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Advancing Physics AS Chapter 1 - Imaging Student notes Specification 5.1.1.1 Imaging only In the context of the digital revolution in communication, this section introduces elementary ideas about image formation and digital imaging, and about the storage of digital information. The material can be taught using up-to-date contexts such as medical scanning. There are opportunities to address human and social concerns. Candidates should demonstrate evidence of: (a) knowledge and understanding of phenomena, concepts and relationships by describing: the formation of a real image by a thin converging lens, understood as the lens changing the curvature of the incident wave-front; the storage of images in a computer as an array of numbers which may be manipulated to alter the image; (b) comprehension of the language and representations of physics by making appropriate use of the terms: pixel, bit, byte, focal length and power, magnification, resolution and by sketching and interpreting: diagrams of the passage of light through a converging lens (c) quantitative and mathematical skills, knowledge and understanding by making calculations and estimates involving: the amount of information in an image = no. of pixels bits per pixel power of a converging lens, as change of curvature of wavefronts produced by the lens; use of 1 1 1 (Cartesian convention); linear magnification; v u f restricted to thin converging lenses and real images v f ; amounts and rates of transmission of information. (d) initiative and independence in learning by giving and explaining their own example of: an application of image formation; Ch 1 Imaging Learning outcomes Section 1.1 Seeing invisible things – Ultrasound, electromagnetic spectrum, ‘seeing’ atoms Images can be formed with many kinds of signals, including ultrasound and all regions of the electromagnetic spectrum Images can be recorded electronically by microsensors; an example is the charge-coupled device (ccd); such images are composed of discrete picture elements – pixels Images on the atomic scale can be recorded by scanning methods; an example is the scanning tunnelling microscope (STM) The resolution of an image is the smallest distance over which a change can be seen Section 1.2 Information in images – Image processing, amount of information, log scales Images can be stored as an array of pixels, each defined by a number; the amount of information stored = number of pixels x bits per pixel. Images can be smoothed by suitable averaging; images can be sharpened by identifying edges; images can be enhanced by increasing contrast or by false colouring. Quantities that cover a large range of values can usefully be displayed on a logarithmic ('times') scale. Prefixes for scientific units are chosen at multiples of 1000. 1 bit of information contains 2 choices (0 or 1); 1 byte of information contains 8 choices (256 = 28 alternatives); information I provides N = 2I alternatives. Section 1.3 With your own eyes – Eye and vision, real image from a thin lens The eye is like an intelligent video camera, sending out a stream of processed signals. It detects edges and movement. A converging lens adds a constant curvature to light falling on it. The curvature added is the power of the lens. Power of lens = 1 / f = 1 / v – 1 / u (Cartesian sign convention) Magnification = height of image / height of object Light takes the same time to travel on all paths from a point on the source to the image via the lens (or mirror). 2 Section 1.1: Seeing invisible things Ultrasound imaging etc Images are introduced with a discussion of an ultrasound scan of a 20 week old foetus. The image is shown on p1 of Student Book, and is the first image in Activity 10S Software based 'Looking at images' Further information about this image can be found on File 10I Image 'The variety of uses of scientific images' Discussion of Activity 10S will focus on the following points to enable students to continue confidently with the exercise themselves using other images: 1. How was the image made? [Show image of foetus and the equipment used to produce it. Display Material 10S Computer screen 'Hospital ultrasound scanning equipment' Use magnification tool to show pixels. Can undo with ‘Edit Undo’. Discuss the image as an array of 256 x 256 pixels each having one of 256 shades of