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FACULTY OF ENGINEERING
LAB SHEET
FUNDAMENTALS OF OPTICS
EOP2016
TRIMESTER 2 (2014-2015)
FO1 – Diffraction of Circular Apertures
FO2 – Polarization of Light
*Note: On-the-spot evaluation may be carried out during or at the end of the experiment.
Students are advised to read through this lab sheet before doing experiment. Your performance,
teamwork effort, and learning attitude will count towards the marks.
Experiment 1 : DIFFRACTION OF CIRCULAR APERTURES
Objective:
Study and measure the diffraction effects of circular apertures.
Equipment Required:
Laser Assembly (LA)
2 Beam steering assembly (BSA-I)
1 Lens chuck assembly (LCA)
1 Target holder assembly (TA-II)
Pin hole targets [0.001” (TP1) and 0.002” (TP2)]
Index cards
Ruler
1. Introduction
The diffraction associated with the size of the aperture determines the resolving power of all optical
instruments from the electron microscope to the giant radiotelescope dishes. In addition, a solid object not
only casts a shadow but it is possible for a bright spot to appear in the center of the shadow.
The diffraction patterns are located both close to the diffraction aperture and far away. The first is called
Fresnel diffraction; the second is Fraunhofer diffraction.
2. Theory
Diffraction of Light: (light bending around an object)
Diffraction is the slight bending of light as it passes around the edge of an object. The amount of bending
depends on the relative size of the wavelength of light to the size of the opening. If the opening is much
larger than the light's wavelength, the bending will be almost unnoticeable. However, if the two are closer
in size or equal, the amount of bending is considerable, and easily seen with the naked eye.
In the atmosphere, diffracted light is actually bent around atmospheric particles -- most commonly, the
atmospheric particles are tiny water droplets found in clouds. Diffracted light can produce fringes of light,
dark or colored bands. An optical effect that results from the diffraction of light is the silver lining
sometimes found around the edges of clouds or coronas surrounding the sun or moon. The illustration
above shows how light (from either the sun or the moon) is bent around small droplets in the cloud.
Optical effects resulting from diffraction are produced through the interference of light waves. To
visualize this, imagine light waves as water waves. If water waves were incident upon a float residing on
the water surface, the float would bounce up and down in response to the incident waves, producing
waves of its own. As these waves spread outward in all directions from the float, they interact with other
water waves. If the crests of two waves combine, an amplified wave is produced (constructive
interference). However, if a crest of one wave and a trough of another wave combine, they cancel each
other out to produce no vertical displacement (destructive interference).
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This concept also applies to light waves. When sunlight (or moonlight) encounters a cloud
droplet, light waves are altered and interact with one another in a similar manner as the water
waves described above. If there is constructive interference, (the crests of two light waves
combining), the light will appear brighter. If there is destructive interference, (the trough of one
light wave meeting the crest of another), the light will either appear darker or disappear entirely.
Experiment:
1) Mount a laser assembly (LA) at the rear of the breadboard.
2) Adjust the position of the laser such that the beam is parallel to the edge and top of a line of tapped
holes in the breadboard.
3) Tape an index card with a small (about 2 mm) hole in it to the front of the laser, so that the laser beam
can pass through it. This card will be used as a screen to monitor the reflections from the components
as they are inserted in the beam.
4) Mount a beam steering assembly (BSA-I) approximately 4 inches in from the far corner of the
breadboard.
5) Adjust the height of the mirror mount until the beam intersects the center of the mirror.
6) Then rotate the post in the post holder until the laser beam is parallel to the left edge and the surface
of the optical breadboard.
7) Place a second beam steering assembly (BSA-I) in line with the laser beam at the lower left corner of
the optical breadboard.
8) Rotate and adjust the mirror mount until the laser beam is parallel to the front edge and the surface of
the optical breadboard.
9) Place an index card in a modified target holder assembly (TA-II) and set it at the end of the
breadboard so that the beam hits the center of the card.
10) Mount a lens chuck assembly (LCA) five inches to the right of the last beam steering mirror and
directly in line with the laser beam. This will be the aperture holder.
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11) Carefully place the pinhole target (TP1) into the LCA, and adjust the mount such that the laser beam
strikes the target approximately in the center. Warning: Large percentage of the laser beam
will be reflected.
BSA-I
LA
Figure 1:
Schematic view
Diffraction of
Light Experiment.
LCA
TA-II
BSA-I
12) Adjust the last beam steering mirror such that the laser beam fills the pinhole. This can best be
accomplished by viewing the back side of the target (beyond the laser) from 450 and looking for a
bright red glow. This will occur when the laser beam (or part of the laser beam) is illuminating the
aperture.
13) Carefully adjust the last beam steering mirror to produce the brightest image on the white card. A
bright central circle surrounded by dark and light circular bands should be seen. This is the Airy disc
pattern. Measure the distance from the pinhole target to the index card in TA-II.
14) Mark and then measure the diameter of the first dark circular band around the bright central circle.
This is a measure of the amount of diffraction caused by the pinhole. Record the value in Table I.
15) Repeat step 14 for the 2nd, 3rd dark fringe and record the value in Table I.
16) The angular subtense of the 1st dark band is related to the wavelength and the diameter of the pinhole
by sin = 1.22/D, where D is the diameter and  is the wavelength. Since the diffraction angle is
small, the sine and the tangent of the angles are equal. The tangent is found from dividing the radius
of the dark band by the distance from the pinhole to the index card. (Fig. 2)
1st dark ring
1/2 = 1.22 D
HeNe
laser
D
Figure 2. Diffraction of Light by Circular Aperture.
Light wavelength, 
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17) Using the wavelength of the HeNe laser,  = 633 nm, calculate the diameter of the pinhole.
18) Replace the pinhole target TP1 with TP2. Repeat steps 11 to 16.
19) Compare the calculated pinhole diameter with the one given by the manufacturer. Is the calculated
diameter close to the real diameter? Justify your findings.
Table I:
1. TP1
Distance from the pinhole to the index card = _______mm
Order of fringe
I
II
III
Fringe width (mm)
2. TP2
Distance from the pinhole to the index card = ________ mm
Order of fringe
I
II
III
Fringe width (mm)
20) Analyze and discuss your tabulated results based on the theory of diffraction of light.
Important Notes:
1) When handling optical components treat the optical surfaces of mirrors with care. Never
touch those surfaces. Use lens tissues or finger cots if available to handle and protect the
surfaces from finger oils and contamination. If not, handle the components by their edges.
Assemble the components over the optical table surface. (Do not lift components any higher
off the table than necessary)
2) The HeNe laser can cause permanent damage to your vision. Never look directly into
the laser tube or at a reflection from a specular surface. Do not wear ring or other shiny
jewelry when working with lasers. Use only diffuse (white 3x5 card) reflectors for
viewing HeNe laser beam. Protect your group member from accidental exposure to the
laser beam. Always block laser beam close to the laser when the experiment is left
unattended.
5
Guideline for lab report and submission:
1) The laboratory report should be nicely typed and should include the following:

