# TVO ILC SPH4U UNIT 4 ASSIGNMENT

```Unit 4: The Wave Nature of Light
42, a) According to my measurement:
The distance between the two sources: d = 2cm = 0.02m
The path distance from each source to the nodal point:
|Pn2S1|=4.8cm=0.048m
|Pn2S2|=5.8cm=0.058m
(Since the nodal point is on the second nodal line, therefore it is written as Pn2)
n=2
|Pn2S2−Pn2S1|=0.058m−0.048m=0.010m
Calculation for The wavelength of nodal point: (n− )λ=|Pn2S1−Pn2S2|
λ=|Pn2S1−Pn2S2|
1 n−
2
0.010
=
2−
2
= 0.0067m
Therefore, the wavelength is 0.0067m.
b) Calculation for The wavelength of antinodal point:
(Since the antinodal point is on the first antinodal line, therefore it is written as Pm1)
|Pm1S1|=5.2cm=0.052m
|Pm1S2|=4.3cm=0.043m
m=1
mλ=|Pm1S1−Pm1S2|
λ=|Pm1S1−Pm1S2|
m
0.052
=
= 0.009m
Therefore, the wavelength is 0.09m.
c) If the frequency of the vibration source is increased, the amount of interference will
increased. And the number of the visible nodal lines and antinodal lines will increase as
well.
d) If the distance between the wave sources is decreased, there will be less interference
between the waves. And the number of the visible nodal lines and antinodal lines will
decrease.
e) If the phase of vibrating sources were changed so that they were vibrating completely
outof phase, the pattern will shift. Where there were antinodes in the previous in phase
pattern, there are now nodes present. Where there were nodes in the previous in phase
pattern, there are now antinodes. The pattern goes to a complete phase shift.
43, The treble notes usually have higher frequency or shorter wavelengths than the bass
notes of the music. The amount of diffraction will decrease as the frequency of vibration of
the wave’s source increases. Therefore, the wave produced by treble notes will have less
diffraction compare to bass notes, and it is able to travel at a shorter distance. So we are
more likely to hear the bass note in the distance.
44, On the one hand, “being wired” with technology gives us more opportunities to be
connected with the outside world. For example, if we want to learn some foreign languages
or Western European cultures, we can make lots of foreign friends through the internet. We
can chat and learn from each other by using the internet, which can make the leaning
process easier and more efficient. Also, we can use cell phones to communicate with our
parents, friends or co-workers over a long distance, and receive messages instantly, which
makes it easier for us to build up a strong relationship. Without the internet, none of these
could happen. And we become so dependent on internet for our daily life, we gather almost
all the information we needed for school, for work or even for entertainment from the
internet. And it became part of our daily life. On the other hand, having a cell phone kept us
more isolated especially on the dining table, since everybody is busy with their smart
phones and less interested in conversations. But overall, I believe the benefits of these
45, The first industrial application related to the interference of light waves is the
spectroscope, and the career related to this application is Chemists. Spectroscope is a
device that can break down the light into its component wavelengths and allows chemists
to analyze the individual wavelength. Since different heated elements will emit different
combination of wavelengths or frequencies, the interference pattern created by these
wavelengths can be used to identify the elements present in the object. This application is
widely used in chemistry labs where chemists can identify elements or structures in
unknown chemicals.
Another industrial application related to the interference of light waves is polarizing
film. And the career related to this application will be the opticians or the people who
design and make these special coatings for lens. For example, some companies need these
people to help them design sun glasses that coated with polarizing films to protect our eyes
from UV lights and reduce the glare on cloudy days.
The third industrial application related to the interference of light waves is
interferometry, which is widely used in the fields of science and engineering for the
measurements of small displacement. For example, astronomers use interferometers to
perform high-resolution imaging and combine signals from telescopes so they work in the
same way as larger and much more powerful instruments that can penetrate deeper into
space
46, a) Wave is the natural property of light, and when the light is shone through the double
slits, it’s like having 2 sources of light that vibrate in the exactly the same way. There will be
the interference of the light waves from the 2 slits. The dark fringe we see on the screen is
the dark areas caused by the destructive wave interference, where crests meet troughs.