grey (p 2). Discuss ‘Making an image with ultrasound’ pp 3-4 and diagram p 3. The delay times of the reflections tell the scanner where the denser tissue of the baby is. This can be illustrated with: Activity 30D Demonstration 'Distance measurement with ultrasound' together with a demonstration of an ultrasonic tape measure. The strengths of the reflections tell the scanner how dense the various tissues are. Check calculations on diagram panel on p 3. Use the diagram panel on p 4 to revise v = f and f = 1/T in the context of the ultrasound scanner. What you should know about waves The amplitude of a wave (symbol A) is the maximum displacement of the medium. This is measured from the undisturbed position. This is measured in metres (m) etc. The wavelength (symbol ) of a transverse wave is the distance between two neighbouring crests or troughs. The wavelength of a longitudinal wave is the distance between two neighbouring compressions or expansions (rarefactions). This is measured in metres (m) etc. The wave speed (symbol v) is the speed of the wave profile such as a crest or compression depending on the type of wave. This is measured in metres per second (m/s) etc. The time for one complete cycle is known as the period (symbol T). This is measured in seconds (s). If the period is 0.5 s, one complete wave is made every 0.5 s, so two complete waves are made every 1.0 s. The number of waves made every second is called the frequency (symbol f) of the wave. Frequency used to be measured in cycles per second but is now measured in hertz (Hz). f = 1/T and T = 1/f wave speed (m/s) = frequency (Hz) x wavelength (m) or v = f 3 2. What is the scale of the image? [actual size/size on image] 3. What does the image tell us, and how? 4. In what way is what you see 'invisible'? 5. What wavelength of radiation, if any, is involved? [Why must the frequency of the ultrasound pulses be so high? See p 3.] 6. What is the resolution of the image (the smallest size of thing that can be distinguished)? This is the size of one pixel in a digital image. The actual size of the object being imaged must be known for this. See p 2. Students work through other examples from Activity 10S Software based 'Looking at images' in ICT suite. Students should address each of the points 1-6 above. Further information about each image can be found on: File 10I Image 'The variety of uses of scientific images' File 20I Image 'Astronomical images: Problems of noise and resolution' File 30I Image 'X-ray images in medical physics' File 40I Image 'Ultrasound images in medical physics' File 50I Image 'Magnetic resonance imaging File 60I Image 'Gamma rays detecting abnormalities' File 70I Image 'Satellite images of towns in Europe' The ideas behind the ultrasound scanning can be revisited using: Activity 40D Demonstration 'How fast sound moves in a solid' Demonstrate digital image capture at work using a Web Cam intended for video conferencing. The image is displayed directly on the computer screen. Activity 20D Demonstration 'Electronic image capture' Images from the Universe Discuss the operation of the charge-coupled device (ccd), an example of a microsensor, for converting light into digitally stored images. A digital image with 1 million pixels would have been made with a ccd with a 1000 1000 array of elements. ’Images from the Universe’ are taken with many wavelengths form the electromagnetic spectrum not just with visible light. The electromagnetic spectrum (see p 7 for a diagrammatic representation) Type of Approximate Approximate Sources of Detectors Notes (uses, radiation wavelength in frequency in radiation dangers etc.) metres hertz Radio 104 to 10-3 104 to 1011 Accelerating Aerial, tuning Broadcasting charges circuit (television and radio), mobile telephones Microwaves 10-1 to 10-3 109 to 1011 Accelerating Horn and Microwave oven, (sub-set of charges dish radar radio (magnetron) waves) 4 Infra-red 10-4 to 10-6 1012 to 1014 Hot objects Phototransist Radiant heaters, or etc. night vision, burglar alarms, remote controls, thermography, i.r. lasers used with optical fibres and CD players Visible light (710-7) to 6 1014 Hot objects, Eyes, Vision (4 10-7) excited atoms photographic film Ultra-violet 10-7 to 10-9 1015 to 1017 Very hot Photographic Fluorescence, objects, film, sun lamps, killing fluorescent fluorescent germs, astronomy lights screen (converted