Optics Basics
A Physics MOSAIC
MIT Haystack Observatory RET 2010
Background image from NASA
Representing Light
As 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.
Image by SKMay
Thomasbrightbill, from flickr, Creative Commons
Other sources, like lasers, send
out light rays in (primarily) one
direction.
Inverse Square Law
• 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.
Image from NASA
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
• 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.
Image from Wikipedia, Drawn by Johan Arvelius 2005-09-26, Creative Commons
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?
James Clerk Maxwell
Telescope
Water on Calm Day
Satellite TV Dish
Image from National Research Council of Canada
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.
qi
qr
qi
qr
qi
qr
From Wikipedia, Image by AndrewBuck, Creative Commons
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
Image from Telescopes from the Ground Up, Amazing Space,
http://amazing-space.stsci.edu/resources/explorations/groundup/,
Image in public domain
• 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.
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
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.
Image from NRAO
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, Chicago
Image by SKMay
James Webb Space Telescope Side View Mirror
Image from NASA
Image by SKMay
Magnifying Mirror
Rearview Mirror
Security Mirror
Image by steve loya, Flickr, Creative Commons
Image by SKMay
Image by Leo Reynolds, Flickr, Creative Commons
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 Matěj Baťha
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.
From Wikipedia, Creative Commons, User Duk
Parabolic Hot Dog Cooker, from
nycg46, found on Flickr
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
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.
Images by SKMay
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.
c
n
v
Some Indices of Refraction
What is the speed of light in water?
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
c
n
v
1.33 
v
3.00  108 m
s
v
3.00 108 m
1.33
Still pretty fast!
s  2.26 108 m
s
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
Lifeguard
water
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
laser pointer
qi
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.
water
qr
target
Note that this results in a
smaller angle of refraction
than the angle of incidence,
since both are measured
from the normal.
Light Rays in Media
Note that
air
glass
qi
• Light bends towards the normal
when entering a slower medium
(higher n)
– qi > qr when ni < nr
qr
qi
• 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.
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.
Image by SKMay
• 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.
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 by SKMay
Image from chrisjohnbecket, from Flickr, Creative Commons
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 Commons
Image 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