit 2is 10,200 nm for a difference of 250 nm.

This path length difference is exactly1/2 a wavelength so the waves from the two slitsarrive at B oscillating out of phase. They add destructivelyand 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 Xbigger 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 configurationhas a focal length of 64 inches (16 x 4).

MagnificationMagnification depends on the ratio of the focal lengthsfor the primary aperture to the eyepiece.

M = focal length of objective / focal length of eyepiece = fo/fe

Therefore for the same eyepiece, in general, the telescopewith the longest focal length can achieve the greater magnification.

Magnification Isn’t EverythingMagnifying something spreads the light out into a largerand 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 bychanging 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 Opticshttp://pls.atu.edu/physci/physics/people/trantham/Applets/lenses/javalens.html

• Wave Additionhttp://pls.atu.edu/physci/physics/people/trantham/Applets/waveaddition/waveapplet

.html

• Two-slit Interferencehttp://pls.atu.edu/physci/physics/people/trantham/Applets/youngslit/javayoungslit.html

• Doppler Shifthttp://pls.atu.edu/physci/physics/people/trantham/Applets/Doppler/javadoppler.html

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 / vNote:

since c = 3x108 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 medium index of refraction

vacuum 1.0000000

air 1.00029

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?

nacrylic = c / v

Light Speed

What is the speed of light waves traveling through acrylic?

V = 3x108/1.7

= 1.76x108 m/s

nacrylic = c / v

1.7 = 3x108/v

Light Speed

What is the index of refraction for a substance in which the

speed of light is only 2.0x108 m/s?

This substance is, or most resembles….glass.

Glass has an index of refraction of 1.50

nunknown = c / v

= 3x108/2x108

= 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.