CONCEPTS OF PHYSICS PART 1 H C VERMA, PhD Department of Physics IIT, Kanpur BHARATI RHA AN Bharati Bhawan PUBLISHERS DISTRIBUTORS Published by BHARATI BHAWAN (Publishers Distributors) 42713 Ans.CONCEPTS OF PHYSICS PART 1 H C VERMA, PhD Department of Physics IIT, Kanpur BHARATI RHA AN Bharati Bhawan PUBLISHERS DISTRIBUTORS Published by BHARATI BHAWAN (Publishers Distributors) 42713 Ans.
CONCEPTS OF PHYSICS [PART 1] H C VERMA, PhD Department of Physics IIT, Kanpur Bharati Bhawan BHARATI RHA AN PUBLISHERS & DISTRIBUTORS Published by BHARATI BHAWAN (Publishers & Distributors) 4271/3 Ansari Road, Daryaganj, NEW DELHI 110 002 Thakurbari Road, Kadamkuan, PATNA 800 003 10 Raja Subodh Mallick Square, KOLKATA 700 013 Shankara Building (1st Floor), 36 Avenue Road, BANGALORE 560 002 20 Jail Road (East), Tharpakhna, RANCHI 834 001 © Author Publication of the solutions of the problems given in this book is strictly prohibited First edition 1992 Revised print 1999 Fourth reprint of 2008 Every genuine copy of this book has a 3-D hologram sticker A 3-D hologram sticker is different from an ordinary sticker Our hologram sticker has the following features • When the book is moved sideways, the lines and the book in the hologram show animation (movement) • There is microscopic lettering in the lines • The hologram also has a large hidden logo and four rows of the words 'BHARATI BHAWAN', which can be seen at only specific angles Concepts of Physics Printed at B B Printers, Patna-800 006 Dedicated to Indian Philosophy & Way of Life of which my parents were an integral part FOREWORD A few years ago I had an occasion to go through the book Calculus by L.V.Terasov It unravels intricacies of the subject through a dialogue between Teacher and Student I thoroughly enjoyed reading it For me this seemed to be one of the few books which teach a difficult subject through inquisition, and using programmed concept for learning After that book, Dr Harish Chandra Verma's book on physics, CONCEPTS OF PHYSICS is another such attempt, even though it is not directly in the dialogue form I have thoroughly appreciated it It is clear that Dr Verma has spent considerable time in formulating the structure of the book, besides its contents I think he has been successful in this attempt Dr Verma's book has been divided into two parts because of the size of the total manuscript There have been several books on this subject, each one having its own flavour However, the present book is a totally different attempt to teach physics, and I am sure it will be extremely useful to the undergraduate students The exposition of each concept is extremely lucid In carefully formatted chapters, besides problems and short questions, a number of objective questions have also been included This book can certainly be extremely useful not only as a textbook, but also for preparation of various competitive examinations Those who have followed Dr Verma's scientific work always enjoyed the outstanding contributions he has made in various research areas He was an outstanding student of Physics Department of IIT Kanpur during his academic career An extremely methodical, sincere person as a student, he has devoted himself to the task of educating young minds and inculcating scientific temper amongst them The present venture in the form of these two volumes is another attempt in that direction I am sure that young minds who would like to learn physics in an appropriate manner will find these volumes extremely useful I must heartily congratulate Dr Harish Chandra Verma for the magnificent job he has done Y R Waghmare Professor of Physics IIT Kanpur PREFACE Why a new book ? Excellent books exist on physics at an introductory college level so why a new one ? Why so many books exist at the same level, in the first place, and why each of them is highly appreciated It is because each of these books has the previlege of having an author or authors who have experienced physics and have their own method of communicating with the students During my years as a physics teacher, I have developed a somewhat different methodology of presenting physics to the students Concepts of Physics is a translation of this methodology into a textbook Prerequisites The book presents a calculus-based physics course which makes free use of algebra, trigonometry and co-ordinate geometry The level of the latter three topics is quite simple and high school mathematics is sufficient Calculus is generally done at the introductory college level and I have assumed that the student is enrolled in a concurrent first calculus course The relevant portions of calculus have been discussed in Chapter-2 so that the student may start using it from the beginning Almost no knowledge of physics is a prerequisite I have attempted to start each topic from the zero level A receptive mind is all that is needed to use this book Basic philosophy of the book