Name. OCR Gateway GCSE Physics. P5: Space for reflection

Transcription

1 Name OCR Gateway GCSE Physics P5: Space for reflection 1

2 Satellites, gravity and circular motion Satellites can have two long solar-cell arrays to produce power, and a number of round-dish antennae to receive and transmit communication signals. Communication satellites usually have a high geostationary orbit so that they maintain the same position above the Earth s surface. Satellites relay telephone and television signals around the planet. Satellite showing two long solar cell arrays Satellites A satellite is an object that orbits a larger object in space. Satellites stay in orbit because of the gravitational attraction between the satellite and the object it orbits. We call this gravity. Many planets, such as Earth and Jupiter, have natural satellites. For example, the Moon is a natural satellite of Earth. During the last 40 years many artificial satellites have been placed in orbit around Earth. The height of an artificial satellite above Earth affects its orbit, which affects what it is used for. An artificial communication satellite is shown below. 2

3 Did you know? The world s first artificial satellite, Sputnik 1, was launched by the Soviet Union in 1957 and took about 98 minutes to orbit the Earth. Question: In what direction is the force on the Moon that keeps it in orbit around the Earth? Question: What is the difference between a natural and an artificial satellite? Gravity Question: Complete the following text using the words that follow: All objects attract each other with a force called. The bigger (more ) an object has, the greater its gravitational pull. Small objects therefore have a small gravitational pull. The planets are held in their orbit around the by gravity, as is the Moon around the Earth. Whenever any object moves in a circular orbit around another, a force such as gravity is needed pulling inwards on that body. This force is generally known as a force. Possible words: centripetal, orbiting, Sun, gravity, mass Geostationary artificial satellites A geostationary satellite is placed in an orbit above the and takes exactly 24 hours to orbit the Earth. This is the same time Earth takes to rotate on its axis so the stays over the same point on Earth. It is ideal for as it provides a constant link. The time for one orbit is called the orbital. It increases with height above the Earth s surface. All geostationary orbit Earth at a height of km above the equator. 3

4 Just three geostationary satellites can cover the Earth. Possible words: Earth, satellites, satellite, communications, period Question: How far does a geostationary satellite travel in one day? (The radius of the Earth = 6400 km). Question: An artificial satellite takes 11 hours to orbit Earth. Is its height above the surface of the Earth greater or less than km? Explain your answer. Gravitational force There is gravitational force between all masses. Larger masses give a larger gravitational force. The further away a mass, the smaller the gravitational force, F When a mass is twice as far away, F quarters. It obeys an inverse square law. If d = distance away F is proportional to 1 / d 2 Orbit times for planets Planets closer to the Sun have shorter orbit times because: They do not travel as far in one orbit. They travel faster because there is a bigger gravitational pull on them. Artificial satellites Artificial satellites in low orbits around Earth have short orbit times. Gravity makes a satellite accelerate towards Earth but because it moves at a tangent and Earth is curved it maintains a near-circular orbit. 4

5 Question: On this image of the Earth: (a) Label the orbit of the artificial satellite (b) Mark the position of the satellite (c) Label gravitational attraction (centripetal force) (d) Label tangential motion Comets A comet has a very elongated orbit so its speed varies considerably as the gravitational force depends on its distance from the Sun. When it is close to the Sun, a comet travels very fast. When it is far away from the Sun, a comet travels very slowly. Question: Use the data to calculate the orbital speeds of Mercury and Earth. Planet Distance from the Sun (million km) Time to orbit Sun (years) Mercury Earth

6 Some uses of artificial satellites Communications: Satellite Earth Stations are used to relay telephone messages and computer data, and to broadcast television signals (satellite television). We can telephone friends and family around the world. If you are telephoning a friend in America, the dish aerial transmits a signal to a satellite. The satellite then amplifies the signal and re-transmits it down to another dish aerial in America. Weather forcasting: Images received from satellites orbiting Earth have made weather forecasts more reliable in recent years. Spying: Military satellites are used. Scientific research: Satellites orbiting Earth can take clearer pictures of objects in Space as they are above Earth s atmosphere. Global Positioning Systems (GPS): Used by ships, aircraft and cars to locate their position very accurately. Currently 24 GPS satellites each transmit radio signals that can be detected by the receiver. Many cars are now fitted with GPS. Question: Suggest why satellites have made weather forcasting more reliable. Question: Why are cars fitted with GPS? Low polar orbit satellites Low polar orbit satellites orbit Earth over the poles at a height of 100km to 200km. They have a typical orbit time of about 90 minutes. As Earth rotates on its axis they pass over a different area on each orbit. 6

7 Uses of low polar satellites Weather forecasting. Satellites in low polar orbit are used for short-range forecasts. They produce visible and infrared pictures. Infrared pictures show hot and cold areas in different colours so are good for forecasting temperatures. Imaging the Earth s surface. Low polar orbit satellites give a detailed picture of Earth s surface. Question: Would the satellite in the previous image be capable of acting as a shortrange weather forecasting satellite? Explain. Geostationary orbit satellites Geostationary orbit satellites stay over the same point on the Earth all the time. Uses of geostationary satellites Communications. Geostationary satellites allow events to be heard and seen in real time, all over Earth. Weather forecasting. Geostationary meteorological satellites are used for longer-term weather predictions. Meteosat a geostationary meteorological satellite Question: Give two advantages of using infrared pictures for weather forecasting. Question: Explain the advantages of the different types of satellite orbit for weather forecasting. Question: Explain why a geostationary satellite must orbit above the equator. 7

