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T.C. MARMARA UNIVERSITY
FACULTY OF ARTS AND SCIENCES PHYSICS DEPARTMENT
PHYSICS LABORATORY – III
DEPARTMENT: NAME: SURNAME: NUMBER:
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T.C.MARMARA UNIVERSITY PHYSICS DEPARTMENT
PHYSICS LABORATORY –III MANUAL
EXPERIMENT NO:
EXPERIMENT NAME:
THE DATE:
GROUP NO:
NAME:
NUMBER:
DELIVERY TIME:
REPORT NOTE:
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EXPERIMENT.1
DETERMINATION OF SPECIFIC HEAT OF METALS
Goal: Measuring the specific heat of metals.
Theory:
If energy is given to a matter without any work, temperature of the matter generally increases. The energy that needed to increase the temperature of matters with equal amounts changes with matter to matter. For example energy that needed to increase temperature of 1 kg of water to 1 °C is 4186 J. While energy that needed to increase temperature of 1 kg of copper to 1 °C is only 387 J. Heat capacity of a matter, C, is heat energy that needed to increase temperature of the matter to 1 °C. According to this definition, when heat unit of Q is given to an object, temperature of the object changes as ΔT. So:
Q=C ΔT
Heat capacity (c) of any object is defined as heat capacity per unit volume. So if energy (Q) transfers to m massed object via heat, temperature of the object changes as ΔT. So specific heat of the object is:
Q
cm T
Specific heat is a measurement of heat susceptibility of given energy. If specific heat of a matter is bigger, amount of energy that can change temperature difference is bigger too. According to this definition, m is mass of matter, Q is transferred energy and ΔT is temperature difference:
Q=mc ΔT
For example, heat energy that increase temperature of 0.5 kg water as 3°C is:
(0.5 kg)(4186 J/kg°C)(3°C)=6,28 x 310 J. When heat transfers to an object, both of Q and ΔT
are positive signed. Because both of energy of system and temperature of object increase. When temperature decreases, Q and ΔT are negative and system releases energy. Specific heat changes with temperature but if temperature range isn’t so wide, the difference is negligible and c is assumed as constant. For example specific heat of water changes %1 between 0-100°C at atmospheric pressure.
Heat capacity of water is the highest one among other matters. The reason of very low or high temperature of huge massed water is high heat capacitiy of water. When temperature of water decreases in winter, heat is transferred from water to air. So this cause winds that blow from waters to lands.
If a piece of iron is heated as much as 100°C in boiling water and then the iron is cooled in a water filled calorimeter, heat that released from iron is equal to heat that taken by calorimeter and water.
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4
2 2 1 2 1(100 ) ( ) ( )Fe Fe aqua aqua Cu Cum c T m c T T m c T T (1)
Fem : Mass of iron, kg
aquam : Mass of water in calorimeter, kg
Cum : Mass of internal container(copper)of calorimeter, kg
aquac : Heat capacity of water, 4200 J/kg
Cuc : Heat capacity of copper, 386 J/kg
Fec : Heat capacitiy of iron, ?
1T and 2T : Initial and final temperatures, °C
Experimental Setup:
Apparatus: 1.) Iron 2.) Calorimeter 3.) Thermometer 4.) Stirrer 5.) Weight
EXPERIMENTAL SETUP AND MEASUREMENTS:
Measurements: 1.) Measure mass of iron and heat it up to 100°C with water. 2.) Weigh internal container of calorimeter and then fill 2/3 of the container by water. Weigh it again and record results to Table.1. 3.) Place calorimeter as Figure.1 and measure initial temperature of water. 4.) Put heated iron to calorimeter and stir water. Measure final temperature of water after reaching thermal balance. (Be careful about thermometer mustn’t touch to iron.)
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Figure.1.1 : Calorimeter Calculations: 1.) Record your measurements and calculations to table below. Table.1 : Measurements
Mass of Iron Fem
kg
Mass of internal container(copper)of calorimeter Cum
kg
Mass of internal container of calorimeter + water Cum + aquam
kg
Mass of water in calorimeter aquam
kg
Initial temperature of calorimeter 1T
°C
Final temperature of calorimeter+iron 2T
°C
2.) Find specific heat of iron using formula(1)
Specific heat of iron Fec
J/kg cal/g
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6
Error Calculation: 1.) Derive dependent error formula using formula (1) and find maximum absolute error of specific heat of iron. 2.) Show the theorical table that include real specific heats. Compare theorical and experimental value of specific heat and calculate percentage error. 3.) Write probable error sources. Conclusions and comments: Write your conclusions and comments about the experiment.