And the bright fringe we see on the screen is the bright band of light caused by the
constructive wave interference, where crests meet crests and troughs meet troughs. b)
Method 1:
Given:
The angle to the 8th maxima: θ=1.12&deg;
Since it’s the 8th maxima: m = 8
Distance between 2 slits: d = 0.00025m
mλ=dsinθ
dsinθ λ=
m
0.00025
=
0.00025
=
= 6.1 x 10-7m (round to 2 significant digits)
Therefore, the wavelength is 6.1 x 10-7m.
Method 2:
Given:
The distance from the 1st minimum to 5th minimum is: 4(∆x)=2.95cm=0.0295m
0.0295m
∆ x=
=0.007375m 4
The distance between each fringe is:
The distance between the slits and the screen: L = 302cm = 3.02m
Distance between 2 slits: d = 0.00025m
Lλ
∆ x= d
λ=(Δx)d
L
0.007375
=
3.02
= 6.1x10-7m
Therefore, the wavelength is 6.1 x 10-7m.
Method 3:
Given:
The distance from the 1st minimum to 5th minimum is: xn5−xn1=2.95cm=0.0295m
The distance between the slits and the screen: L = 302cm = 3.02m
Distance between 2 slits: d = 0.00025m
1
d(xn)
(n− )λ=
2
L
For the 1st minima:
n=1
1
d(xn1)
(1− )λ=
2
L
(1−)λL
λL
xn1=
For the 5th minima:
d =2d
n=5
1
d(xn5)
(5− )λ=
2
L
(5−)λL
9 λL
xn1=
d = 2d
Since the distance from the 1st minimum to 5th minimum is: xn5−xn1=2.95cm=0.0295m
9 λL λL 8 λL 4 λL
xn5−xn1= 2d −2d= 2d = d =0.0295m
d(xn5−xn1)
λ=
4L
0.00025
=
= 6.1 x 10-7m
Therefore, the wavelength is 6.1 x 10-7m
47, a)
Lλ
According to the equation ∆ x= , the
distance between the fringes (∆ x) is d
proportional to the distance to the screen (since they are both numerators). This
means that increasing one will increase the other. Therefore, we can decrease the
distance between the slits in order to decrease the distance between the fringes.
Lλ
According to the equation ∆ x= d , the distance between the fringes (∆x) is inversely
proportional to the distance between 2 slits (since ∆x is the numerator, and the
distance between slits (d) is the denominator). This means that increasing one will
decrease the other. Therefore, we can increase the distance between the slits in
order to decrease the distance between the fringes.
b) Safety precautions:
•
Never point the laser towards people’s eye nor look at it directly since it can
cause eye damage.
Source of errors:
•
There can be errors in distance measurements. In order to minimize this error,
we can repeat each measurement 10 more times and get the average, which can
minimize the variation
48, Laser technology was developed in 1960. The ordinary lights are composed of many light
rays with different wavelengths and spread out as they travel. However, for laser, the lights
have identical wavelength and only have one color, and it does not disperse much as it
travels. Therefore, it can be more intense and precisely focused. Because of these
properties, lasers are widely used as cutting tools for diamond industry. And more
importantly, it is used in eye surgeries, which provides the patients with another chance to
see the world.
49, a) Given:
λ=560nm=5.6&times;10−7m
L=3.0m
The width of the central maximum is twice as the distance between adjacent antinodes.
Therefore, 2 (∆ y )=5.0cm=0.050m
0.050
Thus, the distance between adjacent maximum is: ∆ y=
=0.025m
(∆ y)
λ=w
L
The width of the slits:
λL 5.6&times;10−7&times;3.0 −5
w= = =6.7&times;10 m (Round to 2
significant digits)
∆y
0.025
Therefore, the width of the slits is 6.7&times;10−5m and the distance between adjacent maximum
is 0.025m.
b)
λL
•
i) According to the equationw=∆ y , the distance between adjacent nodes or
antinodes (∆y) is inversely proportional to the width of the slit (since w is the
numerator and (∆y) is denominator). This means that increasing one will decrease
the other. Therefore, when the width of the slit became smaller, the distance
between adjacent nodes or antinodes will increase. And the fringes that make up
the interference pattern will become wider, and there will be fewer fringes visible
on the screen.
•
ii) According to the equationL=w(∆ y) , the distance between adjacent nodes or λ
antinodes (∆ y) is proportional to the distance to the screen (since both of them are
numerators). This means that increasing one will increase the other. Therefore,
when the screen was moved further away, L has been increased, the distance
between adjacent nodes or antinodes will increase. And the fringes that make up
the interference pattern will become wider, and there will be fewer fringes visible
on the screen.