8 More on low polar orbit satellites More on geostationary orbits 8

9 All geostationary satellites must be in the same orbit. This makes it rather crowded! The satellites cannot be too close together as their signals would overlap due to diffraction. Question: Take Earth s radius = r = 6400km. Calculate the speed of a polar satellite 150km above the Earth that has an orbit time of 90 minutes. Question: All geostationary satellites are km above Earth. How fast are they moving? Vectors and equations of motion Direction is important when describing motion. Ideally we should give both a direction e.g. due North and a magnitude e.g. 5m/s. Relative motion When you are moving in a car and another car passes you, both cars can be moving very quickly. However, the relative speed of the second car (difference between the two speeds) may be low. The cars in fast lanes on each carriageway are moving past each other in opposite directions. They pass each other very quickly, giving an impression of very high speed. Their relative speed is high. Question: What is the relative speed of two cars both moving at 100km/h in the same direction? Question: Two trains travelling in opposite directions at 160km/h pass each other. What is their relative speed? Vector and scalar quantities A vector quantity has magnitude (size) and direction. For example, a force of 5N acts vertically downwards (what is the magnitude and direction of this vector which we call force?). Velocity is speed in a named direction. For example, a car travels at 20 m/s due North. Velocity is a vector. 9

10 A vector is drawn on a diagram as a straight line with an arrow, or a + or - sign, to indicate direction. +5m/s 5m to the right -5m/s 5m/s to the left A scalar quantity has magnitude only, for example, a train travelling at 20 m/s. Speed is a scalar quantity; direction does not matter. Question: Complete the following table using the words that follow: Scalar Speed Energy Mass time Vector Possible words: Velocity, Acceleration, Weight, Force Adding vectors When vectors act in the same straight line, their sum is found by adding them algebraically. Question: Find the sum of the following force vectors: (a) 12 N due North and 7N due South (b) 23N South East and 15N North West Resultant of two vectors The resultant of two parallel vectors is found by adding them algebraically as we have previously shown. For example, the combined force vectors of two small tug boats can pull a much larger liner forward if pulling in the same direction. When two forces are not in the same straight line the resultant is found using the parallelogram of forces. If the forces are perpendicular, the parallelogram becomes a rectangle. 10

11 Example: The diagonal of the rectangle gives the resultant, R. This can be found by a scale drawing or by using Pythagoras theorem R = = = 25 R = 5N Question: Tom can row at 4m/s in still water. What is his resultant velocity if: (a) He rows upstream against a current of 1m/s? (b) He rows straight across the stream? Question: Find the resultant of two perpendicular forces of 5N and 12N. 11

12 Speed Speed tells us how fast an object is moving but not the direction in which it is moving. Speed = distance / time Speed changes during a journey. The speed at any point on a journey can be calculated, but it is usually more useful to calculate average speed Average speed = total distance / total time Example A plane travelled 5585km in 3.5hours. Calculate its average speed Average speed = 5585/3.5 = 1596 km/h Question: Give three reasons why the speed of a car may change during a journey. Question: A train covers 550km in 2 hours and 30 minutes. Calculate its average speed. Did you know? Concorde stretches about 20cm in-flight due to heating of her airframe. She is painted in a special paint to accommodate these changes. Travelling westwards, the 5-hour time difference meant Concorde effectively arrived before she left (it took 3.5 hours for the journey). She travelled faster than the Sun! Question: In England at 6AM, what would the time in the USA be? Question: Concorde sets off at 6AM to the USA. Add 3.5 hours on to the starting time and then subtract 5 hours to calculate the time that Concorde arrives in the USA? Now explain what it means when we say that Concorde is faster than the Sun. 12

13 Equations of motion When an object has a constant acceleration in a straight line, the equations of motion are used to find out more about how it moves. The equations use five special symbols: Change in velocity v - u Acceleration = = a = ; hence v = u + at (1) Time taken t Distance travelled u + v s (u + v)t Average speed = = = ; hence s = (2) Time taken 2 t 2 Example: QRIO ( Quest for Curiosity ) is a humanoid autonomous robot, standing 58cm high. It is the world s first two legged robot capable of running (i.e. moving while both legs are off the ground at the same time). Suppose it takes 5 seconds to reach its maximum speed of 0.23 m/s, starting from rest. How far does it travel in this time? Write down suvat and fill in what you know. Now s =? u = 0 (starts from rest) v = 0.23m/s a (not needed) t = 5 seconds (u + v)t ( ) x 5 s = = = 0.58m 2 2 Question: A sports car accelerates at 5m/s2 from rest for 8 seconds. (a) What is its velocity after 8 seconds? (b) How far does it travel in this time? Question: An aircraft flying at 100m/s accelerates at 3m/s2 for 25 seconds. How fast is it moving after? (a) 1 second (b) 10 seconds 13

