PHYSICS 171
UNIVERSITY PHYSICS LAB II
Experiment 11
Geometrical Optics: Reflection and Refraction
Equipment:
Incandescent light source, optical bench, angular translator.
Supplies:
Standard component carrier, special component carrier, glass plate, acrylic plate,
flat front surface mirror, viewing screen with metric scale, aperture mask.
A.
Reflection
When light strikes the surface of material, some light is usually reflected. The reflection of light
rays from a plane surface like a glass plate or a plane mirror is described by the law of reflection:
The angle of incidence is equal to the angle of reflection (i.e., θi = θr).
These angles are measured from a line perpendicular or normal to the reflecting surface at the
point of incidence as shown below.
1
The rays from an object reflected by a smooth plane surface appear to come from an image
behind the surface, as shown in the figure. From equal triangles (in the figure above) it can be
seen that the image distance di from the reflecting surface is the same as the object distance d0.
Such reflection is called regular or specular reflection. The law of reflection applies to any
reflecting surface. If the surface is relatively rough, like the paper of this page, the reflection will
become diffused or mixed, so that no image of the source or object will be produced. This type
of reflection is called irregular or diffuse reflection.
B.
Refraction
When light passes from one medium into an optically different medium at an angle other than
normal to the surface, it undergoes a change in direction, as illustrated in the figure below for
two parallel light ray in a beam of light. This is due to the different velocities of light in the
different media. In the case of refraction, θ1 is the angle of incidence and θ2 is the angle of
refraction.
From the geometry of this figure we have
vt
vt
sin 1  1 and sin  2  2 or
d
d
sin 1 v1

sin  2 v 2
This equation is known as Snell's law. If v1 > v2 (as in the figure above), the rays are bent
toward the normal in the second medium. And if v1 < v2, the rays are bent away from the
normal.
2
For all optical media a quantity called the index of refraction (n) is defined by
c
v
where c is the speed of light in vacuum and v the speed of light in the medium. Snell's law can
then be written
n
sin 1 v1 c / n1


 n2 / n1 or
sin  2 v2 c / n2
n1 sin 1  n2 sin  2
where n1 and n2 are the indices of refraction of the first and second medium, respectively. If the
incident medium is air, n1  c/c = 1.
Pasco Optical System
The Pasco Optical System consists of a laser, incandescent light source, optical bench, angular
translator, prism and twenty-eight small components. When you come to lab class all the small
components will be in a gray container. Please return all these items to the container when you
complete the experiment. You cooperation to keep these parts in order will be appreciated by the
students who will use this station after you, will reduce anarchy in the lab, and minimize
equipment losses. These parts are very expensive. For example, a single slits costs $50.
Most of the small components are identified with paper labels. Because these labels fall off,
each component is identified by it item number using the following color code:
1 = WHITE
5 = YELLOW 10 = RED
For example, the acrylic plate is item #17. On the top you will see one red stripe, one yellow
stripe and two white stripes. Or, consider item #28, the standard component carrier. It has two
red stripes, one yellow stripe, and three white stripes. The complete list of components is shown
in the next page.
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Item
#
Colors
Component Description
Item #
Colors
Component Description
1
w
Calibrated polarizer
15
ry
Diffraction grating 5276
lines/cm
2
ww
Calibrated 140 m retarder 16
ryw
Glass plate
3
www
Hologram
17
ryww
Acrylic plate
4
wwww
Photometer apertures
18
rywww
-22 mm focal length lens
5
y
Variable diaphragm (iris)
19
rywwww
18 mm focal length lens
6
yw
Apertures .5mm, .75mm
20
rr
48 mm focal length lens
7
yww
Apertures 1.0mm, 2.0mm 21
rrw
138 or 152 mm focal
length lens
8
ywww
Diffuser
22
rrww
238 mm focal length lens
9
ywwww
Crossed arrow target
23
rrwww
Flat front surface mirror
10
r
Single slits
Slit width .02,. 04, .08,
.16mm
24
rrwwww
25 mm focal length
concave mirror
11
rw
Double slits
25
Slit width .04 .04 .08
.08 mm
Slit space .25 .50 .25 .50
mm
rry
Viewing screen with
metric scale
12
rww
Multiple slits
26
rryw
Aperture mask
13
rwww
Circular apertures (.04
and .08 mm) and
diffraction patterns
27
rryww
Special component
carrier
14
rwwww
Opaque points .25,. 50,
1.0mm
28
rrywww
Standard component
carrier
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Procedure - Experiment 11
1.
