Physics 106 Lesson #26
Optics:
Optical Instruments
Dr. Andrew Tomasch
2405 Randall Lab
atomasch@umich.edu
Propagation of Light Waves
•
Light waves arrive at
objects and interact
with them in three
basic ways. They can:
1. Reflect (bounce off)
2. Refract (go through)
3. Be absorbed (stop)
•
Not exclusive, all three
may occur
Demonstration
The Law of Reflection
• The incident ray,
reflected ray and
the normal to the
surface are all in
the same plane.
• The angle of
incidence equals
the angle of
reflection.
i   r
Plane Mirrors
• A ray of light from the top of the chess piece reflects
from the mirror
• To the eye, the ray seems to come from behind the
mirror
• Because none of the rays actually emanate from the
image, it is called a virtual image
Refraction
• As light passes from one medium to another it
changes direction at the interface between the
two media
• This change of direction is known as refraction
The Index of Refraction
• Light travels
through materials at
a speed less than its
speed in a vacuum
c
c
n v
v
n
INDEX OF
REFRACTION
Indices of Refraction
Vacuum
1 (exactly)
Air
1.0003
Water
1.333
Ice
1.309
Glass
1.523
Diamond
2.419
Refraction at Surface of Water
http://www.opticalres.com/gentsupp_f.html
Refraction and the
Normal Direction
• Light bends toward the normal when
passing from a lower into a higher
index of refraction
Air: n = 1.00
Water: n = 1.33
Normal Direction to
Air- Water Surface
Light Ray Bends Toward
the Normal in Water
Demonstration
Concept Test #1
While boating on the Amazon, you decide to go
spear fishing. You look into the water and see
where a fish appears to be. Where should you
aim your spear?
1) Beyond where the fish appears
2) In front of where the fish appears
3) Directly where the fish appears
What you see
Where the fish really is
Where the fish really is
A Thin Converging Lens Produces a Real,
Inverted Image for Objects Outside the
Focal Length
A Thin Converging Lens Has a Positive Focal
Length-a Real Image can be Produced on the
Side Opposite the Object.
A Thin Converging Lens Produces
a Virtual, Upright Image for
Objects Inside the Focal Length
The Thin Lens Equation
•Relates the Image Distance (i), the Object
Distance (o) and the Focal Length (f)
•Works for both Converging and Diverging lenses
provided the focal length for a Diverging lens is
defined to be negative.
1 1 1
 
i o f
Dispersion
• The index of refraction for a given material will vary
with the wavelength of the light passing through it
• This means that different colors of light will be
refracted through different angles when passing
through the same medium.
• This is called dispersion and can be demonstrated
with a prism or by observing a rainbow
A Double Rainbow…
The Spectrum of a Prism
White light is a
combination of all
the visible colors
nr< no < ny < ng < nb < ni <nv
Concept Test #2
Which statement about the relative speed of light
traveling in a glass prism is true?
1) Red and violet light travel at the same speed.
2) Violet light travels faster than red light
3) Red light travels faster than violet light.
n=c/vglass so the larger
the refractive index,
the slower the speed.
Red light has a lower
refractive index, so it
travels faster than
violet light.
Where the fish really is
nr< no < ny < ng < nb < ni <nv
Chromatic Aberration
• The dispersion of light as it passes through a refracting
lens causes the different colors of light to have different
focal lengths - red focuses long and violet focuses short
• This undesirable effect causes color “halos” around the
images and is called “chromatic aberration” (“color
error”)
• Coating the lens with thin films of different refractive
indices can partially correct for this - “color- corrected
coated optics”
+
=
Spherical Mirrors
•
•
Spherical mirrors are curved mirrors which
are sections of a sphere.
Two types of spherical mirrors:
1)
2)
•
Concave (inside surface is reflective)
Convex (outside surface is reflective)
Ray tracing shows that the focal length of a
spherical mirror is one half the radius of the
sphere: f = R/2 (simple!)
Spherical Mirrors
Concave
Convex
• Parallel light rays striking a spherical mirror
converge upon or diverge from a focal point
• Concave: real focus, light converges
• Convex: virtual focus, light diverges
The Thin Lens Equation
Works for Spherical Mirrors
•Concave (converging) mirrors have a
positive focal length and can produce real
images
•Convex (diverging) mirrors have a negative
focal length and cannot produce real
images
1 1 1
 
i o
f
Concave
Convex
Concave Mirrors: Real Images
•Light from an object outside the focal point
of a converging mirror will be focused to a
real image in front of the mirror.
Concave Mirrors: Virtual Images
• When an object is located inside the
focal point of a concave mirror, an
enlarged, upright, and virtual image is
produced which appears to be behind
the mirror.
Instruments: Multiple
Lenses and Mirrors
• Strategy: Form a real first image with
one lens or mirror and then hold a
magnifier up to the real image to
produce a final magnified virtual image
The Compound Microscope
• A small object is placed just outside
of a short focal length (high diopter
power) objective lens and the
resulting real first image is viewed
with a second short focal length
eyepiece lens
1630
The Refracting Telescope
• A first real image of a distant object is formed
by a long focal length (low diopter power)
objective lens. The first real image is then
viewed with a second short focal length (high
diopter power) eyepiece lens
M 
f objective
f eyepiece
M is the Angular Magnification
The Newtonian Reflecting Telescope
• A first real image of a very distant (“at infinity”) object is
formed by a long focal length (low diopter power)
objective mirror. The first real image is then viewed with
a second short focal length (high diopter power) eyepiece
lens
• The first real image is brought to the side by means of a
small flat mirror so that the eyepiece and observer can be
out of the way of the incoming light
Newtonian Reflecting Telescope
Parabolic Objective Mirror
Flat Mirror
M 
Eyepiece
f objective
f eyepiece
Spherical Aberration
• Lenses and mirrors with spherical surfaces are easy to
make and understand, but they do not actually focus all
incoming rays to a single point. This effect is called
spherical aberration and is responsible for the “fish
eye” distortion seen through a clear marble.
• Newton understood this effect and therefore based his
reflecting telescope on an objective mirror with a
parabolic shape, which has a perfect single point focus
• Parabolic mirrors are optically perfect, introducing
neither spherical nor chromatic aberration, but they are
very difficult and expensive to make
• Another approach is to “correct the vision” of a
spherical mirror—The Schmidt Camera
The Schmidt Camera
• Schmidt was a 19th
Century optician
who ground
spectacles by day
and astronomical
telescopes by night
• His “corrector
plate” eliminates
spherical aberration
and is too not
difficult to make
Other Telescopes
Schmidt-Newton
Newton-Cassegrain