•
Iii) According to the equationλ=w(∆ y) , the distance between adjacent nodes or L
antinodes (∆y) is proportional to the wavelength of the light (since both of them are
numerators). This means that increasing one will increase the other. Therefore, when
the wavelength of the light is increased, the distance between adjacent nodes or
antinodes will increase. And the fringes that make up the interference pattern will
become wider, and there will be fewer fringes visible on the screen. c)
•
i) If the light was shone through a double slits, all of the interference fringes would
be evenly spaced and of equal intensity.
ii) If the light was shone through a diffraction grating, there will be more constructive and
destructive interference. And it will produce an interference pattern that has brighter,
sharper, and narrower maxima. And fringes will be shaper and more widely spaced.
50, Given:
λ=760nm=7.6&times;10−7m
L=1.5m
d = 1cm/1500lines = 0.00066666cm = 6.6667 x 10-6m
The distance between adjacent bright fringes:
Lλ
1.5&times;7.6&times;10−7
∆ x= d = 6.6667&times;10−6 =0.17 m (round to 2 significant digits)
Therefore, the distance between adjacent bright fringes is 0.17m
51, Lens that coated with polarizing films can protect our eyes from UV lights and reduce
reflections. Light reflected from the surface of the new material will interfere with the
portion of light that has quickly travelled through the thin film and reflected from the
second surface. Two reflected waves are identical, with a path difference equal to twice the
thickness of the film, since they are both portions of the initial wave.
Because both
reflected rays are reaching the eye at almost the same time, two waves must be out of
phase to interfere destructively where crests meet troughs, in order for the light to be
invisible and reduce the reflection. This way, less UV light will be able to pass through the
Independent learning materials, Unit 4, lesson 15, p22)
52, When we rotate the 2 polarizing filters, the angle between the slits in the 1 st polarizing
filter and the 2nd polarizing filter can be arranged from 0&deg; to 180&deg;. We keep the 2nd polarizing
filter at the same position constantly, and only rotate the 1st polarizing filter.
•
•
In the beginning, when the angle between the orientations of the slits in 2 polarizing
filters is 0&deg; or 180&deg; , these 2 polarizing filters can be treated as just one polarizing
filter. When light shone on them, only the light waves vibrating in the same direction
as the orientation of the slits will be transmitted.(light gets polarized) All other
waves will be blocked. And the light intensity will be reduced by 50 percent.
When we rotate the filter, the angle between the orientations of the slits in 2
polarizing filters is between 0&deg; and 90&deg;, or between 90&deg; and 180&deg;,. When light shone
on them, only the light waves vibrating in the same direction as the orientation of
the slits in the 1st polarizing filter will be transmitted. (All other waves will be
blocked) As the light waves get transmitted to the 2nd polarizing filter, only the light
waves vibrating in the same direction as the orientation of the slits in the 2nd
polarizing filter will be transmitted.(All other waves will be blocked)And when And
the light intensity will be reduced by more than 50 percent.
•
If the orientation of the slits in the 1st polarizing filter is perpendicular to the
orientation of slits in the 2nd polarizing filter (as we rotate two filters to 90&deg;), all lights
waves will be completely blocked.
53, a) The oscillator creates electromagnetic waves by creating rapid changing current. An
oscillator consists of a capacitor, which stores energy in the form of an electrostatic field,
and an inductor, which stores energy as a magnetic field. When a charged capacitor is
connected into a circuit, it will discharge through the inductor, causing the inductor to
create a magnetic field. In trying to maintain the current, the inductor charges the other
plate of the capacitor. By the time the inductor’s magnetic field collapses, the capacitor has
been recharged with the opposite polarity. The capacitor proceeds to discharge through the
inductor, which again creates a magnetic field, but with the current moving the other way
through the circuit. The repetition of this process creates an oscillating current, which is
transmitted into the antenna of the transmitter. The accelerating oscillating charges, with
their changing electric field, create a carrying magnetic field, which, in turn, creates a
varying electric field, and so on. This interaction of electric fields and magnetic fields,
perpendicular to one another, creates an electromagnetic wave that propagates through
space. (Retrieved from Independent learning course material, Unit 4, Lesson 16, p12)
b) Nowadays, over 5 billion people are using cell phones which give off a form of energy
have enough energy to change DNA in our body and cause cancer. Many studies have
shown that there’s no strong evidence of relationship between the cell phone usage and
cancer. Until now, the only observed biological effects in human is tissue heating, and it’s
not clear if the effect is harmful. There are some minor effects of change brain activities and
sleep pattern have been reported, however the data collected is not considered as
statistically significant. Some research results show that cell phone usage linked to high
traffic accident rate. However, it is caused by distraction instead of the direct effects caused
by cell phone. From what I learned about cell phone side effects, I will use the cell phone
only when a landline phone is not available, and I’ll not put the cell phone anywhere near
my bed when I sleep from now on. Even though most of the studies published have not
found a link between cell phone usage and health issues yet, more and more studies or
researches are on the way to discover the side effects of using cell phone. Maybe we will
find something in the future.