The motto underlying the book is physics is enjoyable Being a description of the nature around us, physics is our best friend from the day of our existence I have extensively used this aspect of physics to introduce the physical principles starting with common clay occurrences and examples The subject then appears to be friendly and enjoyable I have taken care that numerical values of different quantities used in problems correspond to real situations to further strengthen this approach Teaching and training The basic aim of physics teaching has been to let the student know and understand the principles and equations of physics and their applications in real life However, to be able to use these principles and equations correctly in a given physical situation, one needs further training A large number of questions and solved and unsolved problems are given for this purpose Each question or problem has a specific purpose It may be there to bring out a subtle point which might have passed unnoticed while doing the text portion It may be a further elaboration of a concept developed in the text It may be there to make the student react when several concepts introduced in different chapters combine and show up as a physical situation and so on Such tools have been used to develop a culture : analyse the situation, make a strategy to invoke correct principles and work it out Conventions I have tried to use symbols, names etc which are popular nowadays SI units have been consistently used throughout the book SI prefixes such as micro, milli, mega etc are used whenever they make the presentation more readable Thus, 20 pF is preferred over 20 x 10 F Co-ordinate sign convention is used in geometrical optics Special emphasis has been given to dimensions of physical quantities Numerical values of physical quantities have been mentioned with the units even in equations to maintain dimensional consistency I have tried my best to keep errors out of this book I shall be grateful to the readers who point out any errors and/or make other constructive suggestions H C Verma ACKNOWLEDGEMENTS The work on this book started in 1984 Since then, a large number of teachers, students and physics lovers have made valuable suggestions which I have incorporated in this work It is not possible for me to acknowledge all of them individually I take this opportunity to express my gratitude to them However, to Dr S B Mathur, who took great pains in going through the entire manuscript and made valuable comments, I am specially indebted I am also beholden to my colleagues Dr A Yadav, Dr Deb Mukherjee, Mr M M R Akhtar, Dr Arjun Prasad, Dr S K Sinha and others who gave me valuable advice and were good enough to find time for fruitful discussions To Dr T K Dutta of B E College, Sibpur I am grateful for having taken time to go through portions of the book and making valuable comments I thank my student Mr Shailendra Kumar who helped me in checking the answers I am grateful to Dr B C Rai, Mr Sunil Khijwania & Mr Tejaswi Khijwania for helping me in the preparation of rough sketches for the book Finally, I thank the members of my family for their support and encouragement H C Verma CHAPTER 22 PHOTOMETRY Relative luminosi ty We see an object when light coming from the object enters our eyes and excites the sensation of vision The brightness sensed by the eye depends on the amount of light energy entering into it and the wavelength distribution of this energy In this chapter, we shall study the factors responsible for the sensation of brightness 22.1 TOTAL RADIANT FLUX The total energy of radiation emitted by a source per unit time is called its total radiant flux This radiation contains components of various wavelengths extending even beyond the visible range However, not all wavelengths have equal contribution in making up the total radiation In calculating total radiant flux of a source, the total energy emitted per unit time in the whole range of wavelengths must be calculated The SI unit of total radiant flux of a source is watt 22.2 LUMINOSITY OF RADIANT FLUX The brightness produced by radiation depends on the wavelength of the radiation besides depending on the total radiant flux For example, consider two 10 W sources of light, one emitting yellow light and the other red light Though both emit equal energy per unit time, yellow will look brighter than the red The luminosity of radiant flux measures the capacity to produce brightness sensation in eye A relative comparison of luminosity of radiant flux of different wavelengths can be made by the curve in figure (22.1) The figure represents relative luminosity under normal light conditions for an average person The scale on the vertical axis is chosen arbitrarily We see that for normal light conditions, the luminosity is maximum for wavelength around 555 run and falls off on both sides Radiation is "visible" if its luminosity