Optics-Optical Instruments
UM Physics Demo Lab 07/2013
Pre-Lab Question
What important optical property does a concave mirror share with a thin
converging lens?
Caution-Warning: Today we will make and use optical
instruments to view distant objects through outside
windows. NEVER UNDER ANY CIRCUMSTANCES
ATTEMPT TO VIEW THE SUN with any type of lens,
mirror, or combination of lenses and mirrors, as eye
damage is CERTAIN to occur.
Second Pre Lab Question
Given the extreme danger of attempting to view the sun directly using lenses
and/or mirrors, describe a technique we have already demonstrated in the
previous lab which would permit you safely view a projected image of the sun.
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EXPLORATION
Exploration Materials
Yard stick 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 ¼” diameter cosmetic mirror on stand (concave/flat)
Hand-held magnifying glass
40 W “candle” lamp
Power strip for lamp
Calculator
Clear plastic ruler
Meter stick
Business card
Micro fiber cloth for polishing mirrors and lenses
Definitions
A converging lens is thicker in the center than at its edges.
The reflective side of a concave focusing mirror will hold water like a bowl.
You will find diagrams illustrating a converging lens and a
concave mirror at the end of this worksheet.
Instrument #1: Two Plane Mirrors
You have been provided with two plane mirrors attached to a yardstick
with mounts that can be rotated to any desired angle by loosening the
wing nuts which clamp the mounts to the yardstick, rotating the mirror
to the desired angle and then gently tightening the wing nut until the
mirror is just snugly held in place
1. Arrange the mirrors so that you can view the image in one mirror by looking
into the other. Now adjust the angles so that you can see around a corner
by looking at the image of the second mirror in the first.
A) What is this instrument called?
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B) Draw two mirrors (represented as straight lines) in the diagram below so
that a ray of light will follow the path shown. (Hint: Apply the Law of
Reflection and sketch in the normal direction for each mirror as a dotted
line first).
Instrument #2: Two Converging Lenses I
You have been provided with an optical instrument kit which contains
two lenses, two cardboard tubes, a thin cardboard ring and red plastic
end covers for the tubes. The small “eyepiece” lens is mounted in a
foam plastic ring along with a very small cardboard tube. For the
following experiments we will orient this lens by specifying which way
the cardboard tube should be pointed. Note that the small lens in the
eyepiece can fall out if the eyepiece is dropped.
1. Focus an image of the front projection screen onto the blank side of the
business card with the eyepiece lens (point the cardboard tube toward the
screen) and measure the distance from the image (card) to the center of
the lens with a centimeter ruler. Parallel light rays from the distant bright
screen are being brought to a focus at this distance, the focal length of
the lens. Record the measured focal length below and calculate its
magnifying power in diopters (1/meters). Finally, measure the diameter
of the lens and calculate its f/number. Show your calculations below.
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Eyepiece Lens
Focal Length (cm)
Eyepiece Magnifying
Power (Diopters )
Eyepiece Lens
Diameter (cm)
Eyepiece Lens
f/number
2. Lay the business card on the table and place the tripod lens stand (washer
+ 3 magnetic thumb tacks) over the printed side of the card so some of
the print is visible through the hole. Place the eyepiece on the tripod lens
stand, with the cardboard tube facing upward, away from the
business card. View the print on the business card through the
cardboard tube of the eyepiece, close to your eye.
A) Describe the image (upright or inverted, magnified or original size).
B) Where is the print (object) located relative to the focal length of
the lens (outside f, inside f or at f). Is this image real or virtual?
Why? (Hint: This is review from the last lab).
C) The magnification for a thin lens used as a magnifier is easy to
calculate as M = 25 cm/f where 25 cm is assigned as a standard
comfortable eye-to-lens viewing distance. Calculate the
magnification for the eyepiece and record it below. Show your
calculation. A magnification of 2 is reported as 2X
Eyepiece Magnification
X
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3. Lay the business card on the table and place the tripod lens stand over
the printed side of the card so some of the print is visible through the hole.
Place the eyepiece lens on the stand with the cardboard tube facing
downward, toward the business card and observe the print through
the lens, this time much further from your eye.
A) Describe the image (upright or inverted, magnified or original size).
B)
Where is the print located relative to the focal length of the lens
(outside f, inside f or at f)? Is this image real or virtual? Why?
(Hint: This is review from the last lab).
C) How does the object distance (distance of print from lens) compare
with the focal length of the lens?
