Optics Basics

A Physics MOSAICMIT Haystack Observatory RET 2010

Background image from NASA

Representing LightAs we have already seen, light (and all electromagnetic waves) consists of electric and magnetic fields oscillating perpendicular to each other and to the direction of wave propagation.

While a source of electromagnetic radiation will (generally) send waves out in all directions from the source, it is often convenient to represent these waves as rays, traveling in straight lines and represented by arrows.

Some sources, like light bulbs and stars, send light rays out in all directions.

Other sources, like lasers, send out light rays in (primarily) one direction.Thomasbrightbill, from flickr, Creative Commons

Image by SKMay

Inverse Square Law

Image from NASA

• Like sound, the gravitational force, and the electrostatic force, light (and other electromagnetic waves) follow an inverse square law for intensity.

• As the distance from a source of light increases, the intensity detected decreases with the square of the distance.

• This should make some sense, since the light from the source is being spread over larger areas (proportional to distance2) as the distance increases.

Which Object is Brightest?

Image found at Nasa.gov, photo credit: Dave Jurasevich, Mt. Wilson Observatory

Reflection for Light• What does it mean to be reflective?– As with other types of waves, light reflects off boundaries it

encounters at changes in media.– Materials absorb some of the light that encounters their

surface, transmit some of the light, and reflect some of the light.

– If most of the light is reflected rather than absorbed, we think of it as a reflective surface.

– This depends on the chemical properties of the material.

• Glass transmits most of the light through the medium, but some is reflected. Why can you see yourself in your windows at night but see outside during the day?

Law of Reflection

Image from Wikipedia, Drawn by Johan Arvelius 2005-09-26, Creative Commons

• Law of Reflection: The angle of incidence of a ray equals the angle of reflection.

• Both angles should be measured from the normal, or line perpendicular to the surface.

• The law of reflection applies to all reflection, regardless of the surface or the type of wave being reflected.

Diffuse and Specular Reflection• If the surface is smooth, the reflection is specular. That is,

the light rays all reflect in the same direction.• If the surface is not smooth, the reflection is diffuse. That is,

the light rays reflect in different directions

Images from http://twistedphysics.typepad.com/cocktail_party_physics/optics/

Smooth?• The “smooth”-ness of a surface depends on the size of the

irregularities on the surface compared to the wavelength of the wave being reflected.

• This means that what constitutes smooth for radio waves is different than for visible light or x-rays. (Remember the EM Spectrum)

• In order to be considered smooth, any bumps on the surface must be smaller than the size of the wavelength being reflected. For telescopes, microscopes, and other high precision devices, even smaller irregularities are tolerable. Typically, astronomers seek 1/20 l smoothness for their instruments.

Smooth to What?

Image from National Research Council of Canada

Satellite TV Dish

Water on Calm Day

James Clerk Maxwell Telescope

Two Properties of Being Shiny• In conclusion, in order to be “shiny” for a

particular electromagnetic wave, a surface must be both– Reflective: it must neither absorb nor transmit the

majority of the light incident upon it.– Smooth: with bumps and irregularities on the same

size scale of the wavelength of the radiation being reflected

MOSAIC and reflection

• The MOSAIC system reflects radio waves at a frequency of 11.072 GHz that come from ozone in Earth’s mesosphere onto a feed at the focal point of the dish.

• Because it reflects radio waves, it does not look shiny in visible light, but does look shiny to the 11.072 GHz radiation we are interested in.

Basics of Concave Mirrors

• By making a shiny surface in an appropriate curved shape, you can create a mirror where parallel rays approaching the mirror reflect to a single point (the focal point).

• This is still an example of specular reflection, and each individual ray reflects according to the law of reflection.

From Wikipedia, Image by AndrewBuck, Creative Commons

qiqr

qiqr

qr

qi

Properties of Concave Mirrors• Focal Length (f)

– Distance between the mirror and the focal point (F).– Depends on radius curvature of mirror (r): for spherical mirrors, f = r/2

• Light Gathering Power– Ability of the mirror to gather light. Especially important for telescopes.– Depends on area of telescope. Proportional to (diameter)2

• Resolution– Ability of the mirror to differentiate small features.– Depends on wavelength being observed and diameter of telescope.

• Improves proportional to diameter of telescope.• Improves indirectly with wavelength.