to visible light) X-rays 10-9 1017 upwards Collision of Photographic Medical downwards fast electrons film, diagnosis, with target as ionisation analysis of matter in X-ray tubes effects Gamma 10-11 1019 upwards Radioactive Photographic Studying nuclear rays downwards atoms film, structure, cancer ionisation treatment, food effects sterilisation, measuring thickness ‘Spy in the sky’ (p6) suggests some uses for satellite imaging. Note the references to resolution and to the idea of false colour. ‘Seeing’ atoms Discuss ‘Seeing’ atoms’ and ‘Images for the mind’s eye’ pp 10-11. This includes brief detail of the scanning tunnelling microscope [See A-Z for further details]. Section 1.2 Information in images Image processing Start by considering the possibilities of some image processing software with a demonstration of the key elements of Activity 50S Software based 'Image processing: The surface of Mercury'. The following exercise helps to explain how to smooth sharp edges, remove noise and fond edges. References: Advancing Physics AS pp 16-17 Activities 50S, 60S, 70S and 80S Various operations: (a) Replacing each pixel by the mean of its value and those of its neighbours. (b) Replacing each pixel by the median of its value and those of its neighbours. When a series of numbers is place in ascending order, the number in the middle is the median. 5 (c) Subtracting the N, S, E and W neighbours from four times the value of each pixel. Exercises Calculate only the values for the squares inside the darkened box to avoid edge effects. 1 Smoothing edges by calculating mean values [operation (a)]. 2 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 becomes 0 0 0 1 1 1 Using the mean rounds off sharp corners. 3 (i) Removing noise by calculating mean values [operation (a)]. 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 becomes 1 1 1 1 1 1 (ii) Removing noise by calculating median values [operation (b)]. 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 becomes 1 0 1 1 1 1 1 1 1 1 1 1 Taking mean and median values both reduce noise. Which process is the most effective? 4 Finding edges by subtracting the values of the neighbours [operation (c)]. (i) An image with an edge. 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 becomes 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 6 (ii) An image with a uniform brightness gradient. 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 becomes 1 2 3 4 5 6 1 2 3 4 5 6 Areas of uniform brightness are removed, as are areas where there is a uniform brightness gradient. Regions where the gradient of the brightness changes abruptly are enhanced. Students should go on to try enhancing a variety of images. The essential points to establish are smoothing, noise reduction, contrast and edge enhancement. Activity 50S Software based 'Image processing: The surface of Mercury' (All students start with this) Students try at least one example of image enhancement: Activity 60S 'Image enhancing: Volcanoes on Io' or Activity 70S 'Medical uses of x-ray images' or Activity 80S 'Medical uses of ultrasound images The key points to stress are that images are made of pixels, that a pixel is defined by a number, and that modifying images means doing arithmetic on pixels. The most important general modification to emphasise is averaging which is a good way of removing random or rapid fluctuations in all sorts of experiments. [Students can get some striking and sometimes artistic effects with image processing software such as PhotoShop.] Amount of information and log scales Introduce powers of 10 with ‘Powers of Ten’ video (9 minutes). Decimal and binary number systems Decimal: 102 101 100 2 4 7 The number 247 (two hundred and forty seven) is made up as follows: (2100) + (410) + (71) Binary: 22 21 20 1 0 1 The number 101 in binary represents the number (14) + (02) + (11) = 5 in decimal. The two values used in the binary system are the digits 1 and 0. A binary digit is called a ‘bit’. Electronically the idea of bits may be represented by a lamp that is ‘ON’ or ‘OFF’ or by a voltage that is ‘HIGH’ or ‘LOW’. 