4. Now view the image produced by the eyepiece lens on the stand through
the hand magnifier.
A) Describe the image (upright or inverted, magnified or original size).
B) Where is the image from the lens on the stand (called the objective
lens for this instrument) located relative to the focal length of the
hand magnifier (outside f, inside f or at f)? Is the image formed by
the lens on the stand real or virtual? Why?
C) Is the image an accurate representation of the print? If not,
describe any distortion you may observe.
D) What instrument uses two lenses arranged in this way?
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The distortion you observe in the image is due to the use of a spherical
shape for the lens surfaces and is called spherical aberration (“spherical
shape error”). Using lenses with a parabolic shape eliminates this
distortion, but parabolic surfaces are much more difficult to make.
Instrument #3: Two Converging Lenses II
1. Measure the focal length and diameter of the large lens from the
Refracting Optics Kit and record the focal length, diameter, magnifying
power and f/number for this lens below. Show your calculations.
Large Lens
Focal Length (cm)
Large Lens Magnifying
Power (Diopters )
Large Lens Diameter
(cm)
Large Lens
f/number
Now assemble the large lens and the eyepiece into the cardboard
tubes so that the large lens is at one end of the larger diameter
cardboard tube covered by the cardboard ring, while the eyepiece is
in the end of the smaller diameter tube, with the smaller cardboard
tube inserted into the larger tube so that it can slide back and forth.
The very small cardboard tube inside the eyepiece should be pointed
out of the end of the smaller tube so you can look through it. There is
an example of the assembled instrument available for you to copy,
and your instructor can help you to assemble these parts correctly.
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2. Looking through the very small cardboard tube, point the instrument out a
window and focus an image of distant objects through a window by sliding
the smaller cardboard tube in and out of the larger one.
A) Describe the image (upright or inverted, magnified or original size).
B) Where is the distant object located relative to the focal length of
the large lens (outside f, inside f or at f)? How does the object
distance for the far away objects compare with the focal length of
the large lens?
C) Where is the image from the large lens (called the objective lens
for this instrument) located relative to the focal length of the
eyepiece (outside f, inside f or at f)? Is this image from the large
lens real or virtual? Why?
D) Is the image viewed through the instrument an accurate
representation of the distant objects? If not, describe any
distortion you may observe
E) What is this instrument called?
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F) The magnification for this instrument can be calculated as the ratio
of the focal length of the two lenses. Call the magnification M, the
focal length of the large objective lens fo and the focal length of the
eyepiece lens fe . A (+) sign is used to indicate an upright image
and a (-) sign is used to indicate an inverted image. Using these
principles, suggest a formula for the magnification of this
instrument and record it below. (Hint: Based on the size of the
image you observe, should the magnification be a number greater
or less than 1?) Once you have developed your formula, check it
with your instructor.
G) Now use your formula to calculate the magnification of your
instrument. Be sure to include the appropriate (+) or (-) sign.
Instrument Magnification
X
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A Converging Mirror
1. Examine the large diameter cosmetic mirror.
A. Examine an image of your face in each side of the mirror. Are the
images the same? If not, describe how they are different.
2. Point the mirror at a bright distant object, either the front projection
screen or distant objects through an outside window. If you are using the
projection screen, be sure that you are at least half way across the room
from it. Using the blank side of the business card in your hand as a small
screen, try to project an image onto the card
A. One side of the mirror is flat, the other concave (dished in like a
bowl). Which side of the mirror will focus an image onto the card?
B. Describe the image (upright or inverted).
C. Where is the distant object located relative to the focal length of
the converging mirror (outside f, inside f or at f)? How does the
object distance for the far away objects compare with the focal
length of the mirror?
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D. Record the focal length of the focusing side of the mirror, the
mirror diameter, f/number and diopter magnifying power for the
mirror below. Show your calculations.
Converging Mirror
Focal Length (cm)
Converging Mirror
Magnifying Power
(Diopters )
Converging Mirror
Diameter (cm)
Converging Mirror
f/number
E. Does a converging mirror function in the same way as a converging
lens? Explain.
F. Predict what you will observe on a distant wall if you place the
candle lamp at the focal point of the converging mirror.
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G. Test your prediction from part (F) by performing the experiment
and describe your results. Given your observations, what practical
applications can you suggest?
H. Recall the relationship between image distance, object distance
and focal length we demonstrated for a thin converging lens:
1/i + 1/o = 1/f
Based on your observations do you expect the converging mirror
to obey this relationship?
