Optics Experiments
Exp. (1)
Week: …………….
Date:
/
/
Using a Diffraction Grating to Analyze the
Spectrum Emitted by a Mercury Light Source
Objective:
1. You will perform experiments to understand the diffraction of light using
Hg light source and diffraction gratings.
2. Determine the diffraction gratings element (a+b=d).
Equipments:
Diffraction gratings, Spectrometer, and spectral discharge (Hg) tubes.
Theory:
The diffraction grating was first suggested by the American
astronomer David Rittenhouse in 1785 but was ignored until it was reinvented by Fraunhofer in 1819. Diffraction gratings are made by ruling
equally spaced parallel grooves into a glass or metal surface. The diffraction
grating is useful in analyzing various light sources. It is constructed of
numerous equally spaced parallel slits, generally too small for us to see with
our eyes. Normally, these gratings are made by using a precision-ruling
machine to etch parallel lines on a glass plate or by etching parallel lines on
a photographic slide. When the gratings are constructed to allow11 the light
to pass through them, they are called transmission gratings. If they are
constructed using reflective material, they are called reflection gratings. As
illustrated in Figure 1, Consider parallel (collimated) light rays incident
perpendicularly upon a diffraction grating of spacing d between the lines
(Fig. 1). The path length difference between successive paths from the input
plane to the output plane is given by dSinθ. These rays will pass through the
grating and emerge at all angles (this could not be happening if light rays
were particle like). However, if these emerging light rays from adjacent lines
1
Optics Experiments
on the grating are in phase, an image or a constructive interference pattern
will be formed. This takes place only if the following conditions are
satisfied:
d Sin n  n
(1)
Where θn is the angle of observation as measured from the normal to the
grating, λ is the wavelength of light rays, and n is an integer specifying the
order of diffraction; n can be positive, negative or zero. Equation 1 states
that the wavelength of light rays hitting the grating can be determined if the
spacing of the transparent lines of the grating and the angle of constructive
interference are known.
The mechanism of the given Light Source described as the following, when
a low pressure gas in a glass tube is excited by the input of a large amount of
energy, the atoms or molecules that make up the gas become excited. When
the molecules return to their unexcited state, they give of a just few
particular frequencies (colors) of light.
You will be supplied with Hg discharge tubes containing a gas at low
pressure. Figure 2 shown the spectrum of the Hg lamp.
d Sinθ
Figure 1
The principle of diffraction grating.
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Optics Experiments
Yellow
Green
Blue Violet
Figure 2
Diffraction Spectrum of Mercury.
Light source
Figure 3
The spectrometer consists of o light source, an adjustable slit, and the collimator that
produces a parallel beam of light. This beam interacts with the grating that is mounted on
the stage. The outgoing beam is observed with the telescope. The telescope rotates
around a vertical axis; its angle can be read with a precision of 30” (arc seconds).
3
Optics Experiments
Method:
1. Turn on the Hg lamp. It needs a few minutes to warm up. You will know
it is ready when the emitted light has a warm white glow. Place the lamp in
front of the slit. As illustrated in figure (3) Center it by eye as well as you
can.
2. Take the reading of the varner o that corresponds to the direct light; then
set up grating to the incident light. The final adjustment is to set the liens
of the grating parallel to the axis about which the telescope turns.
3. set the telescope so that the reading on attached varner is o +90. The
telescope is then at right angle to the direction of light proceeding from
the collimator.
4. Turn the grating till the image, which is simply reflected data the surface
of the grating and read the varner scale attached to the table. The plane of
the grating now makes an angle 45o with the incident light. Add 45 o to
the reading of the table and set it to this angle. The plane of the grating
will now be perpendicular to the incident light.
5. View the first diffracted image, making the slit as narrow as convenient.
6. Repeat this on both sides of the line of direct vision and thus measure the
angle 2 between the first order on both sides of the spectrometer for
each color.
7. Repeat the above step for the second and third order and tablet
your data in the following table.
8. Plot the relation between the  as x-axis and Sin  as y-axis
determine the grating element d.
DO NOT REFOCUS THE TELESCOPE.
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Optics Experiments
Results:
Mercury wavelengths in air
Yellow
5790.66 A0
Yellow
5969.60 A0
Green
5460.74 A0
Blue
4358.33 A0
Violet
4046.56 A0
n=1
θL
θR
n=2
θ
θL
θR
n=3
θ
θL
θR
Violet
Blue
Green
Yellow
Order n
Slope
The Grating element d
1
2
3
The Grating element is davg
5
θ
Optics Experiments
Exp. (2)
Week: …………….
Date:
/
/
Determination of the laser wavelength using the
laser diffraction.
CAUTION
DO NOT LOOK INTO THE LASER BEAM OR ITS
REFLECTION
Objective:
To investigate the diffraction using various types of apertures.
