18 Optics
Name
Lab
Inquiry Physics
The study of light has led to the development of such items as eyeglasses, magnifying lenses, binoculars, microscopes,
telescopes, fiber optic cables, various types of mirrors, and so forth. In this laboratory you will investigate some of the basic
properties of light rays as they bounce or bend. These properties form the theory base for all of the devices mentioned above.
You will be using a light ray box that can send out one or more light rays at various mirrors and lenses. Your group will
receive three "Optics Lab Data Sheets" on which you will place the mirrors and lenses to study their properties. Someone in
the lab group should read the directions aloud to the other group members. This lab introduces many new terms and
concepts.
Part 1. The Law of Reflection
There is a basic law of reflection that applies to any bouncing beam of light; it holds for mirrors and other devices. Most
mirrors have a reflective substance (mercury or silver in more expensive mirrors; aluminum in cheaper mirrors) sealed to the
back of a very clean, smooth piece of glass and covered with a protective coating. Light rays that reflect from the mirror
actually do so from the back of such a mirror. Other mirrors may simply be polished metal.
Mirrors come in a variety of shapes and sizes. We will begin with the simplest mirror, a plane mirror. It is so named because
its reflecting surface forms a mathematical plane or flat sheet.
!
Place the plane mirror on Optics Lab Data Sheet #1 over the appropriate box. Align
the reflecting surface along the line segment MNP. The line segment NO on the paper is
a normal: a line perpendicular to the reflecting surface.
!
Adjust the laser so that it sends out a crosshair of light. Shine the light beam toward the
mirror along line segment QN. Make sure the beam is centered on the line and strikes
the mirror at point N. This beam heading toward the mirror is called the incident ray
and the angle between it and the normal is called the angle of incidence (see figure
at right). Use a protractor to measure and record it in the table.
!
Now trace the reflected ray on the data sheet. Use your protractor ruler to draw a clean,
long line.
!
Measure the angle of reflection, the angle between the reflected ray and the normal
line (see figure at right).
!
Now shine the ray along line RN. Trace the reflected ray and record the angles of
incidence and reflection in the table.
Incident Ray
Angle of Incidence ()
Angle of Reflection ()
QN
RN
1.
Your results should lead to an obvious law of reflection which relates the angle of incidence to the angle of reflection.
State that law in your own words (answer in complete sentences).
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Part 2. Spherical Mirrors
The law of reflection also applied to curved mirrors, such as concave and convex spherical mirrors. These mirrors are slicedoff portions of a sphere. The concave mirror reflects light off the inside of the spherical section while the convex mirror
reflects light off the outside. You will be using curved pieces of lexan with a mirror coating on the back as your concave and
convex mirrors. DO NOT change the mirror curvature. Trade another group for the other type of mirror.
Concave Mirror
*
Line up the curved piece of metal polished on its concave side on the thickened line on Optics Lab Data Sheet #1. You
will note that the mirror is approximately part of a large circle (actually, a sphere) with a radius of somewhere between
10 and 15 centimeters. A mirror with a radius of 11 cm is said to have a radius of curvature of 11 cm as measured
from the center of curvature (the center of the sphere) to the middle point on the mirror, called the vertex. The line
from the center of curvature to the vertex is called the principal axis of the mirror.
*
Adjust the laser so that it sends out a crosshair beam of light. Shine the beam along each of the lines on the data sheet
that point to the left (toward the concave mirror). Note that the center ray runs along the principal axis. Make sure the
laser beam centered on each of the lines down their entire length.
*
Trace the three reflected rays (one of them is difficult to see...can you deduce where it is?). Use a ruler to make the
tracings straight and extend them until they all intersect. The point at which they intersect lies along the principal axis
and is called the focal point. The distance from the focal point to the vertex is called the focal length.
2.
Measure the focal length for your concave mirror and give its value in centimeters:
3.