7 Exercise (a) Convert the following 4-bit binary numbers into decimal numbers: 1111 1010 0010 0111 (b) Convert the following 8-bit binary numbers into decimal numbers: 00010000 11111111 10101010 01010101 (c) Write the following decimal numbers as 8-bit binary numbers: 25 100 255 180 The next section uses logarithmic thinking. We use logarithms every time we check the size of a computer file in bytes (I byte = 8 bits). It will be shown that the space needed to store a file is a logarithmic measure of the amount of information in it. A message which can only be 'yes' or 'no' (or 'with sugar' or 'without sugar') has only two alternatives. We need one bit (zero or one) to store it. One pixel of a grey scale image can have 256 different alternative values. But 256 bits are not needed to store it. Eight are enough, because there are 256 different numbers, which can be represented by eight binary digits, or bits. The decimal value of the binary number 11111111 is (127) + (126) + (125) + (124) + (123) + (122) + (121) + (120) which is (128 + 64 + 32 + 16 + 8 + 4 + 2 + 1) which is 255. From 0 to 255 there are 256 numbers. That is, the number N of alternatives which can be represented by information I bits is just N = 2I. When I = 7, N = 27 = 128 and when I = 8, N = 28 = 256. Thus if you add one bit of information you double the number of alternatives. 8 Display Material 50O OHT 'Bits and bytes' Display Material 60O OHT ''Plus' and 'times' scales of information' Bits and bytes ‘Plus’ and ‘times’ scales of information One byte stores 256 alternatives Number of alternatives = 2 number of bits Decimal Number of 8 bits = 1 byte 4 bits 2 bits 1 bit value alternatives If 8 bits of information are used: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 number of alternatives = 28 = 256 0 0 0 0 0 0 1 0 2 21 =2 In general, if the amount of information is I bits: 0 0 0 0 0 0 1 1 3 0 0 0 0 0 1 0 0 4 22 =4 number of alternatives = 2I 0 0 0 0 0 1 0 1 5 0 0 0 0 0 1 1 0 6 If the number of bits increases by one, the number of alternatives doubles. Informaton is measured on a ‘plus’ scale; number of alternatives on a ‘times’ 0 0 0 0 0 1 1 1 7 scale: 0 0 0 0 1 0 0 0 8 23 =8 0 0 0 0 1 1 1 1 15 ‘PLUS’ SCALE ‘TIMES’ SCALE 0 0 0 1 0 0 0 0 16 24 =16 (LINEAR) (LOGARITHMIC) 0 0 0 1 1 1 1 1 31 Amount of information Number of alternatives 0 0 1 0 0 0 0 0 32 25 =32 increase by equal additions increase by equal multiples 1 1 1 1 1 1 amount = I number of alternatives = 2I 0 0 63 0 1 0 0 0 0 0 0 64 26 =64 amount = log2 N number of alternatives= N 0 1 1 1 1 1 1 1 127 1 0 0 0 0 0 0 0 128 27 =128 1 1 1 1 1 1 1 1 255 The OHT ‘Bits and Bytes’ shows that the number of alternative values which can be represented grows rapidly as the amount of memory used 1 0 0 0 0 0 0 0 0 256 28 =256 increases. The discussion leads to work on logarithmic scales, in the form of ladders of quantities where adding one rung of the ladder multiplies the quantity by some amount. The link between adding one kind of quantity and multiplying another is the heart of the matter. Consider the meaning of logarithms numerically using base 10 and base 2. log10 1000 = 3 because 103 = 1000. log2 8 = 3 because 23 = 8. Exercise (a) Write down log10 1000000 (b) What is the number whose logarithm to the base 10 is 5? (c) Write down log2 32 9 (d) What is the number whose logarithm to the base 2 is 10? Display Material 70O OHT 'Comparing Display Material 80O OHT 'Logarithmic logarithms of base 2 and 10' ('times') ladder of distance' Comparing logarithms base 2 and base 10 Logarithmic ladder of distance Logarithms and bases logarithms of A ladder of distances in multiples of metres numbers logarithms of numbers to 10 1024 1000 numbers to base 2 3 base 10 9 512 Examples 1021 galaxy Equal multiple scales 8 256 1018 1 Em (exa) A logarithmic scale is one on nearest stars which equal spaces correspond log2 (128) = 7 7 128 100 2 log10 (100) = 2 1015 1 Pm (peta) to equal multiples. 6 64 1012 1 Tm (tera) In this distance scale each distance to the Sun upward step multiplies the 109 1 Gm (giga) distance by 1000. 5 32 the Earth 106 1 Mm (mega) Each downward step divides the distance by 1000. 4 16 log10 (16) = 1.2 log2 (10) = 3.4 103 small town 1 km (kilo) (approx) 10 1 Each upward step adds 3 to 100 human body 1m the logarithm (base 10) of the 3 8 distance. 10–3 width of a hair 1 mm (milli) Each downward step subtracts 2 4 10–6 microchip element 1 m (micro) 3 from the logarithm of the distance. 