Apparatus:
Laser, slits with apertures, viewing screen
Theory:
The purpose of this experiment is to study the diffraction patterns
produced when collimated, monochromatic light (i.e. laser light) passes
through various arrangements of apertures and is observed on a viewing
screen. When the apertures are sufficiently small, the light intensity on the
viewing screen exhibits variations (successive maxima and minima) which
depend upon the wavelength of the light and the size and number of the
apertures. The existence of the patterns is confirmation of the wave nature of
light. While all optical phenomena (including the properties of lenses) can
be understood on the basis of the wave theory, it is only when the light is
monochromatic and well-collimated, as it is in a laser and the apertures
narrow, as it is in the slide you will use, that the wave properties are easily
observed. We will observe the following phenomena: Single Slit Diffraction
(Figure 1). A single slit diffraction pattern results when the light passes
through one aperture in an otherwise opaque surface. The light intensity on
the viewing screen exhibits a bright central peak surrounded by subsidiary
peaks. The difference in the distance that light from one edge of the slit
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Optics Experiments
travels compared to light from the center of the slit is called the path
difference and equals a sinθmin. When the path difference between light from
one edge of the slit and light from the center of the slit is a multiple of half
of the wavelength, the waves destructively interfere and there is a minimum
in the pattern.
Figure 1
Single slit diffraction with a minimum at point Q. The light from the slit is equivalent to
many in-phase, parallel pairs of point sources on either side of the center of the slit. Pairs
of points on either side of the center of the slit differ in phase by half a wavelength,
meaning that they will destructively interfere. This explains the minimum at point Q.
The intensity minima occur at angular positions θmin with respect to the
incident beam as follows:
a

Sin  min  m
2
2
(1)
a Sin min  m 
(2)
From figure (1) one can note that;
Sin  min 
y
L2  y 2
y
Sin


min
Where L>>y then
L
7
(3)
Optics Experiments
Substituting equation (3) in (2) we can get the following relation
ay
 m
L
(4)
Where a is the width of the single slit and m = ±1, ±2, etc. where m refers to
the order of the minima (first, second, third. etc.). The viewing screen is
located at a distance L from the aperture. A particular feature (e.g., an
interference minimum) occur a distance y from the center of the pattern at
angle θmin. The spatial intensity variation in a sample diffraction pattern is
illustrated in Figure 2, graphed as intensity vs. distance y.
Figure 2
Single slit diffraction pattern.
We produce the diffraction patterns by directing light from a laser
onto a single slit pattern. The diffraction patterns are observed by passing the
laser beam through the desired slit and measuring the locations of the
maxima and minima on the viewing screen. The best way to determine the
angles is to measure the linear distance between corresponding features. For
example, you would measure the second diffraction minima on the left and
right sides of the center of the pattern, as shown in Figure 3. Since it is
difficult to be sure exactly where the center of the pattern is located, we
8
Optics Experiments
measure the distance between equivalent features on the two sides of the
pattern and call this distance 2y. Then we find y.
Figure 3
Measure the diffraction patterns on a screen. For a single slit, y represents the location of
the minima. y represents the distance between two features of the same order on the left
and the right of the center of the pattern.
Method:
1. Ask your instructor for the dimensions of the slit patterns in the 3 fields
for your particular slide.
2. Tape a large piece of paper to the viewing screen.
3. Measure the distance, L, between the slide and the viewing screen. Prop
the triangle on the horizontal meter stick and use that to help located and
mark the locations of the minima.
4. Measure the distances between corresponding pattern features to the left
and right of the pattern center 2y. Determine distance y corresponding to six
intensity minima.
5. Write the data in the following table.
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Optics Experiments
6. Plot the order, m (±1, ±2, etc.) on x-axis and the distance y on y-axis, of
the minima. Include the appropriate error bars. Find the slope of plot and its
uncertainty.
7. Compare your calculated values for the wavelength of the laser light to
the accepted value.
Results:
a= 0.08X10-3 m,
L=
m,
m
ym
y
m
L

a
Slope 
Then
λ=
m;
=
A 0.
10
Optics Experiments
Exp. (3)
Week: …………….
Date:
/
/
Determination of the He-Ne laser wavelength using
the Michelson interferometer
CAUTION
DO NOT LOOK INTO THE LASER BEAM OR ITS
REFLECTION
DO NOT TOUCH THE FRONT SILVERED
MIRRORS
Objective:
1. To become familiar with the use of an interferometer and the principle of
interferometry.
2. to measure the wavelength of a light source (He-Neon laser).
Equipment:
Michelsom Interferometer System, He-Ne Laser.
Theory:
In 1881, some 78 years after Young introduced his two-slit
experiment, A.A. Michelson designed and built an interferometer using a
similar principle. Michelson interferometer has become a widely used
instrument for measuring the wavelength of light, and for using the
wavelength of a known light source to measure extremely small distances.
