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 advanced technology outweigh the bad effects it has caused. 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° 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=5.6×10−7m 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 5.6×10−7×3.0 −5 w= = =6.7×10 m (Round to 2 significant digits) ∆y 0.025 Therefore, the width of the slits is 6.7×10−5m 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=7.6×10−7m L=1.5m d = 1cm/1500lines = 0.00066666cm = 6.6667 x 10-6m The distance between adjacent bright fringes: Lλ 1.5×7.6×10−7 ∆ x= d = 6.6667×10−6 =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 lens and reach the eyes, which can protect our eyes from UV radiations. (Retrieved from 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° to 180°. 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° or 180° , 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° and 90°, or between 90° and 180°,. 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°), 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 known as radiofrequency waves. Radiofrequency is non-ionizing radiation, which does not 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. Retrieved from: http://www.who.int/features/qa/30/en/ 2. American Cancer Society: Cellular Phones Web. 27 May 2016. Retrieved from: http://www.cancer.org/cancer/cancercauses/othercarcinogens/athome/ cellular-phones 3. National Cancer Institute: Cell phones and cancer risks Web. 27 May 2016. Retrieved from: http://www.cancer.gov/aboutcancer/causesprevention/risk/radiation/cell-phones-fact-sheet 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. < http://www.timbercon.com/History-of-Fiber-Optics/>. • “Fiber Network Training & Consulting Services ‘What is Fiber Optics’” F-N-T – Home Page. Web. 11 April 2012. <http://www.f-n-t.com/whatisfo.htm>.