Introduction.
 Objective of the experiment.
 Summary of procedures (in passive and past tense).
 Results and discussions.
 Conclusion.
 References
2) Duration of lab report submission: not more than 10 days after the date of your experiment.
3) Lab report submitted to the lab staff of Optical Laboratory.
Marks allocation





Introduction. – 2 marks
Objective of the experiment- 2 marks
Summary of procedures – 2 marks
Results and discussions – 2 marks
Conclusion – 2 marks
6
Experiment 2: POLARIZATION OF LIGHT
Objectives
Explore the laws of Malus and Brewster; construct a linear polarizer/analyzer to prove the law of Malus;
find the angle where minimum reflection of linear polarized light occurs (Brewster's Angle).
Equipment Required:
Laser Assembly (LA)
2 Beam Steering Assembly (BSA-I)
2 Rotation Stage Assembly (RSP-I)
2 Lens Chuck Assembly (LCA)
1 Modified Target Assembly (TA-II)
1 Rotation Stage and Plug (RSP-IT)
1 Microscope slide
2 Linear Polarizer
Index Card
Optical Power Meter
1. Introduction
Since electric and magnetic fields are vector quantities, both their magnitude and direction must be
specified. But, because these two field directions are always perpendicular to one another in nonabsorbing media, the direction of the electric field of a light wave is used to specify the direction of
polarization of the light. The kind and amount of polarization can be determined and modified to other
types of polarization. The amount and direction of light can be controlled through the use of its
polarization properties.
Basic Concepts
1) The polarization direction is defined as the alignment of the electric field, which automatically
sets the direction of the perpendicular magnetic field.
2) Light waves with their electric fields in the same plane are linearly polarized.
3) Polarization is measured by passing light through a polarizer, which transmits light only if its
electric field is aligned in a particular direction. The fraction of light transmitted by the polarizer
indicates the degree of polarization in the direction of the polarizer.
Part A: Law of Malus
2A.1 Theory
The electric field of a propagating transverse electromagnetic wave lies in a plane normal to the direction
of propagation. If assumptions are made that the wave propagate out of the page and normal to it, the
electric field of the wave can be represented by two orthogonal components in a plane perpendicular to
the direction of propagation, as in Fig 2(a). Fig 2(a) is drawn at a particular instant in time because E-field
is time dependent. For linearly polarized light, as the light wave move in the direction of propagation, the
orientation of the E-field vector in the x-y plane is constant, i.e no angular variation, then the light beam
is defined as linearly of plane polarized and the E-field can be written as
E  xˆE0 x cos( kz  t )  yˆE0 y cos( kz  t )
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Figure 2(a): Representation of the electric field and its two orthogonal components. The
electromagnetic wave is propagating out of the page.
2A.2 Malus’s Law
Consider natural or unpolarized light of intensity I(0) to be incident on an ideal linear polarizer. Let the
transmission axis of this polarizer be at an angle of  with respect to the vertical. Only light with it’s
electric field vector parallel to the axis of the polarizer will be transmitted through the polarizer.
If we let this light be incident on a second polarizer, sometimes called an analyzer, whose transmission
axis is at an angle of  with respect to the vertical. By Malus’s Law, the intensity of the light emerging
from the the second polarizer is given by
I ( ) 
1
I (0) cos 2 (   )
2
If we consider the situation where light from the second polarizer is incident on a third polarizer whose
transmission axis is at an angle of  with respect to the vertical. The intensity of light emerging from the
third polarizer us given by
I ( )  I ( ) cos 2 (   )
1
 I (0) cos 2 (   ) cos 2 (   )
2
Another related quantity is that of percent polarization. This is basically a measure of the extent to which
the light which we are studying is polarized. To calculate the percent polarization of a sample of light, the
following formula should be used.
 I  I min
% Polarizati on   max
 I max  I min