Sources:
1. World Health Organization: What are the risks associated
With mobile phones and their base stations? Web. 20 September 2013.
2. American Cancer Society: Cellular Phones Web. 27 May 2016.
cellular-phones
3. National Cancer Institute: Cell phones and cancer risks
54)
Essay : Fibre optics
Today is the age of fast technology and immediate response. Thus, reliable communication
methods are the backbone in today’s world, important to all, from large businesses to
students. Almost every communication network contains fiber optics. Fibre optics is mostly
used because of their convenience. For instance, to prevent large numbers of customers from
being affected in an outage, network builders use fibre optic cables to divide their network
into smaller service areas. This results in better customer relations and better service. Fibre
optic cables also come with a great advantage of fast return path, allowing fibre optic cables
to be used for internet and telephone connections.
Before proceeding to the history of fibre optics, let’s clarify what fibre optic is. Fibre optics is
the conduction of light through long rods of fibre. At fundamental levels, fibre rods can be
made of out glass of plastics. Fibre optic cables are very useful, because they can transmit
voice, images and other data at close to the speed of light (3.00 x 108 m/s).
The following diagram shows the basic properties of a commonly used fibre optic cable:
In 1854, John Tyndall presented to the Royal Society that light could be conducted through a
curved stream of water, proving that a light signal could be bent. Then, in 1880, Alexander
Graham Bell came with an invention that transmitted a voice signal on a beam of light; he
named his invention ‘Photophone’. In the 1920’s, Englishman John Logie Baird and American
Clarence W. Hansell stepped in after many had taken a shot at this endless discovery of
transmitting voice and light over rods. They came with an idea of using arrays of translucent
rods to transmit images for television and facsimiles correspondingly. As years passed, they
only and the greatest problem to a practical use of fibre optics was in attaining the lowest
signal (light) loss. In 1961, Elias Snitzer of American Optical in printed a theoretical description
of single mode fibres. Single mode fibre had a core so small it could carry light with only one
wave-guide mode. But, it wasn’t satisfactory because communication devices needed to be
able to function over much longer distance and required a light loss of no more than 10 or 20
decibels per kilometre. It was in 1964, when Dr. C.K. Kao identified a critical specification. He
stated that for long range communication device they needed purer form of glass to help
reduce light loss. Then finally in 1970, a team of researchers began experimenting with a
material capable of extreme purity with high melting point and a low refractive index, known
as fused silica. Researchers of Corning Glass, Robert Maurer, Donald Keck and Peter Schultz
invented fibre optic wire capable of carrying 65, 000 times more information than copper
wire. Through this fibre optic wire information was able to be carried by a pattern of light
waves what could be decoded at a destination even a thousand kilometres away. It was this
team that solved the greatest obstacles presented by Dr. Kao. This was a major achievement
in the world of technology and fibre optics, and today more than 80 percent of the world’s
long-distance traffic is carried over optical fibre cables. More than 25 million kilometers of the
cable that the researchers Maurer, Keck and Schultz designed has been installed globally.
Sources:
•
“Timbercon ‘History of Fiber Optics’” Timbercon “Education” Web. 11 April 2012. &lt;
http://www.timbercon.com/History-of-Fiber-Optics/&gt;.
•
“Fiber Network Training &amp; Consulting Services ‘What is Fiber Optics’” F-N-T – Home Page.
Web. 11 April 2012. &lt;http://www.f-n-t.com/whatisfo.htm&gt;.
```