Instructor Outline: Optics-Optical Instruments
UM Physics Demo Lab 07/2013
Lab length: 70 minutes
Lab objective: To instruct the students about optical instruments formed from
multiple optical elements: periscopes, compound microscopes, refracting telescopes
and reflecting telescopes.
Materials
Yard stick periscope mirror mount
2 51 mm square flat mirrors
Refracting telescope kit – objective, eyepiece, foam cylinder, cardboard ring in red
plastic cylinder, two cardboard tubes
Microscope stand — three magnetic thumb tacks + ½” steel washer
5 ¼” diameter cosmetic mirror on stand (concave/flat)
3 1/4” diameter cosmetic mirror on stand (concave/flat)
Hand-held magnifying glass
40 W “candle” lamp
Power strip
Calculator
Clear plastic rulers
Meter stick
Business card
Micro Fiber cloth for polishing mirrors and lenses
Exploration: 25 minutes - Group Lab Work
The students assemble a simple periscope from two plane mirrors and produce a ray
tracing diagram illustrating how the optical path of the periscope is based on the law
of equal angles for reflection from a plane mirror.
Next, the students measure the focal length, f/number and diopter magnification of
the eyepiece from the refracting telescope. Next, they use the eyepiece of the
telescope as a simple magnifier and observe a magnified virtual, upright image for a
printed page which is at an object distance less than the focal length. This is review
from the previous lab. They then calculate the magnification for the simple magnifier
as M=25 cm/f. Next they place the eyepiece on a stand which puts the printed page
just outside the focal length of the lens, now the objective of a compound
microscope. They observe that the image is now inverted (and hence real) and
produce a compound microscope by viewing the image from the objective through
the hand magnifier, which functions as a low-power eyepiece. They can also use the
small inset magnifier as a high-power eyepiece. Next they measure the focal length
of the refracting telescope objective lens and predict what they will see if they view a
distant object with the combined objective/eyepiece assembled as a telescope. They
then view distant objects and calculate the angular magnification of the refracting
telescope as:
– (objective focal Length)/ (eyepiece focal length)
Analysis: 5 minutes – Lecture
Real and virtual images formation by a thin converging lens are reviewed from the
previous lab. The optical paths for the compound microscope and telescope are
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
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reviewed. Dispersion is demonstrated with a prism as motivation for making
telescopes with mirrors instead of lenses to avoid chromatic aberration.
Exploration: 15 minutes – Group Lab Work
The students next investigate the properties of a spherical mirror, demonstrating
that it brings parallel light from infinity to a single focus. They then demonstrate
that a lamp placed at the focus will be projected as an image at infinity, the same as
for a lamp placed at the focus of converging thin lens. They deduce that a light
house beacon can be made with a concave mirror as well as a converging lens
Analysis: 5 minutes – Lecture
The thin lens equation is reviewed and shown to be valid for the converging concave
spherical mirror, the only difference being that the image and object distances are
positive on same side of the mirror, rather than on opposite sides as for the thin
lens. The relationship between focal length and radius of curvature f = R/2 is
introduced.
Application: 15 minutes – Group Lab Work
The students are lead to suggest a design for a reflecting telescope which uses a
plane mirror to direct the real image outside of the beam of the primary mirror.
They then construct this telescope using two cosmetic mirrors (5 ¼” spherical, 3 ¼”
flat) and the hand magnifier as a low power eyepiece. They draw a ray tracing
diagram for the optical path of the reflecting telescope they have built.
Analysis: 5 minutes – Lecture
The Newtonian reflecting telescope optical path is reviewed and Newton-Cassegrain
and Schmidt-camera optical paths are also discussed.
Suggested Demos:
Astronomical type Newtonian reflecting telescope
Concepts developed:
1. The Law of Reflection states that the angle of reflection is equal to the
angle of incidence for a reflected ray of light. The angles are defined with
respect to the direction perpendicular to the reflecting surface called the
normal.
2. Images where the light actually emanates from the location of the image
are called real images. Images where the light only appears to emanate
from the image location but does not actually do so are called virtual
images. The image of a lamp filament projected by a thin converging lens is
real. The image in a plane mirror is virtual.
3. Two plane mirrors can be combined to form a simple periscope which
allows the user to view images of objects from around a corner or below an
obstruction.
4. If an object is placed inside the focal length of a thin converging lens, an
upright magnified virtual image is observed. The angular magnification
for the simple magnifier can be calculated as 25 cm/f.
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5. If an object is placed just outside the focal length of a lens (called the
objective) a real, inverted image is formed. Viewing this real image inside
the focal length of a second simple magnifier (called the eyepiece) produces
a magnified virtual image which remains inverted. This combination of
two lenses is called a compound microscope. Short focal length objectives
and eyepieces produce the greatest magnification.
6. Viewing the inverted real image formed by a long focal length objective
lens with a second simple magnifier (eyepiece) produces a refracting
telescope. As with the compound microscope, the final image is inverted
and magnified. The magnification for this telescope is easily calculated as –
fobjective/ feyepiece where the minus sign indicates that the overall image is
inverted. Long focal length objectives and short focal length eyepieces
produce the highest magnifications at the price of a narrow field of view.
7. For a compound microscope, the object to be viewed is placed outside but
very close to the focal point of the objective lens. For the refracting
telescope, the object to be observed is very far away (“at infinity”). For a
compound microscope, the highest magnification is achieved when both
the objective and the eyepiece have short focal lengths (high diopter
magnifications). By contrast, the highest magnifications for a refracting
telescope are achieved with a long focal length (low diopter magnification)
objective lens and a short focal length (high diopter magnification)
eyepiece.
8. Light passing through a refractive medium such as glass is separated into
its component colors, as demonstrated by the rainbow of colors that emerges
when white light falls on a glass prism or water droplets, forming a rainbow.
This phenomenon, called dispersion, is undesirable in a telescope requiring
special coatings on the lenses to correct it. When dispersion is present in
lenses it is called chromatic aberration—“color distortion”.
9. Concave mirrors with a spherical shape will focus parallel rays of light to a
focal point in the same manner as a thin converging lens, this time on the
same side of the mirror as the object. The focal length of the mirror is easy
to calculate as ½ the radius of curvature of the mirror: f=1/2 R.
10.One method to reduce chromatic aberration and the absorption of light
passing through a telescope is to use a focusing (concave) mirror for an
objective rather than a lens. The most basic of these designs is called a
Newtonian reflecting telescope in honor of its inventor, Isaac Newton.
11. A concave spherical mirror does not perfectly focus parallel rays to a single
point. Rather, rays near the edge of the mirror focus shorter than those near
the axis of the mirror (paraxial rays). This distorts the resulting image and
is called spherical aberration. Thick lenses made with spherical surfaces
also exhibit spherical aberration, giving rise to the “fish eye” distortion seen
when using the lens as a magnifier.
12. Spherical aberration can be eliminated from the images formed by mirrors
and lenses by using a parabolic shape for the curved surfaces, but parabolic
surfaces are much harder to produce.
13. A thin corrective lens can also be used to correct telescopes for spherical
aberration, allowing large, easy to produce spherical mirrors to produce
sharp images. This technique produces a telescope called a “Schmidt
Camera” in honor of the 19th century optician who developed the prescription
for the corrective lens and successfully produced telescopes of this design.
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
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