Figure 1 shows a diagram of a Michelson interferometer. A beam of light
from the laser source strikes the beam-splitter. The beam-splitter is designed
to reflect 50% of the incident light and transmit the other 50%. The incident
beam therefore splits into two beams; one beam is reflected toward mirror
M1, the other is transmitted toward mirror M2. M1 and M2 reflect the beams
back toward the beam-splitter. Half the light from M1 is transmitted through
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Optics Experiments
the beam-splitter to the viewing screen and half the light from M2 is
reflected by the beam-splitter to the viewing screen.
M2
M1
Figure 1
Tracing rays in the interferometer.
In this way the original beam of light splits and portions of the resulting
beams are brought back together. The beams are from the same source and
their phases highly correlate. The He-Ne laser beam we use makes a small
spot, so the interference is hard to see. To make it bigger we insert a lens
between the laser and the beam splitter. When a lens is placed between the
laser source and the beam-splitter, the light ray spreads out. An interference
pattern of dark and bright rings, or fringes, is seen on the viewing screen, as
shown in Figure 2. This spreads out the beam and makes it easier to see the
interference. However, this spreading also means that only the central ray of
the laser beam is still traveling on a straight line through the interferometer.
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Optics Experiments
All the surrounding rays are traveling at some angle, depending on how
close to the center of the beam they are. Thus rays at different radii from the
center of the laser beam travel a different total distance through the
interferometer. This causes the interference pattern we see to look like a
bulls eye or target shape, with rings of bright and dark fringes instead of just
one spot. During the experiment we will be counting bright-dark-bright
fringe cycle. To do this you should pay attention to the center spot of the
bulls eye pattern, not to the outer part.
Figure 2
Interference Pattern
Since the two interfering beams of light were split from the same initial
beam, they were initially in phase. Their relative phase when they meet at
any point on the viewing screen, therefore, depends on the difference in the
length of their optical paths in reaching that point. By moving mirror M2,
the path length of one of the beams can be varied. Since the beam traverses
the path between M2 and the beam-splitter twice, moving M2 one-quarter
wavelength (λ/4) nearer the beam-splitter will reduce the optical path of that
beam by one-half wavelength (λ/2). The interference pattern will change; the
radii of the maxima will be reduced so they now occupy the position of the
former minima. If M2 is moved an additional one-quarter wavelength (λ/4)
closer to the beam-splitter, the radii of the maxima will again be reduced so
maxima and minima trade positions. However, this new arrangement will be
indistinguishable from the original pattern. By slowly moving M2 a
measured distance dm, and counting m, the number of times the fringe
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Optics Experiments
pattern is restored to its original state, the wavelength of the light (λ) can be
calculated as:
2 d  m
Then
2d
 
m
(1)
If the wavelength of the light is known, the same procedure can be used to
measure dm.
Basic operation of the interferometer
The Michelson Interferometer is shown in Figure 3. The alignment of the
beam splitter and the movable mirror, M2, is easily adjusted by loosening
the thumbscrews that attach them to the interferometer. The fixed mirror,
M1, is mounted on an alignment bracket. The bracket has two alignment
screws to adjust the angle of the mirror. The movement of M2 toward and
away from the beam-splitter is controlled and measured using the
micrometer knob. Each division of the knob corresponds to 1 micrometer
(10−6 meter) of mirror movement.
Screen
Beam splitter
Laser
M1
Micrometer
Figure 3
Michelson Interferometer.
14
M2
Optics Experiments
Method:
1. Swing the beam-splitter out of the way of the laser beam. Adjust the
laser's position until the beam reflected from the movable mirror M2 reenters the laser. That is, the mirror reflects the light perfectly back into the
barrel of the laser.
2. Rotate the beam-splitter so its surface is at an angle approximately 45 0
with the incident beam from the laser beam, so that part of the beam is
reflected onto the stationary mirror M1. Put a screen at the `output' of the
interferometer. (Think of the laser as the `input' and the moveable mirror and
the stationary mirror as the two `arms.' The laser beam will leave the
interferometer through the remaining side.) There should be two sets of
bright spots on the screen. Adjust the beam-splitter slightly until the two sets
of spots are as close together as possible. Fasten down the beam-splitter with
its little screw.
3. Using the alignment screws, adjust the angle of M1 until the two sets of
laser spots are superimposed on the viewing screen (the two brightest spots
must be superimposed).
4. Place the lens holder on the optical bench. Be sure its edge is flush against
the alignment rail. Then place the 18 mm focal length lens on the lens holder
(it attaches magnetically). Adjust the position of the lens on the holder so the
light from the laser, now spread out by the lens, strikes the center of the
beam-splitter. If you have performed the alignment correctly, you will see an
interference pattern of concentric rings on the viewing screen. If the
alignment is not just right, the center of the fringe pattern may not be visible
on the screen. Adjust the alignment screws on M1 very slowly as needed to
center the pattern.
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Optics Experiments
5. Turn the micrometer knob one full turn counterclockwise. Continue
turning counterclockwise until the zero on the knob is aligned with the index
mark.