EXPERIMENT 1. DETERMINATION OF SPECIFIC HEAT OF METALS:
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EXPERIMENT.2
VISCOSITY COEFFICIENT OF GLYCERIN
Goal: Measuring the viscosity coefficient of any liquid by Stoke’s Law.
Theory:
Stoke’s Law: If viscous liquid flows around a globe or a globe moves in a still viscous liquid, a
friction force acts on the globe. We will call this friction force. Because of the viscosity of
liquid, the globe moves with a constant speed, .
According to Stoke’s Law, flow speed is in direct proportion to the friction force and
inversely proportional to radius of globe .
where is viscosity coefficient.
Now we consider a viscous liquid with a falling globe inside. If initial speed of globe is zero
then the friction force is also zero at the beginning. There are only gravity and ascending force
acting on the globe.
Gravity:
Ascending Force:
where is mass density of liquid and is mass density of globe. According to the Newton’s
Second Law, we find the initial acceleration of globe.
Net Force:
In addition to gain velocity due to this acceleration, the globe is acted by an additional force
which is expressed by Stoke’s Law. This additional force is nothing but the friction force
which is mentioned above. Since speed increases, the friction force increases proportionally.
Finally, globe gains a limit speed which gives a friction force equal to the net force acting on
the globe. After that, the acceleration wanishes and the globe moves with a constant speed
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which is called as “final speed”. We may find this speed by making the net force equal to the
friction force.
where is viscosity coefficient of liquid and is the thermal speed of the globe.
Apparatus:
1. Glycerin
2. 100ml graduated cylinder
3. Thermometer
4. 5 steal balls in different radius
5. Stopwatch
Experimental Setup:
1. Fill the graduated cylinder with glycerin. Wait for the bubbles wanish.
2. Clean the balls from grease and oil by sopping in sodium hydroxide. (After that hold the
balls with tweezers!)
3. Measure the diameters of balls with your micrometer and calculate each radius. Write
your results in Table 1.
4. Mark the specified levels A and B where balls fall with constant speed.
5. Let balls go one by one from the surface of glycerin. Keep the falling time from A to B.
(three times for each ball)
6. Use your thermometer to take the temperature of glycerin.
Calculations and Analyses:
Quantities:
Mass density of steal ball:
Mass density of glycerin:
Gravitational acceleration:
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Lenght of A-B:
Temperature of glycerin:
Table 1: Falling Time,
Thermal
Speed,
Steal Balls
Viscosity
Coefficients
Diameter,
Radius,
1. Calculate the thermal speeds and write these down into related columb of Table 1
2. Calculate the viscosity coefficients etc. and get the aritmetic mean of these
quantities.
3. Draw the graph according to Table 1 and calculate the slop of the graph.
4. Calculate the viscosity coefficient of glycerin at the temperature T with this formula
5. Calculate the viscosity coefficient of glyserin at
6. Compare your results with the accepted values in other literatures.
Error Calculation:
1. Calculate your percentage error for .
2. Derive the relative error formula from .
3. Calculate the maximum absolute error for each measure.
4. Calculate the average standart deviation with
5. Itemize the possible causes of error.
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10
Results and Comments:
Write down your results and interpret your conclusions in accordance with your information you gain in this experiment
EXPERIMENT 2. VISCOSITY COEFFICIENT OF GLYCERIN
11
11
EXPERIMENT.3
THIN EDGES LENS
Goal: Finding focus of thin edges lens
Theory:
Transparent media at least one surface of it is spherical is called lens. If edges according to the middle of the lens are thin, it is called thin edges lens. Otherwise edges according to the middle of the lens are thick, it is called thick edges lens. Some definitions on lens are described in the figure 1.