1 2 10–9 molecule 1 nm (nano) –12 1 pm (pico) 10 atomic nucleus 0 1 1 0 × 1000 quark 10–15 1 fm (femto) 10–18 1 am (atto) 1 × 1000 210 = 1024 If base index = number 103 = 1000 10 = log2 (1024) Then index = logarithm base (number) 3 = log10 (1000) Display Material 90O OHT 'Logarithmic Display Material 100O OHT ('times') ladder of time' 'Logarithmic ('times') ladder of mass' Logarithmic ladder of mass A ladder of masses in multiples of grams Examples 1021 Equal multiple scales 1018 1 Eg (exa) A logarithmic scale is one on 1015 1 Pg (peta) which equal spaces correspond to equal multiples. 1012 1 Tg (tera) In this mass scale each 109 1 Gg (giga) upward step multiplies the mass by 1000. 106 a car 1 Mg (mega) Each downward step divides 103 1 kg (kilo) the mass by 1000. 100 1g Each upward step adds 3 to the logarithm (base 10) of the 10–3 a mosquito 1 mg (milli) mass. 10–6 1 g (micro) Each downward step subtracts 3 from the logarithm of the 10 –9 1 ng (nano) mass. 10–12 1 pg (pico) 10–15 1 fg (femto) × 1000 –18 10 1 ag (atto) × 1 1000 10 Logarithmic ladder of time A ladder of times in multiples of seconds Examples 1021 Equal multiple scales 1018 age of Universe 1 Es (exa) A logarithmic scale is one on 1015 1 Ps (peta) which equal spaces correspond to equal multiples. 1012 1 Ts (tera) In this time scale each 10 9 1 Gs (giga) upward step multiplies the one year time by 1000. 106 1 Ms (mega) Each downward step divides 103 1 ks (kilo) the time by 1000. 100 1s Each upward step adds 3 to the logarithm (base 10) of the 10–3 flap of a fly’s wing 1 ms (milli) time. –6 Each downward step subtracts 10 1 s (micro) 3 from the logarithm of the 10–9 light crosses a room 1 ns (nano) time. 10–12 1 ps (pico) –15 × 1000 10 1 fs (femto) 10–18 1 as (atto) 1 × 1000 Display Material 110O OHT 'Logarithmic ('times') ladder of speed' Logarithmic ladder of speed A ladder of speeds in multiples of metres per second Examples 1021 No speeds Equal multiple scales greater than 1018 speed of light 1 Em s–1 (exa) A logarithmic scale is one on 1015 1 Pm s–1 (peta) which equal spaces correspond to equal multiples. 1012 1 Tm s–1 (tera) In this speed scale each 109 1 Gm s–1 (giga) upward step multiplies the speed by 1000. light speed 106 1 Mm s–1 (mega) Each downward step divides 3 the speed by 1000. 10 1 km s–1 (kilo) 100 walking speed 1 m s–1 Each upward step adds 3 to the logarithm (base 10) of the –3 speed. 10 1 mm s–1 (milli) –6 10 continental drift 1 m s–1 (micro) Each downward step subtracts 3 from the logarithm of the –9 10 1 nm s–1 (nano) speed. 10–12 1 pm s–1 (pico) 10–15 1 fm s–1 (femto) × 1000 –18 10 1 am s–1 (atto) × 1 1000 Computer files Remember: the number N of alternatives which can be represented by information I bits is just N = 2I and I = log2 N. 11 The space needed to store a file is the number of bits (or more realistically – bytes) which is a logarithmic measure of the amount of information in it i.e. the logarithm of the number of alternatives. The number of alternatives will be a very large number when referring to a computer file; the logarithm of that number is much smaller and more manageable. A ‘bit’ is a small amount of information. It is common to work in bytes, where 1 byte is 8 bits. In word-processing, one byte is used for one character (such as a letter). A large file will contain many bytes of information so it is better to work in kilobytes. One kilobyte is 2 10 or 1024 bytes but we normally call this 1000 bytes for simplicity. One megabyte is 220 or 1048576 bytes but we normally call this 1000000 bytes for simplicity. Exercise (a) Show that a 10 kilobyte word-processed file may contains less than 2000 words if the author writes an average of 6 characters per word. (b) Estimate the size of a computer file in kbytes if it contains a 4000 word essay. Digital images In the context of digital images, a ccd image is a 2 dimensional array of pixels. The larger the number of pixels in an image, the better the resolution. Each pixel of a grey scale image may require 1 byte (8 bits) of information (28 = 256 variations of grey) whereas each pixel of a colour image may require 3 bytes (3 8 = 24 bits), one for each of the primary colours. A high resolution colour image with 1 million pixels will therefore require 3 106 bytes of information (approximately 3 megabytes). The amount of information stored = number of pixels bits per pixel. Colour images require a lot of bytes of memory if stored on a computer. Downloading large files takes a long time if the information can only be transferred at, say 56000 bits per second. Time for download = number of bits to be transferred transfer rate in bits per second Exercise (a) The image of the Moon completely fills a ccd containing 1000 000 elements. The diameter of the Moon is 3.5 106m. Calculate the resolution of the image. (b) Calculate the number of bits of information required for each pixel if the image is coloured and there are 3 bytes to a pixel. 