Download Practical No 6

Practical No 6
STUDY OF PROPERTIES OF ELECTROMAGNETIC WAVES
In this practical a laser is used to confirm experimentally the Malus’s law, measure the speed of light
and confirm the Lambert’s law. For more information about lasers and their applications in medicine see the
theoretical background to this practice.
Equipment:
Device set-up: semiconductor laser (emission wavelength – 650 nm) with a rotary analyzer,
computer with software to perform automatic recording of light intensity. Computer, light meter, instrument
measuring the speed of light.
Course of measurements:
Students perform the following types of audiometric measurements:
A. Malus`s law.
B. Measurement of the speed of light in an optical fiber.
C. Lambert cosine law.
Part A. Malus’s law
ATTENTION !
Do not touch the laser’s headstage
Do not expose your eyes to the laser’s beam
1. Turn on the computer.
2. Turn on the computer software by clicking twice the icon „Malus’s law” displayed on the monitor’s
screen. Insert the data required.
3. Turn on the laser. Take the external polarizer away from the stage.
4. Run the program „Malus’s law” by clicking the icon with the white arrow in the upper left corner on
the monitor’s screen.
5. The analyzer will be brought automatically to its initial position. Then the diode „Ready” will light.
6. After about 3 seconds the measurements will be started automatically. During the measurements the
diode „Measurement” will light.
7. In the lower left corner of the screen an angular position of the analyzer can be observed. The
measurement starts at the angle of –5o and ends at the angle of 365o. On the right side of the
monitor there is a window with the plot, in which the light intensity is being plotted as a function
of the angular position of the analyzer (black curve). After the end of measurements the table with
the results of measurements will be available.
8. After the end of measurements another curve, which is the theoretical curve of the Malus’s law
(blue curve), will appear on the plot. According to the law:
I(θ) = Iocos2θ
(1)
1
Where: I(θ) – value of light intensity as a function of the angle between optical axes of the polarizer and the
analyzer, Io – maximal value of light intensity, θ - angle between optical axes of the polarizer and the
analyzer.
After the end of measurements the diode „Measurement” will extinct. Instead, the diode „Zeroing”
will light. Then, the analyzer will be brought to its initial position. After the end of zeroing the
program will automatically turn off.
9. Put the external polarizer (a slide) into the laser beam at any angle between 20o and 70o. The angle
should be read as the angle obtained by prolonging the line connecting the points A and B (the
points are indicated on the external polarizer) to the scale on the stage. The external polarizer
should be put inside the circle drawn on the analyzer’s plate.
10. Repeat the measurements from the point No 4 to the point No 7.
11. Read the angular shift of the maxima of the experimental curve (with the external polarizer) in
relation to the theoretical curve (with no external polarizer) and compare this value to the angle
measured using the angle-gouge. Write both values to the table in the report’s sheet.
12. After the measurements and after the zeroing turn off the multimeters, the laser, and, finally the
computer.
Part B. Measurement of the speed of light in an optical fiber
ATTENTION ! Laser radiation is dangerous for your eyes.
Avoid any contact with the laser light!
The laser light beam (electromagnetic wave of a frequency 2 MHz) generated by the source L is splitted into
two beams, the first one is approaching the detector D1 situated near the source, whereas the second one is
propagated through a fiber to the detector D2. The beams are approaching the detectors at different times.
The measured time shift is higher than in reality due to some delay generated by the electronic system. In
order to compensate for this error the time shift is measured for two different fibers: one with a length of 3
meters (the orange one) and one with a length of 5.35 meters (the blue one). The difference of the time shifts
between these two fibers is proportional to the speed of light in the fibers.
Device set-up: one semiconductor laser (emission wavelength – 650 nm), phase shift detector.
Course of measurements.