14 (c) 20 seconds (d) 25 seconds What do you notice about your answer? More on equations of motion Using equation (1) to replace v in equation (2): [u + (u + at)]t 2 s = = ut + ½ at (3) 2 Using equation (1) to replace t in equation (2) 2 2 (u + v) (v u) v - u s = = 2 a 2a 2 2 hence: v = u + 2as (4) Using these four motion equations, if three of the suvat quantities are known then the other two can be found. Example: A sprinter reaches a speed of 20m/s from rest after running 20m Find her acceleration. s = 20m u = 0 v = 12m/s a =? t (not needed) Using 2 2 v = u + 2as 2 12 = 0 + (2 x a x 20) = 40a hence a = 3.6m/s 14

15 Falling under gravity Ignoring air resistance (or falling a short distance), all objects accelerate towards the Earth at 10m/s2 due to gravity. An object thrown up from the Earth decelerates at 10m/s2. Its acceleration, a = -10m/s2 and at its highest point its velocity, v = 0. Question: Brian hits a ball vertically upwards at 18m/s. How high does it go? Question: How long does it take a car to travel 125m while accelerating from rest at 5m/s2? Projectile motion A projectile is the name given to any object that moves in Earth s gravitational field, such as: Balls (footballs, tennis balls, netballs, cannon balls) Missiles Darts Long-jumpers All projectiles that are thrown horizontally or at an angle to the ground follow a curved path described as parabolic. The path of a projectile is called its trajectory. 15

16 Question: In the box below show 3 sketches showing the trajectory of a tennis bath: (a) Tennis ball thrown vertically upwards (b) Tennis ball thrown horizontally (c) Tennis ball thrown at 45 degrees to the horizontal Why does the tennis ball follow a parabolic path (think combination of two forces). Newton s projectile Newton suggested that a projectile fired from a very high peak (V) on Earth would never hit the ground if it were launched with enough initial speed. Instead, it would remain in orbit around Earth, prevented from flying away by the force of gravity and never getting closer to the surface due to Earth s curvature. This is the principle used to put satellites into orbit today. Newton did not have the technology to test his theory. Question: On the above diagram of the Earth, show the trajectory of a ball thrown from the very high peak (label V ), moving in orbit around the planet. Question: Jack threw a ball out of the window of his holiday cabin on a Swiss mountain in a horizontal plane. Gravity pulled down with a vertical acceleration = 10m/s2. How far did it fall at the end of the first second? How far did it fall at the end of the third second? 16

17 Calculations on projectiles v = u + at 2 s = ut + ½ at s = (u + v)t v = u + 2as These equations of motion can be applied to the motion of projectiles. Example: A darts player stands 3m from a darts board. The dart leaves her hand horizontally and takes 0.2 seconds to hit the board. Calculate: (a) the initial velocity of the dart. (b) the vertical height the dart falls in flight. Answer: (a) The initial velocity is in the horizontal direction. Horizontally there is no acceleration, so initial velocity = distance / time = 3.0 / 0.2 = 15m/s (2) What distance does it fall vertically by the time it hits the board? s =? u = 0, v = not needed a = 10m/s2 2 s = ut + ½ at = (0 x 0.2) + (1/2 x 10 x 0.2 x 0.2) = 0.2m Question: In archery why do you miss the bull-eye if you aim directly at it? Question: A bullet is fired horizontally at a speed of 200m/s at a target 100m away. (a) Calculate how far away the bullet has fallen when it hits the target. (b) How far would the bullet have fallen if it had been fired at half the speed? 17

18 Analysing projectile motion Imagine that a ball is thrown horizontally. After a while it falls to the ground, bounces, rises then falls, bounces again e.t.c. A bouncing ball can be shown as a stroboscope image. A light flashing at regular time intervals allows successive positions of the ball to be seen. If air resistance is ignored, a ball projected horizontally: Has constant velocity (notice as the ball is moving horizontally, in the same time intervals, c = d = e). Has steadily decreasing vertical velocity as it accelerates upwards (notice as the ball is moving vertically, in the same time intervals, a > b. Also the ball has increasing vertical velocity as it is accelerating towards the ground (notice that f < g. The sequence of images revealed by a strobe light shows that a ball s trajectory is a parabola. The ball moves fastest near the ground and slowest at the top of the arc. The ball s horizontal speed is approximately constant whilst the vertical speed is changing. The horizontal distance a projectile travels is called its range. 18

19 Question: Consider this stroboscope photograph of two falling balls. Label and annotate it showing both vertical and horizontal displacements. Explain what the stroboscope is showing. Question: The time lapse between each photograph of a ball was 0.1 seconds. (a) Measure the horizontal distance between 2 successive yellow balls in centimetres (b) Convert this into metres Now calculate the average horizontal velocity = distance / time = Question: Draw a curve on the stroboscope trace to show a ball thrown at half the horizontal speed as the yellow one. Forces on projectiles If air resistance is ignored, once a projectile has been released the only force acting on it is gravity. 19