is not zero As the luminosity falls off gradually, there are no sharp cut-offs of visible region Wavelength (nm) Figure 22.1 22.3 LUMINOUS FLUX : RELATIVE LUMINOSITY In general, the radiation emitted by a source has components corresponding to a wide range of wavelengths Different component wavelengths have different energies (in a given time) and different brightness producing capacities The radiant flux is a quantity directly representing the total energy emitted per unit time The luminous flux is a quantity directly representing the total brightness producing capacity of the source Its unit is called, lumen The luminous flux of a source of 1/685 W en-lifting monochromatic light of wavelength 555 run is called one lumen In other words, a W source emitting monochromatic light of wavelength 555 nm emits 685 lumen Relative luminosity of a wavelength refers to the fraction luminous flux of a source of given wavelength luminous flux of a 555 nm source of same power It is often represented as a percentage Thus, figure (22.1) represents the relative luminosity as a function of wavelength It should be clear that the luminous flux depends on the radiant flux as well as on the wavelength distribution Concepts of Physics 450 where A is the area intercepted by the cone on a sphere of radius R centred at the apex of the cone (figure 22.2) Example 221 Find the luminous flux of a 10 W source of 600 nm The relative luminosity at 600 nm is 0.6 Solution : The luminous flux of a W source of 555 nm = 685 lumen Thus, the luminous flux of a 10 W source of 555 nm = 6850 lumen The luminous flux of a 10 W source of 600 nm is, therefore, 0.6 x 6850 lumen = 4110 lumen Figure 22.2 For radiation having a range of wavelengths, the luminous flux gets contribution from each wavelength 22.4 LUMINOUS EFFICIENCY Total luminous flux per unit radiant flux is called luminous efficiency Thus, Total luminous flux Luminous efficiency = (22.1) Total radiant flux The luminous efficiency of a monochromatic source of 555 nm is 685 lumen/watt by definition The luminous efficiency of a monochromatic source of any other wavelength is the relative luminosity of that wavelength multiplied by 685 lumen/watt An electric lamp glows when electric energy is given to it However, not all the electric power given to it is converted into radiant flux The term luminous efficiency is used in a slightly wider sense for such a light source It is defined as the luminous flux divided by the power input to the source Thus, it is the efficiency with which the power input to the source is used to produce brightness We may call it overall luminous efficiency Overall luminous efficiency Luminous flux emitted (22.2) Power input to the source A good fraction of power given to a filament lamp is used to heat the filament to a certain temperature at which it glows Also, a good fraction of the emitted radiation has a wavelength where the relative luminosity is small or zero The overall luminous efficiency of a filament lamp is rarely more than 50 lumen/watt 22.5 LUMINOUS INTENSITY OR ILLUMINATING POWER In the chapter on Gauss's law, we shall describe in detail what is a solid angle In brief, the solid angle measures the angular divergence of a cone and is defined as A , 0.1 R2 It is clear that the solid angle does not depend on the radius of the sphere The SI unit of solid angle is called a steradian written in short as sr The luminous intensity of a source in a given direction is defined as I= dF do) ' (22.3) AF Figure 22.3 where dF is the luminous flux of the radiation emitted by the source in a small cone of solid angle dw constructed around the given direction The luminous intensity is also called just intensity in short An ideal point source emits radiation uniformly in all directions If the total luminous flux of the source is F, its intensity in any direction is (4n sr) as the total solid angle at a point is 4n sr For an extended source, the intensity is different in different directions The SI unit of luminous intensity is lumen/steradian This is called a candela written in short as “cd" Luminous intensity is also called illuminating power Candela is one of the seven base units of SI It is defined precisely as the luminous intensity of a blackbody of surface area — cm placed at the freezing 60 temperature of platinum at a pressure of 101, 325 N/m in the direction perpendicular to the surface 22.6 ILLUMINANCE When radiation strikes a surface, the surface gets illuminated We define the illuminance of a small area as follows If dF be the luminous flux of the radiation Photometry striking a surface area dA, the illuminance of the area is defined as E = cA y• dA (22.4) The illuminance is, therefore, the luminous flux incident per unit area It is the illuminance which is directly related to the brightness of an illuminated area The SI unit of illuminance is lumen/m and is called lux 22.7 INVERSE