Compare the focal length to the radius of curvature. What do you think is the general relationship between these two
distances? (complete sentences required)
The images of a mirror (what you see when you look at it) always form where the reflected light rays intersect or appear to
intersect. The light rays bouncing off a concave mirror usually converge and intersect in front of the mirror and form what
we call real images. Such images are always upside-down or inverted. They are sometimes larger or smaller than the
original object forming the image. We say they are either enlarged or reduced when compared to the object size.
Convex Mirror
Replace the concave mirror with the convex mirror (make sure the mirror side is on the left as you look down at the sheet).
Now shine the laser down each line and carefully trace the reflections.
These rays do NOT intersect in front of the convex mirror because they diverge or spread apart. Nevertheless, you can
make them intersect if you remove the mirror and extend the rays BACKWARD behind the mirror. Do this using your ruler.
The intersection of the light rays behind the mirror is where the image one would see appears to form. Since the image forms
behind the mirror where there isn't any actual light to be focused, the image is a type of optical illusion and is called a virtual
image. Virtual images are always right-side up or erect.
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4.
When rays parallel to the principal axis strike a convex mirror, at what exact location do they intersect?
5.
What kind of image (real or virtual) does a plane mirror form? Explain.
The images formed by a convex mirror are always reduced in size. This makes it possible to use them to see a broad area; we
say they have a wider field of view than plane mirrors. This makes them ideal for passenger-side rear-view mirrors on
automobiles where a wide field of view can help eliminate a driver's blind spot. They are also used in stores to view several
aisles at once and deter shoplifting as well as on blind corners
Part 3. Double Convex Lens
You've seen how light reflects; now we look at how it refracts, or bends as it passes through a lens. Place the double convex
lens in its spot on Optics Lab Data Sheet #2. Again shine three parallel light rays into the lens. Trace the refracted rays
that emerge from its far side.
6.
Do the refracted rays converge or diverge?
7.
Which type of mirror caused reflected rays to do that?
8.
The point where rays intersect if extended forward or back is again called the focal point. On which side of the lens is
the focal point?
9.
What is the focal length for your lens?
10. Convex lenses are used to correct farsightedness, which occurs when
the human eyeball is too shallow. To see a clear image, rays need to
focus on the retina at the back of the eyeball, but in a farsighted person's
eye, the lens inside the eyeball focuses the image behind the retina. (See
figure at right.) How could convex contact lenses or convex eyeglasses
correct this condition?
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Part 4. Double Concave Lens
answer in complete sentences
Now place the double concave lens in its spot and again shine three parallel beams at it and trace the refracted rays.
11. Do the refracted rays converge or diverge?
12. Which type of mirror caused reflected rays to do that?
13. On which side of the lens is the focal point, the laser side or the other side?
14. What is the focal length?
15.
Nearsightedness is illustrated in the figure at right. Using the
diagram, what causes nearsightedness?
16. How could concave lenses correct this condition?
Part 5. The Law of Refraction
Just as mirrors bounce light according to a certain law of reflection, lenses bend light according to a law of refraction. Next
you will collect data on light entering a lens at various angles and measure the angles of refraction, the angles between
the normal line and the refracted rays. This will lead you to a mathematical relationship between the angle of incidence and
the angle of refraction.
Place the water filled semi-circular lens on Optics Lab Data Sheet #3. The normal line on the sheet is perpendicular to the
flat side of the lens at point O. You will be shining a light beam along this normal line and then shifting it away from the
normal in 10 degree increments to observe how the refracted rays behave.
First adjust the laser so that it sends out a crosshair beam of light. Shine the light beam along the normal line. Make sure the
beam is centered on the line and strikes the lens at point O. The angle of incidence is the acute angle between the light ray
and the normal line.
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17. What is the angle of incidence for a ray on the normal line?
18. Look at the ray exiting the lens. Was the light refracted? Explain.
Now shine the light ray along the 10˚ line toward point O. You may be able to see a dim reflected ray as well as a brighter
refracted ray. Carefully trace the refracted ray that emerges from the curved side of the lens and measure its angle of
refraction (the acute angle between the emerging ray and the normal line on the curved side of the lens; see the figure below).