20 Gravity always acts vertically downwards so, since F = ma, the projectile has a downwards acceleration. This only affects the vertical velocity, accelerating the projectile at 10m/s2 as it moves down and decelerating it at 10m/s2 as it moves up. There is no force in a horizontal direction so horizontal velocity is constant. Question: Why does a projectile have a downward acceleration? Question: Why does a bouncing ball rise to a lower height on each successive bounce? Question: How does the angle at which a tennis ball is hit affect its range? Question: Suggest the angle that gives the maximum range. Resultant velocity Velocity is a vector. It has both magnitude and direction. The resultant velocity of a projectile at a point on its trajectory is the vector sum of the horizontal (VH) and vertical (VV) velocities at that point. By definition these are perpendicular vectors. The resultant velocity, v, is represented by the diagonal of the vector rectangle shown. The value of v is found using Pythagoras theorem: V = VH + VV and its direction with the horizontal by: tan θ = VV / VH 20

21 Example: Find the resultant velocity of a ball at a point in its trajectory where VH = 12m/s and VV = 9m/s V = VH + VV = = = 225 so V= 15m/s tan θ = 9 / 12 = 0.75; θ = 41 degrees The resultant velocity at this point is 15m/s at 41 degrees to the horizontal. The trajectory of a long-jumper is a parabola. Question: In order for the long-jumper to jump the longest horizontal distance what should θ be? Question: A new javelin that had its centre of gravity moved forward was introduced in Suggest why this led to shorter distances being achieved. Question: Sam kicked a football horizontally off the edge of a wall 0.8m high. (a) How long did the football take to reach the ground? (b) The ball travelled a horizontal distance of 6m before hitting the ground. At what speed did it leave the wall? Momentum Momentum makes it easier to understand all sorts of collisions, from snooker balls to cars, as well as explosions such as fireworks. 21

22 Pairs of forces Forces always occur in pairs. Imagine two people, A and B, both on skates. If A pushes B with a force of 50N (the action force), then B will push back with a reaction force of 50N. They will therefore move away from each other. In general, the action force of an object A on an object B = reaction force of B on A Hence every action has an equal and opposite reaction. Question: What happens if you blow up a balloon and then release it? Name the action and reaction forces. Question: The forward force of the gun on the bullet is the action. What is the reaction? Question: Two cars collide head on: What are the opposite reactions in this collision? Complete: The force on the red car due to the green car is. Action and reaction We have weight because we are attracted to Earth due to gravity. The Earth is also attracted to our bodies; this is the reaction force. Action, force on boy due to gravitational attraction of Earth. Reaction, force on Earth due to gravitational attraction of our body. These pairs of forces: Are equal in magnitude (size) Are opposite in direction Act on different objects Are the same types of force. 22

23 The Moon orbits Earth due to mutual gravitational attraction. Question: Draw a man standing on the Earth. Show with annotated force arrows the 6 principles mentioned. Momentum The momentum of an object increases if there is an increase in either or both: The mass The velocity Momentum = mass (m) x velocity (v) Momentum is a vector quantity. It has direction. It is measured in kilogram metre per second (kgm/s). Example Find the momentum of a car of mass 1000kg travelling due North at 20m/s. Momentum = 1000 x 20 = kgm/s due North. Question: Santosh kicks a football. What is the reaction force to the push of his boot on the football in an easterly direction? Question: If you jump off a stool you move towards the Earth due to gravitational attraction. Why does Earth not move up towards you? Question: Calculate the momentum of a sprinter of mass 50kg running due west at a speed of 8 m/s. 23

24 More on pairs of forces There are two pairs of forces acting on the kitten Blue pair: one force is due to the Earth pulling on the kitten (label this a ). The other force is due to the kitten pulling on the Earth (label this b ). Red pair: one force is the downward push force of the kitten on the Earth (label this c ). The other force is due to the Earth pushing up on the kitten (label this d ). These four forces are all the same size. Question: If the kitten jumps in the air which are the only pairs of forces now acting? Forces in collision If in a collision the velocity of an object of mass m changes from u to v in a time t, the force on the object can be found using: m(v-u) Force (f) = ma = = t mv-mu t Hence force = change in momentum time When two objects collide they push each other with an equal and opposite force on each other, independent of their relative masses. 24

25 Example: A car of mass 1200kg was travelling at 20m/s when it hit a wall with a force of 8000N. How long did it take to stop? F = -8000N, since the force of the wall on the car acts in the opposite direction to the car s motion. m(v-u) mv-mu Force (f) = ma = = or Ft = mv-mu t t x t = (1200 x 0) (1200 x 20) -8000t = therefore t = 3 seconds Question: Ali and Jake are skating. Ali pushes Jake with a force of 400N for 0.5 seconds. If Jake has a mass of 50kg, calculate his increase in velocity. Question: Beth opens a bottle of champagne. The cork, of mass 5g, flies out in 0.1 seconds with a velocity of 8m/s. What force acts on: (a) the cork? (b) the bottle? Collisions A collision occurs every time a ball is struck when playing sport (pool, hockey). Meteorites Meteorites are balls of dust and rock. They can sometimes hit the Earth with a great force. It is believed that a huge meteorite hitting the Earth led to the extinction of the dinosaurs. NASA crashed its Deep Impact spacecraft into comet 9P/Tempel 1 on 4 July 2005 to learn more about the make-up of comets. Millions of kilograms of fine dust particles and water sprayed into Space. 25