12 (c) Calculate how many different colours are available. (d) Calculate the number of bits in the image file and show that it will take over five minutes to download this file if a modem operating at 56 000 bits per second is used. [In practice, digital cameras use data compression methods to reduce the size of the image file. A 3 Mbyte file may be reduced to 1 Mbyte.] Section 1.3 With your own eyes Eye and illusion Cross-section of the eye vitreous humour iris (controls light into eye) retina (light-sensitive cells) cornea (refracts light and protects eye) fovea (where retinal cells are eye pupil densest) blind spot optic nerve aqueous humour ciliary muscle (controls lens thickness) eye lens (focuses light onto retina) Page 19 gives a simple description of the eye [See A-Z for more detail]. The eye is like an intelligent video camera, sending out a stream of processed signals. The retina consists of two types of light-sensitive cells. Rods predominate except in and near the fovea which is at the centre of the retina. Rods respond to different intensities and they are not colour sensitive which is why objects away from the centre of the field of vision are seen in shades of grey, not in colour. Several rods are joined to each nerve fibre so less detail is seen in images away from the centre of the field 13 of vision. Cones are sensitive to red or green or blue light. These types of cells are found in and near the fovea. They are most densely packed in the fovea so an image formed on this part of the retina is seen in greatest detail. Many important features can be seen on the model available. Activity 150D Demonstration 'Models of the eye' The model shows how the cornea does most of the focussing; the lens inside the eye (not available in this demonstration) is needed to focus at different distances (accommodation). The use of correcting lenses for coping with short and long sight can be demonstrated. A separate 2 dimensional model with adjustable power lens can be shown to illustrate accommodation. Remember that most of the focusing (curvature of wave fronts added) is done at the cornea; the eye lens adds an adjustable further small amount of curvature. It is helpful to compare focussing on a Web Cam with focussing of the eye. Activity 140E Experiment 'The intelligent eye' These experiments show how the eye and brain work together and also enable the width of the fovea to be estimated. The rods and cones are cross-connected with inhibiting links, so as to enhance contrasts at edges. Hence the eye detects edges and movement very effectively. Activity 130D Demonstration 'Grey step: Edge enhancement in the retina' The Hermann grid can be used to test the function of inhibiting links (see p20). Display Material 120O OHT 'The Hermann grid' Lenses and real images Only real images formed by converging lenses are discussed. Real images are those that can be formed on a screen. See the formation of a real image in space using: Activity 160D 'Image in mid-air' Display Material 160O Display Material 170O OHT 'Rays and waves' OHT 'Rays and waves focused' 14 Wave and ray points of view: Wave point of view: The lens adds curvature to the wave entering it Ray point of view Wave point of view focus Ray point of view: Wave point of view: Light travels out in Light spreads out in focal length f straight lines from a spherical wave fronts small source from a small source Ray point of view: The lens bends the rays, bringing them to a focus focus Ray point of view: Wave point of view: Light in a parallel beam or Wave fronts in a parallel from a very distant source beam or from a very distant has rays (approximately) source are straight (not parallel to one another curved) and parallel Activity 200D Demonstration 'Focusing water ripples' This introduces idea of lens adding curvature. The image-lens distance when the object is at infinity is known as the focal length, f. The waves coming from infinity have no curvature and the lens adds curvature to the