- ask the tutor for connecting the first fiber
- turn on the POWER of the measuring device
- set the F/L switcher in the position F (fiber)
- check out whether the diode O/K is lighting. If not, press the button RESET
- leave the device for about 10 minutes to stabilize parameters
- after this time press the button RESET and, while the button is pressed, check out whether the screen
displays the sign +/- and zeroes. If yes, leave the button and read the value of time delay displayed on the
screen in nanoseconds. If not, press the button RESET and turn the knob ZERO to adjust the display to
+/- and zeroes. Then, leave the button and read the value of time delay displayed on the screen in
nanoseconds.
- write down the value of the time delay displayed on the screen to the table and ask the tutor for
connecting another fiber
- repeat the measurement of the time delay for another fiber and write down the results
2
Calculate the speed of light in the fiber applying the following formula:
V = (L2 – L1)/[K(T2 - T1)]
(2)
where: V – speed of laser light in the fiber, L1 – length of the orange fiber (3 m), L2 – length of the blue fiber
(5.35 m), K – constant equal to 2, T1 – time delay for the orange fiber, T2 – time delay for the blue fiber.
Finally, calculate the refraction index (n) of the fiber according to the definition:
n = c/v
(3)
where: c – speed of the light in a vacuum equal to 3x108 m/s, v - speed of laser light in the fiber calculated
using the equation (2).
Part C. Lambert’s cosine law
The aim of this part of the practical is experimental testing of Lambert’s cosine law and calculation of
luminous intensity.
Fig. 1.- Solid angle. O – apex of a cone and the center of a ball, S – spherical surface cut by the generatrix of
a cone, r – ball’s radius.
Basic photometric quantities
Solid angle is a part of space cut out by the surface of a cone. Solid angle ω is proportional to the spherical
area, S, cut out by the surface of a cone, and inversely proportional to the square of the sphere's radius, r (r is
a distance between apex of a cone O and the surface cut out by this cone): ω= S/r2.
If the area of S is equal to r2, such a solid angle is called a unit solid angle or steradian (sr). Maximal solid
angle can be equal to 4π steradian, because by definition ω= S/r2 = 4πr2/r2 = 4π, we can also say it is the
ration of the sphere surface (4πr2) to the square of its radius – r.
3
Fig. 2. Schematic presentation of basic photometric quantities.
P – light source, ∆Φ - part of luminous flux contained in a solid angle ∆ω, R – axis of luminous flux,
I – luminous intensity, E – illuminance, α – angle between the line perpendicular to the illuminated surface
and the direction of luminous flux, S – illuminated surface.
In photometry, luminous flux Φ is the total amount of energy (in the range of visible radiation) sent by a
source in all directions during a unit of time.
A light source sending light with the same power in all directions is called isotropic.
Luminous intensity (I) is:
I = ∆Φ /∆ω
(4)
if angle ∆ω approaches 0.
The unit of luminous intensity is the candela [cd]. The candela is the luminous intensity, in a given direction,
of a source that emits monochromatic radiation of frequency 540 × 1012 Hz and that has a radiant intensity in
that direction of 0,001464 W/sr. Candela is one of SI base units.
The unit of luminous flux is lumen [lm].
Lumen is a luminous flux of a light source that uniformly radiates 1 candela in all directions inside a solid
angle of 1 steradian (1 lm = 1cd/1sr). If the source is isotropic the total flux is equal to 4π lumens.
Illuminance (E) of a surface is defined as:
E = ∆Φ /∆S
(5)
where ∆S is the fragment of the surface perpendicular to the luminous flux. The unit of illuminance is lux
(lx); this if illuminance given by a luminous flux of 1 lumen incident on a surface of 1 square meter.
The dependence of illuminance on luminous intensity can be written as:
E = (I/r2) cos α
(6)
Where: α is an angle between an axis of luminous flux and the line perpendicular to an illuminated surface,
and r is a distance of an illuminated surface from a light source.
The equation (6) is Lambert’s cosine law called also „cosine emission law”. This law is valid only for socalled point light sources that is sources whose dimensions are small compared to the distance from a light
source to an observer. Lambert’s law can be used for all light sources whose diameter is more than 10 times
smaller than the distance from a light source to an illuminated surface.