26 Question: Give three examples of collisions in sport. Question: Mark is building a wooden fence. Give two examples of collisions he makes use of. Did you know? Adults and children over 1.5m tall must wear seatbelts in the rear of a car. If there is a small child, they must be in a suitable child seat. More about collisions Hence force = change in momentum time Short impact time large force. Large impact time small force Car safety Seatbelts and air bags in cars increase impact time, decreasing the force and reducing injury to people in the car. Avoiding sports injuries Sporting injuries when landing are reduced by increasing the time taken to stop. A gymnast can do this when landing by bending her knees. Question: Why does this prevent injury? Question: Explain how crumple zones work. Mention momentum in your answer. 26

27 Question: Why do pole-vaulters land on foam mattresses? Conservation of momentum In any collision, if no external forces act, the total momentum before the collision is equal to the total momentum after the collision. Explosions An explosion is the opposite of a collision. In an explosion, objects move apart instead of colliding. Momentum is still conserved. Firing a gun Before firing a shell, the total momentum is zero. After firing the shell, the total momentum is again zero so the momentum of the shell forwards equals the momentum of the gun backwards and the gun recoils. Rocket propulsion The rocket moves up while the hot gases move down. The momentum of the rocket upwards is equal to the momentum of the hot gases downwards. 27

28 Question: A car of mass 1200 kg travelling at 30 m/s runs into the back of a stationary lorry. Find the mass of the lorry if the car and the lorry move at 4 m/s after impact. Question: Imagine a man standing in a rowing boat. He then puts out one foot to stride forward to reach ashore. The boat moves away from the shore and he falls into the water. Explain this phenomenon. Satellite communication Radio waves have wavelengths varying from a fraction of a mm up to 10km. The highest frequency (smallest wavelength) radio waves are called microwaves. The higher the frequency of a radio wave, the more penetrating it is. This means that: High frequency radio waves pass through the Earth s atmosphere. Low frequency radio waves are stopped by the Earth s atmosphere. Some radio waves are reflected by part of the Earth s atmosphere. 28

29 Geostationary satellites stay above the same point on Earth. They are about km above Earth so can only be reached by high frequency waves such as microwaves. Low-orbit satellites can be reached by low frequency (longer wavelength) radio waves (show this on the above diagram). Did you know? Radio waves are given off by stars, sparks and lightning. This is why you hear interference on your radio in a thunderstorm! Large parabolic antennae used for sending and receiving radio signals Question: What is the orbit time of a geostationary satellite? Question: Suggest one use for a low-orbit satellite. 29

30 Using microwaves Question: Complete the following text using the words that follow: High frequency can travel km into Space to reach an artificial satellite placed in geostationary orbit above the equator. This allows the satellite to rotate with Earth, remaining stationary above the same point on Earth s surface. Microwave are: Sent into Space from a transmitter. Received, and re-transmitted back to Earth by a geostationary satellite. Picked up by a parabolic. Possible words: amplified, receiver, signals, transmitter, orbit, microwaves Question: What is the difference between radiowaves, which are skywaves, and Space waves in terms of their frequency? 30

31 Choosing the best frequency for satellite communication The reflects radio waves with frequency below 30MHz (30 million hertz), so higher frequency microwaves are needed for satellite communication. However, the cannot be too high. Radiowaves (microwaves) with frequencies above 30GHz (30 000) million hertz) are easily absorbed and scattered by rain, dust and other atmospheric. This reduces the of the signal. Possible words: effects, strength, frequency, ionosphere Question: What is the frequency range in GHz used for satellite communication (it corresponds to a wavelength of between 10cm and 1cm)? The dishes on this mast receive, amplify and relay mobile phone, microwave and radio signals Question: Use the equation v = f λ to find the velocity of microwaves having a frequency of: (a) 3 GHz (b) 30 GHz Question: Why are microwave signals amplified by a satellite before re-transmission back to Earth? Question: Why can a radio wave of frequency 25 MHz not be used for satellite communication? 31

32 The ionosphere The ionosphere is a region of the atmosphere between 100km and 500km above Earth, where molecules have been ionised by radiation from the Sun. Radio waves undergo a series of refractions as they enter the different layers and speed up, until total internal reflection occurs. Waves reflected off the ionosphere can be reflected from Earth s surface, especially from water, allowing the waves to travel to the other side of Earth. Sending microwaves Microwaves have a very small wavelength, only a few centimetres, so they do not spread out very much, even when travelling large distances. There is only one possible geostationary orbit so it is very crowded. The satellites cannot be too close together or they would receive unwanted signals. As microwaves are sent as a thin beam, this is not a major problem. Question: Why do satellites transmitting signals from geostationary satellites have a greater problem than from polar orbit satellites? Question: Suggest why water reflects microwaves better than land. Diffraction When a wave hits the hard edge of a material and is deviated from its original path, we say that it has been diffracted. Diffraction causes waves to spread out when they pass through a gap or around a large object. Longer wavelengths diffract more than shorter wavelengths 32

33 Question: In the above diagram, the hill is in the way of the radio transmitter dish and the radio receiver dish. How does the second dish receive the radio waves? Receiving radio and television (TV) programmes An aerial is required to detect waves in the air for radio and terrestrial TV signals. Satellite TV signals require a dish to pick up weak microwave signals from a geostationary satellite. TV aerial TV dish Question: Why are TV signals picked up by a satellite dish on a house very weak? 33