Figure 3.1
f; focus of lens, do and di; the distance of image and object from the lens, ho and hi heights of image and object, respectively. Between these quantities there are two relations;
Several do-di values pair can be obtained by changing the location of object. If graph 1/do against to 1/di is drawn, points intersect the horizontal and vertical axes of the graph give the values of f.
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12
Figure 3.2. Graph 1/do against to 1/di
Experimental Setup:
Apparatus: 1.) Light source 2.) Thin edges lens 3.) Screen 4.) Ruler 5.) Paper tape EXPERIMENTAL SETUP AND MEASUREMENTS:
1.) A long strip of paper is placed on table.
2.) Keep away candle from the lens as it could be. And mark the location of the clear image and the object. Then write them to table 1.
3.) Change the location of the thin edges lens and write do-di values to table 1 by getting a clear image again on the screen.
4.) Repeat this process at least ten times.
Measurements: n do(cm) di(cm) 1/ do (1/cm) 1/ di (1/cm) (di/do)=m f (cm)
1 2 3 4 5 6 7 8 9
10
13
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Calculations: 1.) By using formula (1), calculate the focus of thin edges lens mathematically that used in this experiment. 2.) Use ten different measuring results, plot 1/do against to 1/di and find the focus of thin edges lens by using graph intersects the axes. 3.) Do the error calculation by comparing theoretical and experimental value of focus. 4.) Calculate the maximum relative error in any measurement from formula (1). 5.) Find the average standard deviation by using calculated f values. 6.) Write error causes in order. 7.) Write the results and comments about experiment via obtained data. 8.) Interpret your conclusions.
EXPERIMENT 3. THIN EDGES LENS
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14
15
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EXPERIMENT.4
REFRACTION OF LIGHT
Goal: Observing of refraction of light in different medias and calculate the index of refraction.
Theory:
Figure 4.1.The energy spectrum and visible light region
The light beam which is called as “white light” includes different wavelenght of light beams and in the visible spectrum people can observe between 400 and 700 nm wavelenght. This is because the radiation from sun included photons with a large variety of energy values.
Figure 4.2. Beams of sun light
Light travels in straight lines until it encounters another material where it is partially reflected and partially transmitted. The light travels until it meets with a surface and then it is reflected, transmited or absorbed.
After light hits to the surface it has two components : reflected and transmitted. The angle of incidence is equal to the angle of reflection and the angles do not depend on the nature of the material. In refraction the angle of the ray when transmitted through the material changes and depends on the speed of light in the two materials.
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The ratio of how we can illuminate a material depends of the photons that are hit the surface. If the surface absorbs the light totally that means we may not see the material because there will be no reflected light.
Sometimes material can only absorbes some waveleghts so that waveleght will not be reflected. Think about the Sun light which shines the “grass”. After light beam hits the leafs of the grass only green light is reflected and all others are absorbed.
Some materials are transparent. These ones let the light beam transfer inside and light beam will continue its way without losing its energy (maybe just a little energy lose as heat). Thats how the window pane works.
Nature of Light:
Light velocity in vacuum is 300; 000 km/s or 3.108
m/s. Nothing can move faster than this value (nonrelativistically).
Figure 4.3. incident ,refracted and critical angle
n1sin (θ1) = n2 sin(θ2)
θ1 is the angle between the incoming (incident) light and the Normal and θ2 is the angle between
the outgoing (refracted) light and the Normal. When a light beam comes from a medium with a
higher index of refraction and goes to a medium with smaller index of refraction, the beam will be
move away from the Normal and the refracted angle will be bigger than incident angle. But the
refracted angle can not be bigger than 900
. If it is, the light will not transfer to second medium and
will move inside the first one . There will be a maximum limit on the incident angle so as to observe
refraction which is called critical angle θc and above this value the light will not transfer to second
medium . That is called total internal reflection.
Experimental Setup:
Apparatus: 1.) Light source 2.) Materials with different index of refraction 3.) graded angle sheet (attached on the lab. sheet) 4.) Ruler, protractor 5.) Calculator
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EXPERIMENTAL SETUP AND MEASUREMENTS:
1. Place the material on the sheet and use point source and focus it on the origin.
Figure.4.1
2. Use the incident angle values which are given in the table and adjust your point source to these angles. Then one by one measure outgoing angle and fill the table.