Measure the angle to the nearest half-degree and record it in the table below. Then shine the light ray along the remaining 7
lines, trace the refracted rays, and fill out the table.
Angle of Incidence ()
Angle of Refraction ()
0.0 (normal line)
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
20. Looking at your completed table, is the light bending toward or away from the normal when it refracts?
21. Is the light bending more at lower or higher angles of incidence?
We want to fit an equation to your data, so input your data into a computer using Excel or Graphical Analysis with the angle
of refraction on the x-axis and the angle of incidence on the y-axis. Include all 9 data points from your table.
Plot the graph and find a best-fit linear relationship. The initial plot will have only a slight curve and will have a high
corrolation or regression coefficient. (The closer the corrolation is to 1.00 – above or below - the better the fit.)
Nevertheless, a better linear fit can be found. Willebrörd Snell, a Dutch physicist, discovered the precise relationship in the
1600's.
Snell discovered that a certain trigonometric function, when applied to both angles, gave the best relationship. You are going
to find out which trig function works best for your data by graphing various modifications of . First, record your slope, yintercept, and corrolation values in the table on the next page for the unmodified refraction , incidence data.
Next, take the tangent of all the angles and record the resulting statistics in a table. Then do the same for sine and cosine.
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Plotted Data
slope (m)
y-intercept (b)
corrolation ( r coeff.)
refraction , incidence
tan r , tan i
sin r , sin i
cos r , cos i
25. The best fit will have the lowest y-intercept and highest corrolation. Which function did that?
26. Remember that once you have a linear plot, the formula y = m x + b applies. The "y" is not , of course, but some trig
function of ; the same holds for the "x". What is the appropriate linear equation for this data?
The slope, you will recall, is merely a proportionality constant between the x and y variables. It turns out that each substance
that can bend light has its own particular constant, called the index of refraction. The slope of your best line, the index of
refraction of the water used in the lens, should be approximately _______.
Have your instructor inspect your results.
Enrichment - If your group finishes early, explore the following questions:
Is refraction reversible?
Shine light rays along the refracted rays you have traced on the lab paper, toward the curved side of the lens. What paths do
the emerging light rays follow?
Can light bend so far that it won't emerge from a lens?
Note how the rays that emerge from the flat side of the lens are bending more and more as you shine light down the outermost
original refracted ray paths. Shine a light ray toward the curved side of the lens at a high angle of incidence (greater than the
last line you traced when taking refraction data). What does the light do?
Trace both the incident ray and the ray that emerges from the lens. Measure the angles between the entering and exiting rays
and the normal line. You should discover something interesting. How do the angles compare, and what does this tell you the
light is doing?
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18 Optics
Name
Worksheet: Ray Diagrams
Inquiry Physics
Mirror Terms
Write the names of the numbered parts of the concave mirror shown below beside the appropriate blanks.
A LIGHT RAY (DASHED LINE) IS SHOWN REFLECTING OFF THE MIRROR TO HELP ORIENT YOU.
1.
2.
3.
4.
5.
6.
Mirror Ray Diagrams
Ray diagrams are used to predict the image characteristics for mirrors and lenses. An image forms where the
light rays intersect or appear to intersect. The ray diagram can tell you the image type (real or virtual), where the
image forms, its size relative to the object (same size, reduced, or enlarged), and its orientation (erect or inverted).
The following rules apply:
1. Light rays coming from a distant object are travelling parallel to each other.
2. Parallel light rays striking a concave or convex mirror are REFLECTED through the focal point.
To construct your ray diagrams for spherical mirrors, draw the following light rays from the top of the object:
1.
2.
A ray travelling from the top of the object, parallel to the principal axis, that reflects through the focal point (the
focal point is in front of a concave mirror; behind a convex mirror).
A ray travelling from the top of the object that travels through the focal point and then reflects back parallel to
the principal axis.