6. Tape a blank piece of paper on your viewing screen, make a reference
mark on the paper between two of the fringes. You will find it easier to
count the fringes if the reference mark is one or two fringes out from the
center of the pattern.
7. Rotate the micrometer knob slowly counterclockwise. Count the fringes
as they pass your reference mark. Continue until a predetermined number of
fringes has passed your reference mark (count at least 10 fringes). As you
finish your count, the fringes should be in the same position with respect
To your reference mark as they were when you started to count.
8. Record dm, the distance that the movable mirror moved toward the beamsplitter as you turned the micrometer knob. Record, the number of fringes
that crossed your reference marks during the mirror movement. Remember,
each division on the micrometer knob corresponds to one micron (10 −6
meters) of mirror movement.
9. Repeat the previous step measurements at least five more times.
Measurements
10. Write the data in the following table.
11. Plot the relation between the number of fringes m as x-axis and the
distance dm as y-axis.
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Optics Experiments
Results:
m
dmX10-6 M
Slope=
λ = 2XSlope
=
λ=
M
A0.
17
Optics Experiments
Week: …………….
Exp. (4)
Date:
/
/
Microwave Optics
CAUTION
ALTHOUGH THE MICROWAVE
TRANSMITTER ONLY HAS LOW POWER, ONE
MUST AVOID LOOKING DIRECTLY INTO THE
MICROWAVE.
Objective:
1. Investigate the polarization of the produced microwaves.
2. Measurement of the wavelength of microwaves through the production of
standing waves with reflection at the Reflector.
3. Measurement of the wavelength of microwaves using the interference
through double slits.
4. Study the diffraction of the microwaves through a single slits.
Apparatus:
Microwave transmitter, Microwave receiver, components holders, Meter
scale, goniometer, slide with single slit and slide with double slits.
Theory:
The term microwave denotes electromagnetic waves in the
wavelength range of about 0.1to 10cm. And the term optics is appropriate
because many phenomena observed with visible light can be duplicated with
microwaves. Microwaves are good for transmitting information from one
place to another because microwave energy can penetrate haze, light rain
and snow, clouds, and smoke. Shorter microwaves are used in remote
sensing. These microwaves are used for radar. Microwaves, used for radar,
are just a few inches long. The microwave tower can transmit information
like telephone calls and computer data from one city to another.
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Optics Experiments
In our experiments we shall study the properties and behavior of this
microwave. The first essentials for an experimental of microwave are
Transmitter and microwaves receiver shown in figure 1.
Microwave Transmitter with Power
Supply
Microwave Receiver
Figure 1
There are many types of source like as what so called Klystron and Gunn
diode transmitters. Microwave detectors use a principle very similar to that
of detectors in ordinary a radio-receivers. In our experiment we use The
Gunn Diode Microwave Transmitter which provides 15 mW of coherent,
linearly polarized microwave output at a wavelength of 2.85 cm. The Gunn
diode acts as a non-linear resistor that oscillates in the microwave band. The
output is linearly polarized along the axis of the diode and the attached horn
radiates a strong beam of microwave radiation centered along the axis of the
horn. The Microwave Receiver provides a meter reading that, for low
amplitude signals, is approximately proportional to the intensity of the
incident microwave signal. A microwave horn identical to that of the
Transmitter's collects the microwave signal.
i) Polarization of electromagnetic waves:
Microwaves, as all electromagnetic waves, oscillate transversally and
thus have two degrees of freedom related to the direction of polarization. In
19
Optics Experiments
other words, the directions of their electric and magnetic fields are
perpendicular to the direction in which the wave travels. In addition, the
electric and magnetic fields are perpendicular to each other. Fig. 2 shows a
periodic electromagnetic wave traveling in the z-direction.
Polarization is the distribution of the electric field in the plane normal to the
propagation direction.
Z
Electric field
Magnetic field
Y
X
(a)
(b)
Figure 2
a) A schematic view of an electromagnetic wave propagating along the z-axis. The
electric E and magnetic H fields oscillate in the x-y plane and perpendicular to the
direction of propagation. b) plane polarized wave is one for which the electric field lies
only in the x-z plane.
ii) Standing Wave Formation:
Standing wave patterns are produced as the result of the repeated
interference of two waves of identical frequency while moving in opposite
directions along the same medium. All standing wave patterns consist of
nodes and anti-nodes as shown in figure 3. The nodes are points of no
displacement caused by the destructive interference of the two waves. The
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Optics Experiments
anti-nodes result from the constructive interference of the two waves and
thus undergo maximum displacement from the rest position. The node
occurs at a point x of zero amplitude where
x
n
2
Where
n=0, 1, 2, …
And anti-node occurs at a point x of maximum displacement, where
x
n
4
Where
n=0, 1, 2, …
Anti-node
λ/2
0
0
node
sum
0
0
Figure 3
Standing wave patterns consist of nodes and anti-nodes.
When a thin sheet of plywood is inserted between the two horns part of
wave is absorbed by the wood, part transmitted and part reflected.