3. Draw a graph between the incoming and outgoing angles. What it tells you ?
4. Draw a graph between the sin values of incoming and outgoing angles. What it tells you
5. Incident index of refraction belongs to air. Use the formulation and calculate the index of refraction of unknown material.
6. Do the error calculation by comparing theoretical and experimental value of index of
refractions.
7. Calculate the maximum relative error in any measurements of refractive index.
8. Find the average standard deviation by using calculated n values.
9. Write error causes in order.
10. Write the results and comments about experiment via obtained data.
11. ) Interpret your conclusions.
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EXPERIMENT.4 REFRACTION OF LIGHT
Angle
(θ0) sin(θ0) sin(θi) n0 ni
1 10
2 20 3 30
4 40 5 50 6 60
7 70 8 80
9 90
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20
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EXPERIMENT.5
LIGHT THROUGH A PARALLEL SIDED BLOCK
Goal: Observing of refraction of light in parallel sided block and measuring amount of shift.
Theory:
If a parallel sided block which has 2n refraction index in an ambient that has 1n refraction
index, incident ray that has 1i angle between normal, refracts two times as when it enters and
exits from matter.
Figure 5.1 Snell law for incoming and outgoing rays:
For incoming: 1 1 2 2sin sinn i n i
For outgoing: 2 3 1 4sin sinn i n i
Using these two equations above, we can easily find that 1 4sin sini i and so 1 4i i . This equation
shows that incoming and outgoing rays are parallel to each other. If we want to find amount of parallel shift(d) using trigonometric equations;
2cosL
iAB
, and 1 2sin( )d
i iAB
.
1 2 1 2
2
sin( ) sin( )cos
Ld AB i i i i
iand finally the amount of parallel shift is:
1 1
1
sin( )
cos
i rd L
r (1)
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Experimental Setup:
Apparatus: 1.) Light source 2.) Parallel sided glass block 3.) Millimetric paper 4.) Goniometer EXPERIMENTAL SETUP AND MEASUREMENTS:
Measurements: 1.) Draw three figures that illustrate shape of parallel sided glass block on millimetric paper. 2.) Set incoming angles as 30,50 and 70. 3.) Draw way of outgoing ray. 4.) Measure refraction angles using goniometer and check that your values obtain snell law. 5.) Calculate amount of parallel shift (d) using formula (1).
1 ......L cm
N
1i 2i 3i 4i expd (cm) theod (cm)
1 30 ° 2 50 ° 3 70 °
2 ......L cm
N
1i 2i 3i 4i expd (cm) theod (cm)
4 30 ° 5 50 ° 6 70 °
3 ......L cm
N
1i 2i 3i 4i expd (cm) theod (cm)
7 30 ° 8 50 ° 9 70 °
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Error Calculation: 1.) Compare theorical and experimental value of parallel shift and calculate percentage error. 2.) Find maximum absolute error of any of your measurement. 3.) Write probable error sources. Conclusions and comments: Write your conclusions and comments about the experiment.
EXPERIMENT.5 LIGHT THROUGH A PARALLEL SIDED BLOCK:
Rentech Experimental Set of Fundamental Optics
43
EXPERIMENT 5: Experiment of Polarization
Part 1: Polarizer and Screen
1. Light source, polarizer and screen are placed
on optics track.
1.1. Distance between light source and
polarizer is adjusted to;
.
Distance between screen and polarizer is
adjusted to;
.
1.2. White pointer on polarizer is adjusted to;
.
1.3. Light source is opened and image is
formed on screen (Figure-41a).
1.4. Polarizer is removed from optics track and
whether intensity of illumination of the
image changes or not is observed. If it
changes, its reason is explained.
2. Now, second polarizer (analyzer) is placed
behind polarizer (Figure-41b).
2.1. Distance between analyzer and polarizer is
adjusted to;
.
2.2. Firstly, white pointer on analyzer is
adjusted to;
.
2.3. Next, the angle of analyzer is set as
in condition that the angle of
polarizer is kept unchanged ( )
(Figure-41c).
2.4. After this operation, the angle between
axes of first polarizer and second polarizer
(analyzer) will be;
.