34 Question: When you speak, sound is heard all around, not just in front of your mouth. What happens to sound waves when they leave your mouth? Diffraction of waves Diagram 1: Here the gap is large and there is hardly any diffraction Diagram 2: Here the gap is small and waves diffract The smaller the size of the gap, the greater the diffraction. Question: As the frequency of radio waves increase, their wavelength decreases. Complete the table below with the frequencies given: Wavelength 1mm 10cm 1m 10km Frequency Possible frequencies: 30kHz, 300MHz, 300GHz, and 3GHz Radio waves that are produced by one transmitter on Earth and transmitted to another directly are below (and above 30kHz). They can be reflected down from the ionosphere and are used for radio broadcasts. The lower frequency 30kHz radio waves would be wave radio waves, whilst 30MHz radio waves (VHF) would produce wavelength radio waves. Long and medium wavelength radio waves diffract around hills and as well as following the curvature of the Earth (because of ionosphere). 34

35 Radio waves used for TV signals above 30MHz emitted by transmitters have shorter wave lengths that do not very much so can only be received along a line of sight. We have already said that radio waves between 30MHz (3GHz) and 30GHz are used to transmit pass the to satellites. These radio waves are called and can then be used for TV, car and mobile phones, satellite TV. Possible words: microwaves, ionosphere, diffract, buildings, 30MHz, shorter, longer Question: Why does the aerial receiver achieve good radio reception, but not good TV reception? Question: Explain why radio waves are easily diffracted. Question: City Radio broadcasts on a wavelength of 194m and Radio X (long wave) uses a wavelength of 1500m. Which station would be likely to have better reception to a house at the bottom of a hill? Factors affecting diffraction The amount of diffraction through a gap depends on the: Size of the gap Wavelength Maximum diffraction occurs when the wavelength is equal to the size of the gap. Radio waves have long wavelengths compared to the gaps between hills so diffract easily. This allows them to travel over the horizon. 35

36 Amplitude modulation (AM) Sound waves are a longer wavelength and shorter frequency (not as much energy) as radio waves. They cannot therefore be transmitted a long distance. However, it is possible to change a sound wave into an electrical signal (microphone) of the same frequency. This signal (called the modulating wave) can be mixed with a radio frequency carrier wave producing a modulated result. This has single, separate cycles, which combined together carry the information of the original signal frequency. The amplitude of the carrier wave is continually being modulated to carry this information. Question: Sketch diagrams in the space below to show water waves of wavelength 3cm passing through gaps of: (a) 8cm and (b) 4cm 36

37 Question: Emma s radio has a button marked AM. Explain what AM means. Nature of waves Interference of waves occurs when two sets of waves overlap. Interference of water waves A ripple tank, or shallow tray of water, cab be used to create two overlapping sets of water waves. Two small dippers are attached to a set of wood that moves up and down. Each dipper produces a circular wave pattern and these circular wave patterns overlap to create an interference pattern. The interference patterns are shown below: The pattern shows areas where the waves: Add together giving a big disturbance: this is called reinforcement or constructive interference. Subtract from each other giving calm water: this is called cancellation or destructive interference. 37

38 Sound and light Two overlapping sets of sound or light waves also result in areas of reinforcement and cancellation. Question: Complete the following table using the words that follow: Reinforcement Cancellation Sound Light Possible words: brighter area, darker area, louder area, quieter area Question: Suggest why it is easier to study interference in water waves, rather than in sound or light. Question: Give two differences between sound waves and light waves. Interference of sound waves Two loudspeakers connected to the same oscillator produce the same frequency of sound. If you walk in front of the loudspeakers, about 1m away, you hear alternate loud and quiet sounds Reason: Where sound waves from the two loudspeakers overlap in a certain why, the sound is amplified (gets louder). Where sound waves from the two loudspeakers overlap in another way, the two sounds are cancelled out. 38

39 Interference of microwaves Microwaves with a wavelength of about 3cm pass through two 3cm gaps formed by three vertical metal plates. The receiver, connected to a meter, is moved along a line parallel to the plates. The meter reading increases and decreases regularly. Whenever two sets of waves overlap: Output is a maximum when the waves meet in step (two crests arrive together) and reinforce. Output is a minimum when the waves meet out of step (crest and trough arrive together) and cancel. Question: When demonstrating interference of microwaves, why must the gaps between the metal plates be about 3cm? Question: What would be the effect, if any, of making the gaps smaller? Question: Why is it difficult to demonstrate interference with light? 39

40 Explaining interference patterns To produce a regular interference pattern, the two waves must be identical in every way; for example, have exactly the same frequency and amplitude. Constructive interference occurs when the path difference from the two sources is a whole number of wavelengths. Destructive interference occurs when the path difference from the two sources is an odd number of half wavelengths. This can be demonstrated using a monochromatic light passing through double slits. The bands of constructive and destructive interference light patterns are produced on the screen. Two waves (one emerging from each of the slits) will constructively interfere (producing a bright band) if the path difference = nλ, where n = 0, 1, 2 e.t.c Two waves (one emerging from each of the slits) will destructively interfere (producing a dark band) if the path difference = (n + ½ )λ, where n = 0, 1, 2 e.t.c Question: When demonstrating interference of sound, the frequency of the sound was increased. What would you notice? Question: Suggest why a regular interference pattern is only produced when two sets of waves are from the same source. 40