SQUARE LAW Consider a point source S and a small area AA around the point P at a distance r from the source (figure 22.4) Suppose, the angle between SP and the normal PN to the area is Also suppose, the luminous intensity of the source in the direction SP is I 451 different directions If the source is in the form of a small plane surface, the radiation is emitted only in the forward half that is in a solid angle 2E around the forward normal Even in this half, the intensity is different in different directions The intensity is maximum along the normal to the surface and decreases as we consider directions away from this normal For many surfaces, if the luminous intensity along the normal is 4, it is 1= Jo cose (22.6) in a direction making an angle with the normal Equation (22.6) is called Lambert's cosine law The surfaces which radiate according to the Lambert's cosine law are called perfectly diffused Maximum Intensity Emitting Surface Figure 22.5 22.9 PHOTOMETERS Figure 22.4 The solid angle subtended by the area AA at the source is Oct = DA cose r The luminous flux going through this solid angle is AF = /Ace DA cos0 =I A photometer is used to compare the intensities of two point sources The basic principle is as follows Two screens are placed side by side One screen is illuminated by the source S1only and the other screen by the source S2 only Light falls on the two screens at equal angles The distances d, and d2 of the sources from the screens are so adjusted that the two screens look equally bright If II and /2 be the intensities of the sources, we must have for equal illuminance r2 The illuminance at Ail is E_ or, (22.5) I cos0 E-r We note that (a) the illuminance of a small area is inversely proportional to the square of the distance of the area from the source and (b) the illuminance of a small area is proportional to cos() where is the angle made by the normal to the area with the direction of incident radiation The first observation is known as the inverse or, I1 I2 2 d2 Il di2 T2 = c: A simple design proposed by Bunsen is now described (figure 22.6) It consists of an optical bench fitted with three vertical stands The stands can slide along a straight rail on the bench square law 22.8 LAMBERT'S COSINE LAW An ideal point source emits radiation uniformly in all directions In general, sources are extended and such a source has different luminous intensity in (22.7) Figure 22.6 Concepts of Physics 452 The distance between any two points on the rail may be read from a meter scale attached to the bench The central stand contains a white paper with a grease spot The other two stands carry the sources S1 and S2 to be compared Two plane mirrors M1 and M2 are placed behind the central stand at proper inclination so that one side of the spot is imaged in one mirror and the other side of the spot is imaged in the other mirror The two images can be seen simultaneously One of the sources is kept fixed at a distance from the spot and the position of the other is adjusted till the two spots seen in the mirrors appear equally bright The distances d1 and d2 of the sources from the spot are measured in this condition In this condition, the light falling on the spot from the two sources has equal intensity If II and /2 be the intensity of the two sources, we have for equal illuminance, /1 • _1 - z d2 dz or, Worked Out Examples A source emits 12.0 J of light of wavelength 620 nm and 8.0 J of light of wavelength 580 nm per second The relative luminosity at 620 =I is 35% and that at 580 mu is 80% Find (a) the total radiant flux, (b) the total luminous flux and (c) the luminous efficiency Solution : (a) The total radiant flux = Total energy radiated per unit time = 12 J/s + J/s = 20 J/s = 20 W (b) The luminous flux corresponding to the 12 W of 620 nm radiation is 0.35 x (12 W) x 685 lumen/W = 2877 lumen Similarly, the luminous flux corresponding to the W of 580 nm radiation is 0.80 x (8 W) x 685 lumen/W = 4384 lumen The luminous flux of the source is 2877 lumen + 4384 lumen = 7261 lumen 7260 lumen (c) The luminous efficiency - Total luminous flux Total radiant flux - 7260 lumen - 363 lumen/W 20 W A circular area of radius 1'0 cm is placed at a distance of 2'0 m from a point source The source emits light uniformly in all directions The line joining the source to the centre of the area is normal to the area It is found that 2'0 x 10 -3lumen of luminous flux is incident on the area Calculate the total luminous flux emitted by the source and the luminous intensity of the source along the axis of the area radiates uniformly in all directions, the total luminous flux is 4n x 2.0 x 10 3lumen Fx 10 -4 = 320 lumen The luminous intensity = AF/Aco 2.0 x 10 -3lumen - 25 cd It x 10 - — sr The overall luminous efficiency of a 100 W electric lamp is 25 lumen/W Assume that light is emitted by the lamp only in the forward half, and is uniformly distributed in