2.5. Change of intensity of illuminance of the
image on screen is monitored.
3. Same steps are repeated, changing the angle
of analyzer as increase of 30° between
.
3.1. According to each change of angle, how
intensity of illuminance of the image on
screen changes is observed.
(a)
(b)
(c)
Figure 41: Intensity of light of the image on screen of light
passing from polarizer (a), intensity of light of the image
on screen of light passing from analyzer (b), and the
angle of analyzer with respect to the axis of polarizer (c).
Rentech Experimental Set of Fundamental Optics
44
3.2. When difference of angle between polarizer and
analyzer is , whether image is formed on
screen is determined. If there is no any image on
screen, its reason is explained on experimental
report.
Two polarizers are used in experimental set-up. Light
passes from these polarizers through plane marked
0° and 180° on scale of polarizer. As a result of this,
light passing from first polarizer is linearly polarized.
If direction of second polarizer is same as direction of
vibration of linearly polarized light, that light passes is
observed. If the angle between these two directions
is 90°, that light does not pass is seen.
4. What is polarization?
If components of an electromagnetic wave vibrate in
different directions, phenomenon of reduction of this
vibration to one direction is called “polarization”.
5. What is direction of polarization?
Direction of vibration and direction of propagation of
electric field component of an electromagnetic wave
form plane of polarization, direction of vibration of this
electric field component is called direction of
polarization. Direction of vibration of electric field
vector is chosen for direction of polarization of light
wave.
6. The angle between axes of polarizer and
analyzer is . How does change intensity of
light passing from analyzer with change of
angle ?.
When the axes of polarizer and analyzer are parallel
with each other ( or ), intensity of light
passing from analyzer becomes maximum, in the
case of that the axes are perpendicular to each other
( or ), intensity of light becomes
minimum (zero).
Rentech Experimental Set of Fundamental Optics
26
There are two types of waves, depending on
direction of vibration (shape of propagation). They
are transverse and longitudinal waves. Waves of
which direction of propagation and direction of
vibration are perpendicular to each other are
transverse waves.
Electromagnetic waves are transverse waves.
Waves of which direction of propagation and
direction of vibration are parallel with each other are
longitudinal waves. Sound waves are longitudinal
waves.
Displacement per time of waves is velocity of
waves. Velocity of a wave depends on frequency of
wave and wavelength. It is given by the following
relation:
Here,
In light waves, electric and magnetic field vector are
perpendicular to each other and direction of
propagation. Electric field (E) and magnetic field (B)
of electromagnetic wave change as perpendicular to
each other. In addition, electric and magnetic field
vibrate in same phase. In other words, electric field
and magnetic field increase or decrease together.
Velocity of propagation of electromagnetic waves is
perpendicular to these two fields.
Electromagnetic waves have a feature of
polarization. If components of a wave vibrate in
different directions, phenomenon of reduction to
only one direction is called polarization. Direction of
polarization of an electromagnetic wave is taken at
direction of electric field. If electric field vibrates at
only one direction, it is expressed as linearly
polarized. Direction of vibration of electromagnetic
wave’s electric field is direction of polarization
(Figure-28a).
6. Polarization
(a)
(b)
(c)
Figure-28: Vibration of electric field vector in non-polarized
light and in polarized light (a), polarized light that has angle
θ between its axis and vertical axis is polarized after it
passes from polarizer (b), when axis of polarizer is
perpendicular to axis of analyzer, analyzer does not pass
light (c).
fv (Experimental) (48)
)/( smv : Velocity of wave.
)(m : Wavelength.
)(Hzf : Frequency.
Rentech Experimental Set of Fundamental Optics
27
If the angle between linearly polarized wave and
polarizer is (Figure-28b), magnitude of electric
field vector of wave is given below:
cos0EE (49)
If intensity of light of polarized light is , intensity of
light passing from polarizer will be as below:
2
0 cosII (50)
Here,
:0I Intensity of light.
: The angle between linearly polarized wave
(incident light) and axis of filter.