Absorption will be greatest when the wood is near an anti node in the
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Optics Experiments
standing wave, and it is least near node. Thus move the wood along the axis
and measure the positions of several constructive max and min. One can
determine the wavelength, where the distance between two max or min. is
equal to (λ/2).
iii) Interference of the microwave:
The ideal two slit pattern, Young's Experiment, is produced by
directing monochromatic light through two infinitesimally narrow slits in an
otherwise opaque surface. In this lab we study two slit pattern using the
microwave.
The
path
difference
between
the
microwaves
from
corresponding locations in the slits is d sin θMax, where d is the center to
center distance between the slits as shown in figure 4. When the path
difference between microwaves from corresponding locations in the slits is a
multiple of the wavelength of the microwave, the waves constructively
interfere. Therefore, the intensity maxima, M λ, occur at angles θMax based
on the following relation, where d is the distance between the slits and M =
±1, ±2, etc. where M refers to order of the maxima (first, second, third, etc.).
d sin θMax = M λ
Figure 2
Double slit
interference.
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Optics Experiments
The variation of intensity in the pattern formed on the screen is illustrated in
Figure 5.
Figure 5
m=0
m=-1
The intensity
distribution of double
slit
Interference pattern.
m=+1
θ Degree
iv) Diffraction of the microwave:
The diffraction patterns are observed by passing the microwaves
through the desired slit. When the wavelength of the microwaves is greater
than the slit width, the microwaves intensity on the viewing screen exhibits
variations (successive maximum and minimum). The existence of the
patterns is confirmation of the wave nature of microwaves. The microwaves
intensity on the viewing screen exhibits a central peak surrounded by
subsidiary peaks as shown in figure 7. When the path difference between
microwave from one edge of the slit and microwave from the center of the
slit is a multiple of half of the wavelength, the waves destructively interfere
and there is a minimum in the pattern. The intensity minima occur at angular
positions θmin with respect to the incident beam as follows:
a

Sin  min  m
2
2
(1)
a Sin min  m 
(2)
Where a is the width of the single slit and m = ±1, ±2, etc. where m refers to
the order of the minima (first, second, third. etc.).
23
Optics Experiments
a
θmin
Figure 8
The single slit diffraction.
Diffraction by a circular aperture
Almost all optical systems have circular apertures. This means that a point
source will not be imaged into a point image. Instead the light is diffracted
by the entrance pupil at aperture and forms a blurry diffraction limited
image. Shown below are the images of two point sources located an angular
distance θ apart. We see, as the separation between the two sources gets
smaller; the two sources gets smaller, the two diffraction patterns start to
merge. When the first minima of one object are overlain by the max of the
other, we have reached the point that we no longer can tell the difference
24
Optics Experiments
between one and two sources. This is the Raleigh Resolution Criterion.
θmin=1.22( λ/D) in radians.
Method and Results:
1-Polarization
1. Arrange the equipment as shown in Figure 9 and adjust the Receiver
controls for nearly full-scale meter deflection.
Figure 9 Equipment Setup
2. Loosen the hand screw on the back of the Receiver and rotate the
Receiver in increments of 15 degrees. At each rotational position record the
meter reading in the following Table.
3. Repeat step 2 until the Receiver reach 90 degree.
25
Optics Experiments
3. Rotate the receiver in the reverse direction and Repeat step 3 until the
Receiver reach -90 degree.
4. Plot the relation between the angle as x-axis and the intensity of the
microwaves as y-axis.
Results
θ Degree
I μA
θ Degree
0
0
15
-15
30
-30
45
-45
60
-60
75
-75
90
-90
I
μA
2-Standing Waves - Measuring Wavelengths
1. Arrange the equipment as shown in the following Figure.
Semi-Reflector
2. Move the semi-Reflector along the Goniometer arm (no more than a
centimeter) until the meter shows a maximum reading. Then record
the meter reading and the distance from the center of the Goniometer
in the following table.
26
Optics Experiments
3. Move the semi-Reflector (again, no more than a centimeter) to find
minimum meter reading. Then record the meter reading and the
distance from the center of the Goniometer in the following table.
4. Repeat steps 2, 3 six times.
5. Determine the average distance between nodes and anti-nodes. One
can determine the wavelength, where the average distance between
two max or min. is equal to (λ/2).
Results
d cm
I μA
maximum
minimum
maximum
minimum
maximum
minimum
maximum
minimum
Average distance
between nodes=
cm,
Average distance between anti-nodes=
cm,
λ (the wavelength of the microwaves) =
cm.
27
Optics Experiments
3-Double-Slit Interference
1. Arrange the equipment as shown in the following Figure.
2. Adjust the Transmitter and Receiver for vertical polarization (0°) and
adjust the Receiver controls to give a full-scale reading at the lowest
possible amplification.
3. Rotate the rotatable Goniometer arm (on which the Receiver rests)
slowly about its axis. Observe the angle and the Receiver readings.