41 Light travels in straight lines We cannot normally see light travelling through air. However, laser light (a concentrated source of light waves) can be seen and it follows a straight path. When you shop, bar codes are read by a laser. bar code scanner producing laser light here is a bar code Laser pointers are often used when giving a presentation or teaching These examples show that light travels in straight lines. Just occasionally, we see something that appears to contradict this, though there is always a reason for light to change direction, or bend. Question: How does the presence of shadows indicate that light travels in straight lines? Question: Name two other examples of equipment that uses lasers. Did you know? If there is a very tiny hole in a window blind, the light spreads out as it passes through the hole and seems to bend. Wave nature of light In order to produce overlapping light waves to get an interference pattern between light waves from two slits, the slits must be very narrow (about 0.1mm in width) so that the light diffracts. The wavelength of light is between 400 and 600nm ( m and m) 41

42 This was first done in It is much easier to do using laser light. Interference gives strong evidence for the wave nature of light. A diffraction pattern formed by laser light passing through cloth. The diffracted light then overlaps to produce interference. The light can reinforce or cancel producing red and black areas respectively. Thinking of light as a particle cannot account for the cancelling effect due to destructive interference shown in these diagrams and can only be explained by a wave model. Did you know? Electrons have wave properties. They can be diffracted, but their wavelength is much smaller than that of light. Polarisation Electromagnetic waves are transverse waves. Oscillations occur at right angles to the wave direction. In ordinary light these oscillations occur in every direction perpendicular to the wave direction. Polarised light has oscillations in only one plane. 42

43 Question: Why is diffraction essential to produce an interference pattern with two sources of electromagnetic radiation? Question: Can sound waves be plane polarised? Explain your answer. Diffraction pattern for light Two overlapping sets of light waves from the same source interfere to produce a series of bright and dark bands, or fringes. Bright bands are constructive interference. Dark bands are destructive interference. Light diffracting from a single slit also creates a diffraction pattern due to interference between waves from different parts of the slit, but the centre band is much wider and brighter. Polaroid sunglasses Polaroid stops all oscillations except those in one plane. This cuts down the amount of light getting through, making it ideal for sunglasses. Question: Blue light has a shorter wavelength than red light. Suggest how a two-slit interference pattern would change if the blue light was used instead of red. Question: Raj is wearing Polaroid sunglasses. What does he see when he slowly rotates a piece of Polaroid in front of his eyes? 43

44 Refraction of waves A mirage may be seen when the layer of air closest to the ground is warmer than the air above it e.g. above a sunlit road or sandy area such as a desert. The temperature difference causes a gradual change in air density and makes the light bend or refract, so that it looks like there is water nearby. Refraction Refraction occurs when light passes from one medium (or material) to another It often involves a change in the direction of the wave. When a ray of light passes from air into glass the angle of incidence, i, is greater than the angle of refraction, r. Dispersion Sunlight (white light) is made up of a mixture of many different colours. The sunlight is refracted when it passes through raindrops and is split up into its different colours (rainbow). This is called dispersion. You can produce a rainbow or spectrum of colours by passing white light through a triangular prism. Blue light is deviated or bent more than red light. Question: Light passes from air to glass. How does the angle of refraction change as the angle of incidence increases? 44

45 Question: Why does light refract when it passes through raindrops? Why does refraction occur? When light and other electromagnetic waves enter a different medium, the speed of the waves change. When light waves enter an optically denser medium (for example air to glass) they slow down and the waves refract towards the normal; r1 is less than i1. When light waves enter an optically less dense medium (for example, glass to air) they speed up and the waves refract away from the normal; r2 is more than i2. The refractive index indicates the amount of bending. The greater the change in wave speed, the greater the refractive index and the greater the amount of bending. Why does dispersion occur? Dispersion occurs when white light passes through a medium, such as glass or water, because each spectral colour slows down by a different amount on entering the medium and speeds up by a different amount on leaving. This means that the different colours are refracted by a different amount so they separate and spread out. Question: Glass has a greater refractive index than water. Is light bent more or less in water than in glass. Explain your answer. 45

46 Question: Complete each of the diagrams below: Question: Blue light is bent more than red light when it enters glass. Which colour light is slowed down least by the glass? Refractive index Light waves are refracted when they enter an optically denser medium because they are slowed down; their wavelength is smaller. 46

47 Equation 1: refractive index, n = speed of light in vacuum speed of light in medium Example: How fast does light travel in glass of refractive index 1.5 if its speed in a vacuum is m/s? If s = speed of light in glass, 1.5 = / s s = / 1.5 = m/s Equation 2: Snell s Law n = sin i sin r where i = angle of incidence and r = angle of refraction Example: Calculate the refractive index of water if a ray of light entering water at an angle of incidence of 30 degrees has an angle of refraction of 22 degrees. sin i sin 30 n = = = 1.33 sin r sin 22 Explaining dispersion Different spectral colours have different speeds in a medium such as glass and have different refractive indices. This means that each colour has a different angle of refraction on entering or leaving the medium forming a spectrum. Question: Light travels at m/s in water and m/s in a vacuum. Calculate: (a) The refractive index of water. (b) The angle of incidence that would give an angle of refraction of 40 degrees. 47