When non-polarized light passing from a polarizer of
which polarized axis is vertical, light becomes
polarized as vertical. Therefore, polarizer allows
passing only vertical component of incident light. In
the case of use of analyzer, if polarized axis of this
analyzer and axis of polarizer are perpendicular to
each other, light do not pass (Figure-28c).
Two methods are used for polarization of visible
light.
1. To pass light from polarizer,
2. Polarization by means of reflection.
Rentech Experimental Set of Fundamental Optics
28
6.1. Polarizer
Material which selects an electromagnetic wave
vibrating only certain direction from non-polarized
light and obtains polarized light is called polarizer.
When polarizer is used for polarization of visible
light, polarizer allows passing a major part of
incident light in parallel with axis of polarization. In
other words, it allows passing a part of light in
direction of electric field. As a result of this, intensity
of light reduces in half.
When non-polarized light is passed from polarizer,
second polarize is needed to understand whether
light beam is polarized.
When we turn second polarizer by a value between
0° and 180°, light is polarized if intensity of light
changes between maximum and minimum (zero).
Second polarizer used for this purpose is called
analyzer. If intensity of light transmitted to analyzer
is zero at certain position, light is polarized with
%100. Moreover, if intensity of light reaches to
minimum value, light is partially polarized.
As an example, in system of two polarizers, axis of
the first polarizer is vertical and the angle between
axis of the other polarizer and vertical line is 60°. To
find intensity of light passing from analyzer, firstly it
is needed to determine intensity of light passing
from polarizer. Intensity of light passing from
polarizer is a half of intensity of incident light.
Therefore, after non-polarized pass from first
polarizer, its intensity reduces to half (Figure-29a).
012
1II
After light polarized as vertical pass from second
polarizer (analyzer), its intensity decrease:
20
12 )60(cosII
124
1II
As a result, it is found that;
028
1II
As seen, intensity of light passing from analyzer ( )
is equal to 1/8 of intensity of non-polarized light and
polarization occurs at (Figure-29b).
(a)
(b)
Figure-29: Non-polarized light has two equal intensity of
light as horizontal and vertical components. Intensity of
light reduces in half after passing from polarizer (a). A part
of polarized light passes from analyzer (b).
Rentech Experimental Set of Fundamental Optics
49
EXPERIMENT 8: Single Slit Diffraction
Figure-45: Experimental set-up for single slit diffraction (a)
and position of central bright fringe at diffraction pattern
(b).
1. Laser source, single slit plate and scaled
screen are placed on optics track (Figure-
45a).
1.1. In experiment of single slit diffraction, slit of
which width is smallest is chosen.
1.2. Wavelength of laser source used in
experiment is .
1.3. Rectangular slit is put on its holder horizontally
(or vertically) and it is placed in front of laser
source by means of its holder so that they are
close to each other.
1.4. Distance between slit and screen is adjusted
to;
.
This value is noted as distance of screen.
2. Laser source is opened.
2.1. Diffraction pattern formed by laser source, i.e.
bright and dark fringes, is observed on scaled
screen.
2.2. Central bright fringe’s width and brightness is
observed. (Scaled screen used in
experiment has latitudinal and longitudinal
metric ruler.)
If a monochromatic light beam of which wavelength
is λ pass from a single slit of which width is D,
central bright fringe is seen on screen. Intensity of
light of bright fringes on screen declines as it is
approached to sides of screen. So, it is seen that
intensity of light is maximum at central bright fringe
and decreases at sides of screen.
3. At single slit diffraction pattern, distance (x)
between center of central bright fringe and
center of first dark fringe (m=1) is measured
(Figure-45b).
(a)
(b)
Please, don’t look at laser beam directly.
Rentech Experimental Set of Fundamental Optics
50
3.1. Slit width is calculated, using wavelength of
laser ( ), distance between slit plate
and screen ( and measured
distance (x):
4. Experiment is repeated for different slit
width and different screen distance.
5. Why minimum and maximum intensity of
light form at diffraction pattern is explained.
6. Which condition should be satisfied for
occurring diffraction at light wave?.
When slit width is equal to or smaller than
wavelength of light passing from slit, diffraction
phenomenon occurs.
7. How does fringe width ( ) change when
slit width is decreased at single slit
diffraction?.
Fringe width on screen increases.