4. Tablet the data in the following table.
5. Repeat step 3, 4 until the angle reaches 70 degree.
6. Rotate the rotatable Goniometer arm in the reveres direction and
Repeat step 3, 4 until the angle reaches -70 degree.
7. Plot the relation between the angle θ Degree as x-axis and I μA as yaxis.
8. Determine the average value of the angle θmax , which corresponding
the first order fringe (m=1,-1) and using the equation (dsin θmax=mλ)
to calculate λ.
28
Optics Experiments
Results
Right reading
Θ Degree
Left reading
I μA
θ Degree
0
0
5
-5
10
-10
15
-15
20
-20
25
-25
30
-30
35
-35
40
-40
45
-45
50
-50
55
-55
60
-60
65
-65
70
-70
d(the center to center distance between the slits)=
m =1
θmax=
λ
=
Degree,
cm.
29
I μA
cm,
Optics Experiments
4-Diffraction of the microwave
1. Using the method discussed in the interference of the microwaves
through a double slit slide and replaces the double slit slide with a
single slit slide.
2. Repeat steps (1 to 6) which discussed above and record the data in the
following table.
3. Plot the relation between the angle θ Degree as x-axis and I μA as yaxis.
Results
Right reading
θ Degree
Left reading
I μA
θ Degree
0
0
5
-5
10
-10
15
-15
20
-20
25
-25
30
-30
35
-35
40
-40
45
-45
50
-50
55
-55
60
-60
65
-65
70
-70
30
I μA
Optics Experiments
Exp. (5)
Week: …………….
Date:
/
/
Newton’s Rings
Objective:
1. Determine the wavelengths for a given radius of curvature of the lens.
2. Determine the radius of curvature at given wavelengths.
Equipment:
Sodium lamp, convex lens of long focal length (i.e. large radius of
curvature), optical glass plate, a convenient dark background (e.g. a piece of
black paper), a reflecting glass plate, a traveling
microscope and a
converging lens of short focal length and large aperture.
Theory:
Newton’s rings are the localized interference fringes formed when
monochromatic light is incident on a convex lens resting on an optical flat as
shown in figure 1.
Figure 1
Newton’s rings.
Light from a sodium lamp is reflected downwards on to a biconvex lens
rested on an optically flat glass plate. (Note: Focusing of the beam by the
lens causes the rays not to be exactly perpendicular to the glass slab, as
shown in figure 2; the resulting fractional error in tn is of order tn/R and may
be neglected.) The rays reflected (i) at the lower surface of the lens and (ii)
at the upper surface of the flat are in a condition to interfere, the intensity
depending on the path difference, i.e. on the thickness of the air film. The
reflected light passes upwards through the reflecting plate into the objective
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Optics Experiments
of an observing microscope which is focused on the air film. Interference
rings are formed, the central spot being black (providing there is intimate
contact between lens and plate). The central spot being black as a result of
the rays reflected at the lower surface of the lens and air suffers a phase
change of π.
Let the ray shown in Figure 3 correspond to the nth dark ring. Let the radius
of this ring be rn and the thickness of the air film at this point be t n.
Figure 2
Setup for Newton’s rings experiment.
For destructive interference:
The optical Path difference can be given by
2tn cosθ = nλ
(1)
where λ is the wavelength of light used and θ is the incident angle
For normal incident θ=0, then
2tn = nλ
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(2)
Optics Experiments
(N.B. ray reflected from air at glass suffers a phase change of π).
From the geometry of figure 1, one can note that;
R2 =(R-tn )2+ rn2
R2 =R2-2Rtn +tn 2 + rn2
2Rtn = tn 2 + rn2
Where tn 2 << rn2.
There for;
2Rtn = rn2
2tn = rn2 /R
(3)
Substituting equation (3) in (2), then
rn2 = nRλ
(2)
i.e. if rn2 is plotted against n, a straight line will be obtained whose slope is
Rλ.
R
tn
Figure 3
Geometry of Newton’s rings.
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Optics Experiments
Method:
1. Set up the apparatus shown in the figure 2. Set the glass plate with the
black side down, and place the lens on the plate as shown. Above this,
arrange another glass plate at a 45o angle so that the light from the sodium
lamp is normally incident upon the lens and lower plate. The interference
rings which occupy a small region around the center of the lens may then be
viewed with the microscope.
2. Adjust the eyepiece of the microscope until the hairline is seen clearly.
3. Look for the interference pattern, and bring it into focus on the hairline by
sliding the microscope up or down. You may need to reposition the lens so
that the rings are in the middle of the field of view. If the central fringe is not
dark, there is some dirt on the contacting surfaces which must then be
cleaned.
4. Determine the direction in which you must turn the screw to cause the
numbers on it to increase. Going in a decreasing direction, move the screw
until the hairline is centered on the n=0 ring and record the reading.
5. Now rotate the screw until the hairline is centered on the 1st ring and
record the reading.