1.
CONCAVE MIRROR: OBJECT BEYOND C
│ VIRTUAL │
NO IMAGE
Image type:
REAL
Image location:
BETWEEN F & V
BETWEEN F & C
AT C
BEYOND C
BEHIND MIRROR
Image size:
SAME │ ENLARGED │ REDUCED
Image orientation:
ERECT │ INVERTED
2.
CONCAVE MIRROR: OBJECT AT C
Image type:
REAL
Image location:
BETWEEN F & V
BETWEEN F & C
AT C
BEYOND C
BEHIND MIRROR
Image size:
SAME │ ENLARGED │ REDUCED
Image orientation:
ERECT │ INVERTED
3.
│ VIRTUAL │
NO IMAGE
CONCAVE MIRROR: OBJECT BETWEEN F & C
Image type:
REAL
Image location:
BETWEEN F & V
BETWEEN F & C
AT C
BEYOND C
BEHIND MIRROR
Image size:
SAME │ ENLARGED │ REDUCED
Image orientation:
ERECT │ INVERTED
4.
│ VIRTUAL │
NO IMAGE
CONCAVE MIRROR: OBJECT AT F
Image type:
REAL
Image location:
BETWEEN F & V
BETWEEN F & C
AT C
BEYOND C
BEHIND MIRROR
Image size:
SAME │ ENLARGED │ REDUCED
Image orientation:
ERECT │ INVERTED
5.
│ VIRTUAL │
NO IMAGE
CONCAVE MIRROR: OBJECT BETWEEN F & V
Image type:
REAL
│ VIRTUAL │
Image location:
BETWEEN F & V
BETWEEN F & C
AT C
BEYOND C
Image size:
SAME │ ENLARGED │ REDUCED
Image orientation:
ERECT │ INVERTED
NO IMAGE
6.
CONVEX MIRROR
Image type:
REAL
│ VIRTUAL │
NO IMAGE
Image location:
BETWEEN F & V
BETWEEN F & C
AT C
BEYOND C
BEHIND MIRROR
Image size:
SAME │ ENLARGED │ REDUCED
Image orientation:
ERECT │ INVERTED
Lens Ray Diagrams
For lenses, the ray diagram technique is similar. Light rays striking a convex lens parallel to its principal axis are
REFRACTED through its focal point. Images forming on the opposite side of the lens from the object are REAL,
while those forming on the same side are VIRTUAL.
To construct your lens ray diagrams, draw the following light rays from the top of the object:
1. A ray travelling from the top of the object, parallel to the axis of the lens, that strikes the lens and refracts
through the focal point on the other side of the lens.
2. A ray travelling from the top of the object and going in a straight line directly through the exact center of the
lens and continuing on, unbent.
7.
CONVEX LENS, OBJECT BEYOND 2F
From the above diagram you can see that the image is (circle the correct choices):
ENLARGED, SAME SIZE, or REDUCED
8.
INVERTED or ERECT
REAL or VIRTUAL
CONVEX LENS, OBJECT AT 2F
From the above diagram you can see that the image is (circle the correct choices):
ENLARGED, SAME SIZE, or REDUCED
INVERTED or ERECT
REAL or VIRTUAL
9.
CONVEX LENS, OBJECT BETWEEN F AND 2F
From the above diagram you can see that the image is (circle the correct choices):
ENLARGED, SAME SIZE, or REDUCED
INVERTED or ERECT
REAL or VIRTUAL
10. CONVEX LENS, OBJECT AT F
In the above diagram, did the light rays intersect?
If you extended them in either direction, would they intersect?
If an image will form, give its orientation, relative size, and whether it is real or virtual. Otherwise, write "NO
IMAGE".
11. CONVEX LENS, OBJECT BETWEEN F AND LENS
In the above diagram, did the light rays intersect?
If you extended them in either direction, would they intersect?
If an image will form, give its orientation, relative size, and whether it is real or virtual. Otherwise, write "NO
IMAGE".