If the luminous flux hits the illuminated surface perpendicularly (and this is a case in this practical)
cosα equals 1. So the equation (6) becomes:
4
E = I/r2
(7)
In reality light sources are not points but surfaces. In such a case giving the luminous intensity I only is not
enough to characterize luminous properties of this source. If we had two light sources of equal luminous
intensity but of different sizes, the smaller source would seem to be „brighter” for the observer. Therefore an
additional photometric quantity called luminance was introduced. It is defined as the ratio of luminous
intensity I to light source surface area σ.
B = I/σ
(8)
2
The unit of luminance is 1 cd/m .
Fig. 3. Scheme of the experimental setup. 1 – optical bench, 2 – power on/off, 3 – power supply, 4 – light
source with filters, 5 – diaphragm, 6 – light detector, 7 – light meter, 8 – screen, 9 – light meter’s power on,
10 – light meter’s power off, 11 – light meter range switch x1 (1 – 2000 lx), 12 – light meter range switch
x10 (10 – 20000 lx)
Course of measurements:
1. Turn the light source on using the button (2) and set it to the position when white light is emitted.
2. Turn the light meter on using the button (9).
3. Using the button (11) set the light meter at normal range (x1).
4. Set the diameter of the diaphragm to 6 mm and place the detector at the distance of 5 cm from the light
source.
5. Find the illuminance of a detector (E) as a function of the distance between the detector and the light
source (r). Fill in the table of the report’s sheet with the measured values.
Attention: If the measuring range would be exceeded (1 at the left side of the screen would appear) use
the range switch (12). This would result in the presence of small black triangle on the screen; now you
have to multiply all the readings by 10. When the readings would drop below 2000 you can return to a
normal range by pressing the button (11).
6. Change the position of the light source to the position when red light is emitted and repeat the experiment
described in point 5.
7. After finishing of the measurements turn off the light meter and the light source.
8. Plot the dependence of illuminance E on 1/r2 w in standard conditions and in the presence of red filter.
9. Basing on Lambert’s cosine law (7) calculate luminous intensity (I) by finding a slope of E = f(1/r2)
dependence.
5
Required theoretical knowledge:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Nature of light.
Generation of laser’s light (population inversion, optical pumping, parameters of semiconductor laser).
Light polarization.
Properties of laser’s light.
Malus’s law.
Application of lasers in medicine and stomatology.
Methods of measurement of the speed of light.
Phenomenon of the total internal reflection.
Principle of operation of an optical fiber.
Application of optical fibers in medicine (endoscopy).
Basic photometric quantities and their units.
Lambert’s cosine law.
Suggested sources:
1. Wikipedia
2. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
6
Practical No 6
Wrocław Medical University
Department of Biophysics
Study of properties of electromagnetic
waves
Tutor’s signature
.........................................................................
.........................................................................
Students’ names
Faculty:
Date:
Group:
Grade:
1. Attach the printed computer plot that confirms the Malus’s law.
2. Write down the values of the angle of externel polarizer’s position.
Angle read from the
computer plot [°]
Angle read from the
protractor [°]
3. Calculate the speed of light in the optical fiber using the formula:
V=
L1 [m]
L2 [m]
L2 − L1
K ⋅ (T2 − T1 )
K
T1 [s]
T2 [s]
V [m/s]
4. Calculate the refraction index of the optical fiber:
n=
C
=
V
where:
c - speed of light in vacuum (3x108 m/s),
v – speed of light in the optical fiber
5. Illuminance (E) of a detector as a function of the distance between the detectror and the light
source (r).
7
Distance r
[cm]
2
1/r
[1/m2]
Illuminance
E1 [lx]
(diaphragm 6 mm)
Illuminance
E2 [lx]
(diaphragm 6 mm,
red filter)
5
5,5
6
6,5
7
7,5
8
8,5
9
9,5
10
11
12
13
14
16
18
20
25
30
40
50
6. Luminous intensity (I1 at diaphragm 6 mm, I2 at diaphragm 6 mm + red filter).
I1=
[cd]
I2=
[cd]
8