7. Similarly, record the readings for each ring until you reach the 6th one.
6. Record the data in the following data table.
7. Plot the relation between rn2 and n, which gives a straight line its slope,
is R from which calculated lens radius R (where  = 589.3 nm).
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Results:
n
Left reading r
m
Right reading
r
m
The average r
m
r2 m
Slope =
 = 5893 A0
R =
m
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Optics Experiments
Exp. (6)
Week: …………….
Date:
/
/
Abbe’s Refractometer
Objective:
1. To study the relation between refractive index and concentration of
liquid.
2. To determine the refractive of water.
Apparatus:
The given liquid and Abbe refractometer.
Theory:
One specific achievement of Abbe will now be discussed in some
detail, the “Abbe Refractometer.” The refractometer is an instrument used
to measure the refractive index of liquids or solids. It functions based on the
concept of critical angle. A prism of a known refractive index is placed in
contact with the material being measured that has a lower index. Figure 1
show the layout of a commercially available Abbe refractometer which is
used in our experiment.
Light from a diffused source strikes the material at all angles up to grazing
incidence. The light at grazing incidence is refracted into the prism at the
critical angle as shown in figure 2 below.
(The critical angle forms a shadow boundary corresponds to the refractive
index of the sample see figure 2.).
Then, a telescope is used to view this light leaving the prism. The resulting
picture is a shadow boundary starting at the critical angle where no more
light can pass through beyond this angle.
Finally, the shadow is
superimposed on a pre-calibrated scale and the refractive index can easily be
read as in figure 3.
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Figure 1
Figure 2
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Figure 3
The scale is calibrated using an equation that relates the angle of shadow
boundary to the normal of the second face of the prism:
As we know the speed of light in a vacuum is always the same, but when
light moves through any other medium it travels more slowly since it is
constantly being absorbed and reemitted by the atoms in the material. The
ratio of the speed of light in a vacuum to the speed of light in another
substance is defined as the index of refraction (refractive index or n) for
the substance. This law was generalized in the Snell's law for two mediums
1 and 2
n1 sin 1  n2 sin  2
Using this law when the incidence angle in the first medium is 90 the
refraction angle will be the critical angle and for our case the Snell's law will
be:
ns sin 90 = ng sin B
Where
B is the critical angle.
Sin B = ns/ng
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(1)
Optics Experiments
Where ‘ns’ is the sample refractive index and ‘ng’ is the prism index. Then,
using further relationships as seen in figure 4 below, the final equation for
the refractive index of the sample is
ns = SinA [ng2 – (SinD)2]1/2 – CosA SinD
Figure (4)
Numerical example:
* Assume equilateral prism with ng = 1.8, A=600.
* Assume B=560 and observed D = 70.
Then using the formula (2)
ns  sin( 60 ) (1.8 ) 2  (sin( 7)) 2  cos(60 ) sin(7)  1.49
Using the refractometer, this would be the value on the
calibrated scale that the shadow boundary would point to.
(Shows values in formula above)
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(2)
Optics Experiments
The internal scales are designed with this equation 2 and are usually
calibrated to use the sodium D wavelength of light as the source. Therefore,
the Abbe refractometer enables one to read ‘ns’ directly from viewing the
shadow boundary. It is compact, easy to use, and can give an accuracy of
from one to two units in the fourth decimal place.
In our experiment we will determine the refractive index of some liquid at
different concentrations of this liquid. The relation between the refractive
index and concentration can be shown in the following figure 5.
n
nw
C0
C%
Figure 5
Procedure:
1.
To introduce the sample unlock the prism, lift the top prism, spread a
few drops of the sample on the bottom prism.
2.
Close the prisms slowly, and lock the prisms again.
3.
Focus the eyepiece on the scale by rotating it.
4.
Turn the scale adjustment so that the critical ray boundary is visible in
the top part of the viewer (a dividing line between light and dark halves is
visible).
5.
Turn the Amici prism adjustment so as to achromatize the boundary.
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Optics Experiments
The center image shows proper achromatization (white color - sharp
boundary).
6.
Turn the scale adjustment so that the boundary between light and dark
coincides with the center of the cross hairs.
7.
Read and record the refractive index on the top scale in the lower part
of the viewer (the bottom scale is for the concentration ; ignore it). Three
decimal places can be read, the fourth place is estimated.
the image above shows a reading of 1.3433 (notice the smallest division is
0.0005).
8.
Clean the prisms by opening them and wiping them clean (top and
bottom). Use water to remove water soluble compounds, toluene or
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petroleum ether for water insoluble compounds. Be sure not to scratch the
prisms.
9.
Leave the prisms in an open position so they can air dry.
10. Do the above steps again for different concentrations.
11. Record the data in the following table.
12. plot the relation between the refractive index and the concentration of
the given liquid you will have a relation like that of figure 5.