48 Refraction of light at a boundary When light passes from glass or water, to air, most of the light is refracted but there is often a weak reflected ray. If the angle of incidence is big it is possible for all the light to be reflected and none refracted. The surface of the glass acts like a perfect mirror. This is called total internal reflection: total because all the light is reflected. internal because it only happens inside a denser medium. Optical fibres use total internal reflection A diamond is cut so that the faces produce total internal reflection. This makes it sparkle. 48

49 Total internal reflection occurs when: light passes from glass or water or clear plastic, to air. The angle of incidence is large. Question: Draw diagrams to show the path of a ray of light when it passes from water to air in the space provided if the angle of incidence is: (a) small (b) large. Question: Suggest why light has been totally internally reflected is as bright as the original light source. The critical angle When a ray of light emerges from a semi-circular glass block, we can demonstrate the second law of refraction as before i.e. it refracts away from the Normal as it emergesinto a less dense medium e.g. air.. Now if the angle between the ray of light in the block and the Normal increases, a stage is reached when (1) some emerging light passes along the flat face of the block (2) most of the light is internally reflected back into the block. 49

50 The angle shown on the diagram when this occurs is called the critical angle ( c ). When a ray of light inside a dense medium (e.g. glass or plastic) strikes the outer surface at an angle to the 23 which is greater than the 24 angle, then total internal reflection of that light occurs. Question: Draw on diagram 2 another ray of light striking the outer surface and internally reflecting back into the glass prism. Question: Measure the critical angle shown on this diagram. Complete this sentence; Rays of light inside the block must strike the outer surface at an angle of, if they are to be internally reflected back into the block. Uses of the critical angle Because light internally reflects inside transparent plastic, we can make light rays internally reflect inside convoluted tubes such as optical fibres. Optical fibres carry light rays that strike the outer surface at an angle to the Normal, which is greater than the critical angle. Endoscopes are optical fibres. These carry light rays all the length of the small intestine. They then illuminate internal parts of the body and so enable minute television cameras to detect cancers. Question: Continue the path of this light ray as it internally reflects along this endoscope Light can bend round corners along an optical fibre. Total internal reflection happens because the fibre is very narrow and the angle of incidence is always large. Optical fibres are used: To carry telephone calls as pulses of laser light. In endoscopes, used by doctors to look inside the body. 50

51 Question: Why is a ray of light not refracted on entering a semicircular glass block? Question: Explain why a ray of light is turned through 90 degrees inside an isosceles right-angled prism. Total internal reflection Total internal reflection only happens when: A ray of light travels from one medium to another with a lower refractive index (for example, glass to water) so that the angle of refraction reaches 90 degrees before the angle of incidence. The angle of incidence is greater than the critical angle. When light travels from medium 1 into medium 2, which has a lower optical density: Sin c speed in medium 1 speed in vacuum speed in 2 n2 = = = Sin 90 degrees speed in medium 2 speed in vacuum speed in 1 n1 Sin 90 degrees = 1, so: sin c = n2 n1 51

52 Example: Calculate the critical angle for light passing from glass of refractive index 1.5 to water of refractive index 1.3 If moving from glass to water, n water 1.3 Sin 90 degrees = 1, so: sin c = = = n glass 1.5 Hence c = 60 degrees If medium 2 is a vacuum or air, n2 = 1 so sin c = 1 n1 The higher the refractive index of a medium the lower its critical angle. Question: Define what is meant by the refractive index of glass. Question: The refractive index of diamond is 2.4. Calculate the critical angle for diamond. Question: Find the refractive index of Perspex if its critical angle is 46 degrees. Question: Calculate the critical angle for light passing from diamond to Perspex. Optics Today s cameras use a complex arrangement of lenses to zoom in and out. Cinema projectors are also much more sophisticated. Cinema has survived the arrival of television, but will it survive the current rapid developments of new technology? Convex lenses A convex lens, or converging lens, is narrow at each end and bulges in the middle. When light strikes a convex lens, it is refracted by the lens and is brought to a focus. 52

53 The focal length is measured from the centre of the lens to the focus (focal point). Thicker lenses refract light more and are therefore described as more powerful. Powerful lenses have short focal lengths. Question: The above diagrams show two convex lenses; one is thin and the other is thicker. On the thicker lens, draw in the principal axis, focal length and principal focus (both sides). Measure the length of the principal focus of both lenses. Explain your results. Projectors and cameras A projector or camera uses a convex lens to bring light to a focus on a screen or piece of film. This is called a real image; light actually reaches the screen or film. Question: Name two things that contain a lens. Using a convex lens to bend beams of light 53

54 A parallel beam of light from a distant object can be converged to a focus in the focal plane. If the beam of light is parallel to the principal axis it converges to the focal point, F, on the principal axis as shown below: A diverging beam of light from a near object can be converged using a strong convex lens. The light meets at a point beyond the focal plane. Question: If rays of light in the diagram above diverged from a point closer to the convex lens, where would they be brought to a focus? Question: How does the image change when the screen is moved further away from a projector? Cameras A simple camera is a box with a convex lens at one end and a film at the other. Light from an object passes through the lens and is brought to a focus on the film. A real image, much smaller than the object, is formed on the film. Light actually reaches the film, and makes a chemical record of the pattern of light. 54