waves passing through it. The radius of the spherical wavefronts after waves from infinity have passed through the lens is f. The curvature of a sphere of radius r is 1/r, so the lens has added curvature 1/f to the wavefronts. It can be seen that a more powerful lens (shorter focal length) adds more curvature. The power of a lens is a measure of the curvature it adds. power (dioptres) P = 1/f where f is in metres. A camera lens with a focal length of 50 mm, which is 0.050 m, has a power of 1/0.050m = 20 dioptre. When placed together the powers add so a 20 dioptre and 30 dioptre lens placed together with have a total power of 50 dioptre. Exercise Calculate the focal length of a 50 dipotre lens. If you think that’s short, try calculating the focal length of a WebCam lens with a power of 278 dioptre. 15 It is helpful to see a pinhole camera being converted into a lens camera to get a feel for image formation before proceeding to experiments to measure power and focal length. Class experiment Activity 170E Experiment 'Converging lenses: power and focal length' It is useful to discuss how a lens forms an image using: Activity 180D Demonstration 'Where are the parts of an object in its image? Display Material 180O OHT 'Formation of an image' How a lens makes 'a little picture' The lens does not alter the direction of Image of traffic light Traffic light image of red lamp the light, it just alters the curvature of red light on at the bottom the wavefronts. It is useful to recall work on rays of light passing through a rectangular glass block to see why this happens. When drawing ray diagrams for lenses it is usually a good idea to draw a ray form the object that passes through the image of green lamp at the top centre of the lens as this ray never green light on changes direction. images of red and amber lamps: amber in the red and amber middle both on 16 The rule for how lenses shape light (p 23) curvature of waves coming out = curvature of waves coming in + curvature added by lens Since curvature is 1/r where r is the radius of the wavefronts, we have: 1/v = 1/u + 1/f Distances to the right are positive; distances to the left are negative. All measurements are made from the centre of the lens. The Cartesian convention is used; a lens adds curvature 1 / f to the wave fronts going through it. Display Material 190O OHT 'Action of a lens on a wavefront' Lenses change wave curvature image of source source distance from lens to source = u distance from lens to image = v (for example minus 0.2 m) (for example plus 0.1 m) 1 1 1 power of lens = 15 dioptre curvature of wave front after leaving the lens = = = 10 f v 0.1 1 1 1 focal length of lens f = curvature of wave front on reaching the lens = = = –5 power u –0.2 1 = 15 curvature added by lens = power of lens = curvature after – curvature before 1 1 = 0.067 m = – v u = 10– (–5) = 15 dioptre = 67 mm Display Material 200O OHT 'Where object and image are to be found' 17 Lenses add constant curvature 1/f 1 1 =0 + v f zero curvature 1 before curvature after v=f f very distant image of source source f 1 1 1 = + 1 1 v u f curvature before curvature after u v source image of source u (negative) v (positive) 1 1 –1 0= + curvature before zero curvature u f f after u= –f source at very distant the focus image of source f Exercise A camera lens with a focal length of 5 cm forms a clear image of an object on a film when the object is 3 m from the lens. Calculate the distance between the image and the lens. (a) Will the image be more or less than 5 cm from the lens? (b) Calculate the distance between the image and the lens. [Hint: Is the object distance positive or negative?] Class experiment to show that a lens does in fact add constant curvature to the wave fronts. Activity 190E Experiment 'A converging lens adds constant curvature 1 / f ' uses File 130S Spreadsheet Model 'Lens action on a spreadsheet' 18 Exercise (a) Calculate the magnification of the image obtained in the camera example above. (b) What is meant by the negative sign? (c) Why is the magnification less than 1? Illustrate magnification, particularly from the point of view of getting the largest possible image on the retina using a cheap ccd video camera (WebCam): Activity 210D Demonstration 'Modelling the eye with a video camera' Summary video on imaging: ‘Whatever became of X-rays?’ (University of Leeds) This programme explains and illustrates some computer advances in body imaging. Section C questions In Section C there are 30 marks available from two open-ended questions. They have been designed for candidates to have time and freedom to show what they have learned independently. Quality of communication is assessed in these questions. In Module 2860: Physics in Action candidates should demonstrate evidence of initiative and independence in learning by giving and explaining their own example of: 1 an application of image formation (Chapter 1), 2 an application of signal transmission (Chapter 3), 3 choice and use of a sensor for an application (Chapter 2), 4 the relationship between uses, properties and structures of one material (Chapters 4&5). In your studies of Imaging you will have covered enough material to write out a side of A4 on item 1 above. A typical question might start as follows: 19 ‘This question is about an imaging system, producing data that can be stored and displayed by a computer’. Candidates might have written about one of the following: a satellite imaging system using infra-red radiation or microwaves; the ultrasound medical scanner using ultrasound; a radio telescope system that detects radio waves; various electron microscopes. However, any imaging system that involves computer storage and display would be valid. It is usually important to be able to explain how the image is produced and to consider how it is of human benefit or scientific interest. You must understand the nature of the waves or radiation (such as electromagnetic radiation or ultrasound) which carries the information needed to create the image and you should be able to how the information for the image is obtained with the aid of a labelled diagram. You will sometimes be asked how to manipulate the image to enhance its appearance on the computer screen so you should understand about manipulating the pixels. You might also be asked about the resolution of the image or how long it would take to transmit an image of given size. You should choose your own example and carry out some research of your own so that you are well prepared. If you are interested in the medical scanner you should make sure that you know and understand the information available in the textbook and the A-Z of the CD-ROM before doing more research. The A-Z also has detailed information about various electron microscopes. You will have to look further afield for other examples of imaging. We will of course discuss various cases in class to make sure that you understand what is required. Questions and activities Section Essential Optional 1.1 Qu 1-6 AS text p 5 Qu 1-6 AS text p 9 Qu 1-6 AS text p 12 Question 10S Short answer 'Speed, wavelength and frequency' Qu 1-17 Question 20E Estimate 'Large and small distances and times' Qu 1-6 Question 30X Explanation-Exposition 'Different kinds and uses of images' 1.2 Qu 1-6 AS text p 18 Question 60S Short Answer 'A scanning electron microscope image of Velcro' Question 40S Short Answer 'Smoothing Question 70S Short Answer 'Image processing pixels using mean or median' by brightness and contrast control' Question 110S Short Answer 'Bits and Question 80S Short Answer 'The Horsehead bytes in images' nebula' Question 120S Short Answer 'Logarithms Question 90C Comprehension 'Saturn's aurorae and powers' in ultraviolet' Activity 120S Software Based 'How big Question 100C Comprehension 'Betelgeuse in are your computer files?' ultraviolet' Question 130C Comprehension 'X-ray image of the Kepler supernova remnant' 20 Activity 90S 'Spreadsheet models: Image processing’. This provides an insight into the calculations behind image processing. Activity 100S 'Mapping the South Atlantic sea floor' Activity 110H Home Experiment 'Logarithmic ('times') ladders of quantities' Reading 20T Text to read 'A collection of visual illusions' 1.3 Qu 1-6 AS text p 26 Question 160C Comprehension 'Satellite imaging' Question 140S Short Answer 'Response of the human eye to differences in Display Material 140O OHT 'Ouchi illusion' brightness' Display Material 150S Computer screen 'A pointillist painting' Question 150S Short Answer 'Cameras Display Material 210O OHT 'The lens maker's and eyes' equation' Display Material 220O OHT 'Thin lens: proof of 1 / v = 1 / u + 1 / f' File 130S Spreadsheet Model 'Lens action on a spreadsheet' Summary Qu 1-6 AS text p 28 21