8. What is relation of fringe width ( )?.
9. If wavelength of light (λ) used at single slit
diffraction is increased, How does fringe
width on screen ( ) change?.
If wavelength of light used at single slit
diffraction is increased, fringe width on diffraction
pattern increases.
D
mLxm
Rentech Experimental Set of Fundamental Optics
31
Figure-32: Single slit diffraction (a), formation of diffraction
pattern (b), and change of intensity of light at diffraction
pattern (c).
After waves pass from side of an obstacle or a
narrow gap, it changes its direction. This
phenomenon is called diffraction. While
monochromatic light beam incident on single slit
pass from slit gap, it propagates through every
direction as light waves. When these waves
interfere with each other, some waves destruct with
each other by causing that region is dark whereas
some waves construct with each other and bright
regions emerge.
In Figure-(32a), a monochromatic light beam with a
wavelength “λ” incident on a slit with width “D” is
shown. A monochromatic light beam from gap of
which width is “D” meets at point N on the screen at
the distance L. difference between beam passing
from lower side of the slit and beam passing from
the center will be λ/2. Since distance difference to
point N is λ/2, waves from slit interfere destructively
at point N and they emerge dark (minima) fringe.
For dark fringe, the following relation is found:
2/
2/sin
D
(61)
D
sin (62)
Intensity of light is maximum at θ = 0° and minimum
at given angle θ.
Bright (maxima) fringe at point N;
Single slit diffraction pattern formed by light passing
from slit and incident on screen is shown in Figure -
32b. Bright fringes formed at diffraction pattern
weaken through sides of screen. Figure-32c
indicates that distribution of intensity of light as a
function of value of sinθ.
7. Diffraction of Light Wave
(a)
(b)
(c)
mD sin m=1, 2, 3, … (63)
)2
1(sin mD m=1, 2, 3, … (64)
Rentech Experimental Set of Fundamental Optics
32
Here, angle θ determines position of a point on the
screen.
If single slit diffraction is investigated;
1. If << D, then diffraction does not occur.
While a wave travels on linear path, bright
point is seen on screen.
2. If D, it is started to observe diffraction.
Light propagates at all directions after it
passes from slit.
3. If D << , diffraction is observed clearly.
Light beam incident on single slit brings
about many point wave sources at slit
separation. Therefore, light beam from
different points on slit separation interfere
constructively and destructively and so
diffraction pattern is formed.
Intensity of light of bright fringes at diffraction pattern
decreases as sides of screen is gone (Figure-32b).
Figure-(32c) gives distribution of light intensity of
bright fringes as a function of sinθ. Here, angle θ is
angle that determines position of a point on screen.
Figure-33: Distance between a dark fringe formed at
single slit diffraction pattern and central bright fringe.
If at single slit diffraction (Figure-33), distance
between dark fringe and central bright fringe
is , the following relation is written:
Here;
In this equality, distance between central bright fringe
and first dark fringe ( ) is wanted to find, m will be 1.
Fringe width (Δx) is distance between two sequent
bright or two sequent dark fringe. Wavelength is
found in terms of fringe width as below;
L
xD (66)
D
mLxm
(Experimental) (65)
)(mxm: Distance between dark fringe and central
bright fringe.
)(mL : Distance between slit plane and screen.
)(m : Wavelength of light source.
)(mD Width of slit
Rentech Experimental Set of Fundamental Optics
33
As an example, a laser beam with λ=633nm used in
the experiment of single slit and diffraction pattern
emerges on screen at distance L=6 m. On screen,
distance between centers of first dark fringes except
for central bright fringe is calculated as 32 mm (see
Figure-34).
If slit width is calculated from these data;
m=1 is taken for distance between central
bright fringe and first dark fringe.
Distance between central bright fringe and
first dark fringe is;
.
From here, it is found that;
D
mLxm
DLx
1
m
mm
xLD
3
9
1 1016
)10633)(6(
mmmD 24.0104.2 4
Figure 34: Diffraction pattern of beams passing from single
slit on screen.
Single Slit
Wavelength Distance of
screen
Distance of
first dark
fringe
Slit width
(nm) L (m) x1 (m) D(mm)
633 6 16x10-3
. . . . .