Image from Telescopes from the Ground Up, Amazing Space, http://amazing-space.stsci.edu/resources/explorations/groundup/,Image in public domain

Arecibo Radio Telescope

The 300 m telescope at Arecibo, Puerto Rico is designed to observe and transmit radio waves to and from space. As we have seen, radio waves have a much longer wavelength than the visible spectrum. How is that reflected in the size of this telescope? Its smoothness?

Photo by SKMay

Interferometry

Image from NRAO

Another solution to the problem of poor resolution from radio waves involves mathematically combining the signals from multiple telescopes spread over a large area. This is called interferometry.

Combining the signals in this way creates an “effective diameter” for the purposes of telescope resolution equal to the distance between the dishes.

The Very Large Array (VLA) in Socorro, NM consists of 27 identical telescopes in a Y-shaped configuration to allow for interferometry of the signals from all the dishes.

The dishes are on tracks which allow them to be placed at different distances for different observational needs.

Two Types of Curved Mirrors

• Curved mirrors are either concave or convex in shape.

• As we have seen, concave mirrors tend to converge light rays (and thus are used in telescopes).

• Convex mirrors tend to diverge light rays.

• Both types of curved mirrors can produce images, and both have practical applications.

Images from Telescopes from the Ground Up, Amazing Space, http://amazing-space.stsci.edu/resources/explorations/groundup/. Image in public domain

Applications of Mirrors

The Bean, ChicagoImage by SKMay

James Webb Space TelescopeImage from NASA

Security MirrorImage by Leo Reynolds, Flickr, Creative Commons

Magnifying MirrorImage by steve loya, Flickr, Creative Commons

Rearview MirrorImage by SKMay

Side View MirrorImage by SKMay

Spherical Aberration and Parabolas• Spherical reflectors introduce an aberration (error) in focal point.

– This is called spherical aberration, and consists of the light rays not coming to a perfect focus at a single point.

• This aberration does not exist when a parabola is used.– Because of the properties of a parabola, light rays that come into the mirror

parallel to the center line reflect exactly to a single focal point.

Image from Telescopes from the Ground Up, Amazing Space, http://amazing-space.stsci.edu/resources/explorations/groundup/. Image in public domain

Applications of Parabolic Optics

From Wikipedia, Creative Commons, User Duk

The world's larges solar energy dish at the Ben-Gurion National Solar Energy Center in Sde Boker, Israel. From Wikipedia, Creative Commons, user David Shankbone.

Parabolic Hot Dog Cooker, from nycg46, found on Flickr

From Wikipedia, Creative Commons, User Matěj Baťha

Offset Parabola

• Design: – Uses only part of a parabola,

allowing the focal point to be below the dish doing the receiving.

• Advantages– The receiver (located at the

focal point) does not need to block any of the signal

• Note that the dish appears to be pointing in a different direction than it actually is.

Image of Green Bank Radio Telescope (Green Bank, WV) from NRAO / AUI / NSF, from RET 2009

MOSAIC’s Offset Parabola

Images by SKMay

Like the Green Bank Radio Telescope, MOSAIC (and all small television satellite dishes) are offset parabolas. While this dish appears to be pointed towards the ground, it is actually pointing 8˚ above the horizon.

Refraction• Refraction Basics– Recall that the speed of a wave depends on the properties of

the medium it is traveling through.– For light, the speed of the wave depends on the optical density

of the medium. – Light only travels at c (3.0 x 108 m/s), the speed of light in a

vacuum, when it is in a vacuum. (Go figure!)

• Index of Refraction– We can quantify the effect of different media on the speed of

light with the index of refraction (n).– Greater n, slower speeds.

v

cn

Some Indices of Refraction

What is the speed of light in water?

vs

mv

cn

81000.333.1

sms

mv 8

8

1026.233.1

1000.3

Still pretty fast!

Material Index of Refraction

Vacuum 1 (exactly)

Air 1.000277

Water 1.333

Crown Glass 1.52

Flint Glass 1.66

Ice 1.309

Diamond 2.417

Cubic Zirconia 2.20

Human Cornea 1.373

Refraction and Fermat’s Principle of Least Time

• Refraction is the bending of a wave due to a change in the speed of the wave in different media.