  100

where Imin and Imax are the minimum and maximum intensity of the light, respectively.
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Experiment 2A
1) Mount a laser assembly (LA) to the rear of the optical breadboard. Adjust the position of the laser
such that the beam is parallel to the edge and on to of a line of tapped holes in the breadboard top.
Tape an index card with a small (about 2mm) hole in it to the front of the laser, so that the laser beam
can pass through it. This card will be used as a screen to monitor the reflections from the components
as they are inserted in the beam.
2) Mount a beam steering assembly (BSA-I) approximately 4 inches in from the far corner of the
breadboard [Fig 2(b)]. Adjust the height of the mirror mount until the beam intersects the center of
the mirror. Then rotate the post in the post holder until the laser beam is parallel to the left edge and
the surface of the optical breadboard.
Figure 2(b): Schematic view of polarization of light experiment.
3) Place a second beam steering assembly (BSA-I) in line with the laser beam at the lower left corner of
the optical breadboard [Fig 2(b)]. Rotate and adjust the mirror mount until the laser beam is parallel
to the left edge and the surface of the optical breadboard.
4) Place the detector in a lens chuck assembly (LCA) and mount it well beyond the second beam
steering assembly (BSA-I) so that the beam hits the center of the detector.
5) Place two rotation stage assembly (RSA-I) attached with linear polarizer directly in line with the laser
beam between the second beam steering assembly (BSA-I) and the detector. Rotated both the
polarizer so that the transmission direction is horizontal to the table (0). The output of the device will
be proportional to the irradiance of the light (Watts/m2). This quantity is proportional to the square of
the amplitude of the electric field.
6) Rotate the second polarizer (close to the detector) by 10 increments between 0 and 180, record the
angle and the power from the detector (optical power meter) in Table 2A. Compute the transmitted
irradiance, I.
7) Determine the maximum irradiance, I0 and minimum irradiance, Imin.
8) Compute the Irradiance, Itrans as a function of angle of the rotation of the polarizer in the plane
perpendicular to the beam using Malus’s law and record the results in Table 2A.
I trans  I o cos 2 
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Laser beam diameter, d = ____________ mm
Maximum irradiance I0 = ____________ W/m2
Table 2A:

Power (W)
Irradiance, I
(W/m2)
Irradiance
Ratio, I/I0
cos2
Irradiance,
Itrans (W/m2)
Irradiance
Ratio, Itrans/I0
(i) Plot the irradiance versus Cosine Squared Angle.
(ii) Plot the Ratio of irradiances versus Angle.
Analyze and discuss the results of your measurements in comparison to the Malus’s law.
(You may miss the orientation of one of the polarizers by some amount and therefore the two curves
may be shifted along the angle axis. You may have to adjust your plots to make the comparison, but
you should justify any adjustment made in your report.)
(iii) Based on the measurements, evaluate the percentage polarization and discuss the extent of
polarization of the laser light.
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Part B: Polarized Light by Reflection at Brewster’s Angle
2B.1 Theory: Polarization by Reflection – Brewster’s Angle
Another way to produce polarized light is through a particular case of reflection. Consider an unpolarized
beam of light incident on a medium of index of refraction, nt as shown in Fig 2(c). We know that the
electric field vector of the unpolarized light at any instant of time can be decomposed into components
normal to the incident plane and parallel to the incident plane. For a particular angle of incidence, namely
Brewster’s angle B, only the electric field vector oriented perpendicular to the plane of incidence will be
reflected. The transmitted beam will still have polarization components in the parallel and perpendicular
directions.
Brewster’s angle occurs when the angle between the reflected beam and the refracted beam is 90. In
other words,
B   

2
By Snell’s Law, we have
tan  B 
nt
no
which defines Brewster’s angle.
Figure 2(c) Light is incident on a glass block at Brewster’s angle. The reflected and refracted light beams
are 90 apart.
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Experiment 2B
1) Setup the system shown in Figure 2(d).
2) Insert a plug in the 1 inch hole into the rotation stage (RSP-IT). Mount a modified target assembly
(TA-II) without a base onto the rotation stage (RSP-IT) by using a hole in the center of the plug. The
rotation stage (RSP-IT) is then attached to the table with ¼-20 screws. Place the modified target
holder such that the laser beam passes through the center of the filter holder (FC-1). Insert a
microscope slide to the filter holder (FC-1) so that the slide is held firmly in place.
Figure 2(d) Schematic view of Brewster angle experiment
3) Set the rotation stage (RSP-IT) angle to 0. Rotate the stage so that the beam reflected from the slide
is sent back along the input beam (normal incidence). (Note: You can use the index card with the hole
in it to set the beam). Tighten the screw on the post, so that the filter holder is fixed.
4) Rotate the polarizer so that the transmission beam polarization direction is horizontal to the table
(900). This means that the polarization vectors now horizontal and in a plane formed by the laser
beam direction and the normal to the surface of the microscope slide. The plane defined by these two
directions is called the plane of incidence.
5) Attached the detector to a modified target assembly (TA-II). The detector has to follow the beam on
the table to measure the reflected power.
6) Starting at normal incidence, rotate the rotation stage (RSP-IT) away from 0 and observe the
reflected power from the detector. At some point in this process the reflection from the slide will
become very dim and power detected is minimum. Scan past the point of minimum reflection and
observe that the reflected power increases. By successive approximations, bring the stage to produce
the minimum reflection. (You can improve the minimum by slightly tweaking the input polarization
angle by small interval).
7) Record the angle of the Rotation Stage and determine the angle between the beam and the normal to
the surface (Brewster’s angle). Determine the refractive index of the glass slide, by using the air
refractive index is 1.0.
8) Rotate polarizer such that the incident beam is vertically polarized (00). Starting at normal incidence,
rotate the rotation stage (RSP-IT) away from 0 and observe the reflected beam irradiance occurs at
any angle. Evaluate the reflected beam appearance with respect to the angle for this polarization
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state.
9) Remove the polarizer and place it between the slide and the detector, and in line with the laser beam.
Set the rotation stage (RSP-IT) angle to Brewster’s angle. Analyze whether the reflected beam is
linearly polarized and evaluate the direction of polarization relative to the plane containing the
incident and reflected rays of the microscope slide.
Important Notes:
1) When handling optical components treat the optical surfaces of mirrors with care. Never
touch those surfaces. Use lens tissues or finger cots if available to handle and protect the
surfaces from finger oils and contamination. If not, handle the components by their edges.
Assemble the components over the optical table surface. (Do not lift components any higher
off the table than necessary)
2) The HeNe laser can cause permanent damage to your vision. Never look
directly into the laser tube or at a reflection from a specular surface. Do
not wear ring or other shiny jewelry when working with lasers. Use only
diffuse (white 3x5 card) reflectors for viewing HeNe laser beam. Protect
your group member from accidental exposure to the laser beam. Always
block laser beam close to the laser when the experiment is left unattended.
Guideline for lab report and submission:
1) The laboratory report should be nicely typed and should include the following:
 Introduction.
 Objective of the experiment.
 Summary of procedures (in passive and past tense).
 Results and discussions.
 Conclusion.
 References
2) Duration of lab report submission: not more than 10 days after the date of your experiment.
3) Lab report submitted to the lab staff of Optical Laboratory.
Marks allocation





Introduction. – 2 marks
Objective of the experiment- 2 marks
Summary of procedures – 2 marks
Results and discussions – 2 marks
Conclusion – 2 marks
13