13. Determine the refractive index of water from the graph.
14. Determine the concentration at which the line is broken.
Results:
C%
n
n( water)=
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Optics Experiments
Exp. (7)
Week: …………….
Date:
/
/
Optical Activity and Polarization of Light
Objective:
1. Study the effect of the chiral material on the polarized light.
2. Determination of the specific rotation power of the glucose.
Apparatus:
Polarimeter, polarimeter tube, sodium lamp, 100 ml cylinder and optical
active material such as (glucose).
Theory:
Specific Rotation
A beam of light is composed of electromagnetic waves oscillating
perpendicular to direction of light propagation. Normally, light exists in an
un-polarized state. Un-polarized light has electromagnetic oscillations that
occur in an infinite number of planes. A device known as a linear polarizer
only transmits light in a single plane while eliminating or blocking out light
that exists in other planes. The light exiting the polarizer is known as plane
polarized light. When the polarized light beam incident on another polarizer
(called analyzer) it will be two basic cases. First case, when polarizer
parallel to analyzer the polarized light will appear as shown in Figure 1-a,
the second one by rotating the analyzer the light slightly disappears until the
analyzer become normal on polarizer, the light will totally disappear as
shown in Figure 1-b.
Chiral organic molecules are molecules that do not contain a structural
plane of symmetry. They rotate the polarization plane of light as it
propagates through the sample, see figure 2.
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Optics Experiments
Unpolarized
Light
Polarizer
Polarized light
Analyzer
Polarized light
appear
Figure 1-a
Unpolarized
Light
Polarizer
Polarized light
Analyzer
Polarized light
disappear
Figure 1-b
b
b
b
c
c
C a cC
C a
a
d
d
d
The sample
Plane-polarized
light
Plane-polarized
light rotated
Figure 2
These molecules are collectively known as optically active.
Depending on the molecules confirmation, the plane of polarization may
either be rotated clockwise or counter-clockwise. Molecules possessing the
ability to rotate light to the left or counter-clockwise are denoted as
levorotatory (L-) and those that rotate light to the right or clockwise are
referred to as dextrorotatory (D+).
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Optics Experiments
Glucose is a dextrorotatory optically active molecule. The specific
rotation of glucose dissolved in water is +52.6 °/ (dm g/ml) for 589 nm light.
The equation which relates optical rotation to a molecules specific rotation is
given by equation (1)
s 
100 
L C
(1)
Where θs is the specific rotation of an optically active compound, θ is the
observed rotation in degrees, L is the path length in dm, and C is the sample
concentration in grams of mass per ml of solution.
Basic Polarimetry
The optical instrument used to measure rotation due to an optically active
sample is a polarimeter. The main components of a polarimeter are a light
source, polarizer (Nicol prism), sample cell, a second polarizer known as the
analyzer (Nicol prism), and a detector as shown in figure 3.
Detector and
Eyepiece
b
b
c C cb
c
a C a C a
d
d
d
Sample
Unpolarized Polarizer
light
cell
Plane-polarized
light
Analyzer
Plane-polarized
light rotated
Figure 3
As the beam passes through the sample, the plane of polarization will rotate
according to the concentration of the sample and path length of the
container. The amount of rotation due to the sample can be determined using
the analyzer. If the analyzer is oriented perpendicular to the initial polarizer,
theoretically no light will be transmitted if a sample is present. If an
optically active sample is then introduced into the system, the intensity of
transmitted light will be proportional to the amount of rotation in
polarization due to the sample. Thus, the detected light intensity is related to
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Optics Experiments
the sample’s concentration assuming a constant path length.
The light
travels through a Nicol prism to produce plane polarized light. This in turn is
passed through a sample cell held in a cell holder and from there the rotated
light travels to an analyzer Nicol prism and an optical device for detecting
the "balance" point. The analyzer Nicol prism must be rotated such that the
prism axis aligns with the plane of polarization of the light that exits from
the sample. This is the "balance" point. The optical detecting device allows
the observer to determine the balance point.
Procedure:
1. Make sure the two polarizers are parallel. To do this, keep the first
polarizer fixed and rotate the second polarizer until you observe
homogeneity illumination in transmission. At this point the polarizers are
parallel(00 apart).
Homogenous
Illumination
2. Beginning with the prepared concentrated of the sugar solution, put the
liquid into the polarimeter cell and rotates the analyzer to obtain
homogeneity illumination in transmission. Measure the corresponding angle
of rotation.
3. Put the liquid back in the cylinder and prepare another sugar solution. 4.
Repeat step 2 with the prepared sugar solution.
5. Repeat step 3, 4 at least five times sugar solutions.
6. Tablet the data in the following table.
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7. Plot the relation between (C) as x-axis and () as y-axis, you will get a
straight line, its slope = /C.
8. Determine the specific rotation using equation (1).
Please try not to use much more than what you need for these solutions so that we
have enough for everyone!
Results:
L=
cm
C%

Slope=
s
10 3
=
Slope
L
s =
°/ (dm g/ml)
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48