I.
Using the hand magnifier, project an image of the candle lamp
onto a distant wall and carefully observe the colors present in the
image. Are all the colors focusing to the same place on the image?
Explain how replacing the objective lens of a telescope with a
mirror could reduce this effect, called chromatic aberration (“color
error”). (Hint: How does passing through glass affect the colors
of the light?)
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J. Converging mirrors have one disadvantage: they focus rays to an
image on the same side as the object, so that your head will block
the incoming light if you attempt to view the image at the focal
point. Describe how a small diameter flat mirror could be used to
overcome this problem and sketch your design below.
Everyday Applications

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Household mirrors (plane and magnifying)
Periscopes
Lighthouses (can use a converging mirror)
Flashlights (converging mirrors) and Searchlights (converging mirrors
or Fresnel lens)
Theatrical Spot Lights (Fresnel lens or converging mirror)
Astronomical Telescopes (refracting with an objective lens or reflecting
with an objective mirror—both use a refracting eyepiece)
Solar Power (converging mirrors to gather solar energy)
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APPLICATION
A Reflecting Telescope
Materials
5 ¼” diameter cosmetic mirror on stand (concave/flat)
3 ¼” diameter cosmetic mirror on stand (concave/flat)
Hand-held magnifying glass
Eyepiece from Refracting Optics Kit
Micro fiber cloth for polishing mirrors and lenses
1. Place the large converging mirror on a table top so it can view distant
objects through a window (the front projection screen may be used if a
window is not available). Now place the small flat mirror on the table
about 5” in front of the large converging mirror, angled upward so that
you can view the flat mirror over the top of the converging mirror. Adjust
the angles of the two mirrors so that you can see the image produced by
the converging mirror projected onto the flat mirror. Your instructor can
help you arrange this.
A. Describe the image (upright or inverted).
B. Where is the object located relative to the focal length of the
converging mirror (outside f, inside f or at f). Is this image real or
virtual? Why?
C. Now view the image in the small flat mirror with the hand
magnifier and describe the image (upright or inverted magnified or
original size).
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D. Record the focal length, magnifying power, diameter and f/number
for the hand magnifier below. You already have these data from
the last lab, but it only takes a minute to retake the measurements
and recalculate if you need to.
Hand Magnifier
Focal Length (cm)
Hand Magnifier
Magnifying Power
(Diopters)
Hand Magnifier
Diameter (cm)
Hand Magnifier
f/number
E. Using your previously derived formula for the magnification of a
refracting telescope, calculate the magnification of this telescope
using the focal length of the converging mirror and hand magnifier.
Are we justified in using the same formula? Why?
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F. Use the foam eyepiece from the cardboard telescope to view the
image in the flat mirror (look through the cardboard tube end of
the eyepiece). This can be tricky—ask your instructor for help.
What happens to the magnification of the telescope? Does this
make sense based on our formula for calculating the magnification
of the telescope? (Hint: Compare the focal lengths of the hand
magnifier and the eyepiece lens and see what effect this has on the
magnification predicted by our formula).
Challenge Work:
1. You wish to look at your new shoes in a plane mirror mounted on the wall.
The top of the mirror is even with top of your head as shown. Does the
mirror need to extend all the way to the floor for you to be able to see
your feet? Draw a ray from your eye to the mirror to your feet to justify
your answer and be sure that the ray properly obeys the law of reflection
at the mirror surface. Indicate the position of the mirror bottom on the
drawing.
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Summary:
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.
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.
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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.
Reflection
A wave is reflected when it is incident upon a material that redirects it outward.
Reflected waves are redirected according to the law of reflection: the angle of
incidence is equal to the angle of reflection. The angles of incidence and reflection
are defined with respect to the direction normal (perpendicular) to the mirror
surface as shown below.
The law of reflection holds for each of type of mirror, but the result it produces is
different for each. The plane mirror creates an actual-size virtual image of the
object which appears to be behind the mirror. Concave mirrors make incident
plane waves diverge, and convex mirrors cause incident plane waves to
converge. Both of these contribute to the distorted images of faces and bodies
you see in carnival mirrors which often have both convex and concave regions on
the same mirror.
Figure 1: Plane Mirror
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Figure 2: Concave (Converging) Mirror
Figure 3: Convex (Converging) Lens
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Telescopes
Figure 4: (a) Refracting Telescope;
(b) Newtonian Reflecting Telescope
Figure 5: Schmidt Astronomical Camera
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