• This can be thought of a consequence of Fermat’s Principle.– Light travels more slowly in optically dense media, so

it spends less time in them.– Light travels more quickly in media that are less

optically dense, thus spending more time.

Example: Fermat’s Principle for Lifeguards

sand

water

Lifeguard

flailing swimmer

The lifeguard will spend more time running along the beach to get to the flailing swimmer than in the water, because he is a faster runner than he is a swimmer.

How would this ideal path change if the lifeguard were a seal?

I’m a much better swimmer than runner!

Image by SKMay

Example: Fermat’s Principle for Light

air

water

laser pointer

target

The light from the laser will take a path that spends more time in air than water, since it travels faster in air than it does in water.

Note that this results in a smaller angle of refraction than the angle of incidence, since both are measured from the normal.

qi

qr

Light Rays in MediaNote that

• Light bends towards the normal when entering a slower medium (higher n)– qi > qr when ni < nr

• Light bends away from the normal when entering a faster medium (lower n)– qi < qr when ni > nr

The amount of bending will depend on how much slower or faster the new medium is.Note also

• The light is partially reflected (following the law of reflection) at each boundary.

glass air

qi

qi

qr

Convex Lens Basics• By cleverly changing the shape of a refractive medium,

you can produce a lens.• Parallel rays approaching the lens converge to a single

point.• Each individual light ray bends according to Snell’s Law.

Images from Telescopes from the Ground Up, Amazing Space, http://amazing-space.stsci.edu/resources/explorations/groundup/. Image in public domain

Properties of a Convex Lens• Focal Length

– Depends on n• The greater the change in the speed of light, the greater the bending, and therefore,

the smaller the focal length.

– Depends on curvature• The smaller the radius, the greater the bending, and therefore, the smaller the focal

length.

• Light Gathering Power: as with concave mirrors, proportional to area.

• Resolution: as with concave mirrors, improves with diameter and gets worse as the wavelength of the observed radiation increases.

Image by SKMay

Two Types of Lenses• By cleverly changing the shape

of the medium, you can produce a lens.

• Just as with mirrors, lenses can be either concave or convex in shape.

• While Snell’s Law governs the interaction of each light ray with the lens, we can develop some shortcuts by considering special rays, as we did with mirrors.

Images from Telescopes from the Ground Up, Amazing Space, http://amazing-space.stsci.edu/resources/explorations/groundup/. Image in public domain

Applications of Lenses

Image from chrisjohnbecket, from Flickr, Creative Commons

Image by SKMay

Images by SKMay Image by Yerkes Observatory

Dispersion• The index of refraction is not constant for all

frequencies. This is called dispersion.• Because n (the index of refraction) is different for

different wavelengths and frequencies, different wavelengths and frequencies will bend different amounts in the same medium.

• Effects– Prisms– Rainbows– Chromatic Aberration– Atmospheric Effect on radio waves from space

Image by Marlene May

Image of Prism from Telescopes from the Ground Up, Amazing Space, http://amazing-space.stsci.edu/resources/explorations/groundup/. Image in public domain

Chromatic Aberration• Because different wavelengths have slightly different n,

they will bend different amounts in a lens, and therefore have different focal lengths.

• This can be (partially) corrected with an achromatic lens, which introduces a second lens of a different n to bring two wavelengths to the same focal point.

Image from Wikipedia, user DrBob, Creative CommonsImage from Wikipedia, user DrBob, Creative Commons

Dispersion of Radio Waves from Space

• Earth’s Ionosphere acts as a dispersive medium for radio signals from space.

• As the ionosphere changes (due to space weather such as solar flares), the dispersive properties change.

• GPS signals become unpredictable during high variability in solar activity due to this.

• Atmospheric scientists can use the dispersive properties of the ionosphere to study its variations.

Reflecting vs. Refracting Telescopes• Most large telescopes are reflectors rather than

refractors. Why?– Only one surface to make perfectly shaped, which

makes it less expensive and less difficult to produce.– No sagging (glass is viscous fluid) in mirrors; mirrors

can be supported from the bottom– No chromatic aberration in mirrors, and a parabolic

shape eliminates spherical aberration– More compact designs are possible; with secondary

reflectors, the telescope can be smaller than the focal length.

Another Optical Effect• Gravitational Lensing: gravity from massive

objects (usually galaxies) causes light from beyond the massive object to bend.

Images from NASA