Angles of Incidence and Reflection
A.
i)
ii)
Reflections from a Flat Mirror
Position the incandescent light source on the left end of the optical bench, and
place the angular translator about 25 cm from the end of the light source housing.
Make sure the 0 and 180 marks lie on a line parallel to the bench. Finally adjust
the rotating table so that the scored lines run perpendicular and parallel to the
bench.
Attach the aperture mask to the standard component carrier and place it between
the light source and angular translator so that the mask is d centimeters from the
center of the translator. The distance d (about 6.5 cm) is also the measured
distance form the center of the angular translator to the first analyzer holder on the
movable arm.
.
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iii)
Center the viewing screen on the special component carrier designed for
use with the angular translator (it is shorter than a standard component
carrier), and place the assembly on the rotating table of the translator so
that the front surface of the viewing screen coincides with the scored line
on the table which runs perpendicular to the optical bench.
iv)
Now switch on the light and adjust the aperture mask's position until the
entire image is on the viewing screen. With the aid of the millimeter scale
marked on the screen, center the image horizontally.
v)
Now replace the viewing screen with the flat surface mirror such that the
mirror surface coincides with the perpendicularly scored line. Move the
viewing screen to the first analyzer holder on the movable arm.
vi)
B.
Rotate the table a set of number of degrees (starting with 30), and then move the
arm until the reflected image is centered horizontally on the viewing screen. Record
the angle which the arm makes with the mirror. Repeat for various settings of the
rotating table. What is the relation between the angle of incidence and the angle of
reflection? (Angle of incidence is the angle and the incident ray makes with the
normal to the reflecting surface; similarly for the angle of reflection.)
Reflections from Glass and Acrylic:
i)
Replace the flat mirror in part A with the glass plate, taking care that the front
surface of the glass coincides with the scored line.
ii)
Rotate the table until the glass plate rests at an angle of 30 with the optical bench.
iii)
Move the arm until the reflected image is visible on the viewing screen. It may be
necessary to turn out the lights in the room during this part. Two images of the
rectangular aperture will be visible. In part 4 of the data sheet you will be asked to
show why the two images appear and why the image on the left corresponds to the
image from the front surface of the plate.
iv)
The image on the left is the reflection from the front surface of the glass. Center
this image on the screen and record the angle which the translator arm makes with
the glass plate. Repeat the procedure with the rotating table set at several different
angles. What is the relation between the angle of incidence and angle of
reflection?
v)
Replace the glass plate with the acrylic plate and repeat i) - v).
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2.
Measuring the Index of Refraction
A.
Using the same set-up as in part A, place the acrylic/glass plate on the rotating
table so that its front surface coincides with the perpendicularly scored line on the
table.
B.
Place the viewing screen on a special component carrier and put the combination
in contact with the back surface of the acrylic/glass plate. The center of the
viewing screen should line up with the parallel scored line on the table.
C.
With the acrylic/glass plate sitting perpendicular to the bench, adjust the position
of the aperture mask so that one vertical edge of the image on the screen
lines up with the center of the viewing screen.
D.
Rotate the table and record what happens to the previously centered edge. The
figure below shows how to calculate in index of refraction given the angle of
rotation and edge displacement of the image.
Measure the thickness of the plate (t). For three angles of incidence (θ1 = 30, 45,
and 60) measure d, calculate tanθ2, and determine the index of refraction of the
respective plate.
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Data Sheet - Experiment 11
Name
Section #
1.
Angles of Incidence and Reflection
A. Reflections
from a Flat
Mirror
Angle of
incidence
B. Reflections from Glass and
Acrylic
Angle of
reflection
Glass plate
angle of
reflection
Acrylic plate
angle of
reflection
30
35
40
45
50
55
Does the law of reflection hold independent of the material used as the reflecting
surface ?
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2.
Measuring the Index of Refraction of the Acrylic Plate
θ1
t (mm)
tanθ2
d (mm)
θ2 (deg)
n2*
30
45
60
*The three values of n2 should differ only by experimental error.
3.
Measuring the Index of Refraction of the Glass Plate
θ1
t (mm)
tanθ2
d (mm)
θ2 (deg)
n2*
30
45
60
*Here too the three values of n2 should differ only by experimental error.
4. Compare the index of refraction of the acrylic plate to that of the glass plate. Comment:
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5.
In the space below show why two images appear on the viewing screen in part 1.B.iii of
this experiment, and verify that the image on the left comes from the front surface of the
plates. A nicely drawn picture with sufficient explanations is necessary for this proof.
.
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