all directions in this half Calculate the luminous flux falling on a plane object of area cm 2placed at a distance of 50 cm from the lamp and perpendicular to the line joining the lamp and the object Solution : The power input to the bulb = 100 W The luminous flux emitted by the bulb = (25 lumen/W) x 100 W = 2500 lumen Since light is emitted only in the forward half and is distributed uniformly in this half, the luminous intensity is I = AF/Aco 2500 lumen 2n sr The solid angle subtended by the object on the lamp is cm (50 cm) 2500 Sr The luminous flux emitted in this solid angle is AF = /AG) [ 2500 lumen) { 2n sr 2500 sr AG) - Solution : The solid angle subtended by the area on the point source is bao - 141.0 CM) 7C X 10-4sr (2.0-rn) Thus, 2.0 x 10 -3lumen of flux is emitted in x 10 -4 The total solid angle at the source is 4n., As the source =— 2n lumen = 0.16 lumen 453 Photometry A point source emitting uniformly in all directions is placed above a table-top at a distance of 0'50 m from it The luminous flux of the source is 1570 lumen Find the (125 cd) x Thus, illuminance at a small surface area of the table-top (a) directly below the source and (b) at a distance of 0'80 m from the source EB 0'64 m = 122 lux The luminous intensity of a small plane source of light along the forward normal is 160 candela Assuming the source to be perfectly diffused, find the luminous flux Solution : Consider the situation shown in figure (22-W1) Let A be the point directly below the source S and B be the point at 0'80 m from the source emitted into a cone of solid angle 0'02 sr around a line making an angle of 60° with the forward normal B 0.80m 0.50m B Figure 22-W1 The luminous flux of 1570 lumen is emitted uniformly in the solid angle 4n The luminous intensity of the source in any direction is /- Figure 22-W2 Solution : The situation is shown in figure (22-W2) By 1570 lumen Lambert's cosine law, the intensity in the direction SB 4n sr is = 125 cd I= cos60°, The illuminance is E= where Io = 160 candela is the intensity along the forward normal / cosh r Thus, At the point A, r = 0'50 m and = Thus, EA — SA = 80 candela 125 cd - 500 lux 0'25 m At the point B, r = 0'80 m and cos° = — I = (160 candela) [11 The luminous flux emitted in the cone shown in the figure is AF = I Act) 0.50_5 SB = 0'80 - = (80 candela) (0'02 sr) = 1.6 lumen QUESTIONS FOR SHORT ANSWER What is the luminous flux of a source emitting radio waves ? The luminous flux of a W sodium vapour lamp is more than that of a 10 kW source of ultraviolet radiation Comment Light is incident normally on a small plane surface If the surface is rotated by an angle of 30° about the incident light, does the illuminance of the surface increase, decrease or remain same ? Does your answer change if the light did not fall normally on the surface ? A bulb is hanging over a table At which portion of the table is the illuminance maximum ? If a plane mirror is placed above the bulb facing the table, will the illuminance on the table increase ? The sun is less bright at morning and evening as compared to at noon although its distance from the observer is almost the same Why ? Why is the luminous efficiency small for a filament bulb as compared to a mercury vapour lamp ? The yellow colour has a greater luminous efficiency as compared to the other colours Can we increase the illuminating power of a white light source by putting a yellow plastic paper around this source ? 454 Concepts of Physics OBJECTIVE I L The one parameter that determines the brightness of a light source sensed by an eye is (a) energy of light entering the eye per second (b) wavelength of the light (c) total radiant flux entering the eye (d) total luminous flux entering the eye Three light sources A, B and C emit equal amount of radiant energy per unit time The wavelengths emitted by the three sources are 450 nm, 555 nm and 700 nm respectively The brightness sensed by an eye for the sources are XA, X5 and X, respectively Then, (b) XA > X5, X5> X, Xc> X j3 (a) XA> (d) X, > XA, X, > Xg (C) X5> XA,XB > XC As the wavelength is increased from violet to red, the luminosity (a) continuously increases (b) continuously decreases (c) increases then decreases (d) decreases then increases An electric bulb is hanging over a table at a height of m above it The illuminance on the table directly below the bulb is 40 lux The illuminance at a point on the table m away from the first point will be about (c) 20 lux (b) 14 lux (d) 28 lux (a) 10 lux Light from a point source falls on a screen If the The intensity produced by a long cylindrical light source at a small distance r from the source is proportional to 1 , (c) — (d) none of these —2 (b) —3 A photographic plate placed at a distance of cm from a weak point source is exposed for s If the plate is kept at a distance of 10 cm from the source, the time needed for the same exposure is (b) 12 s (c) 24 s (d) 48 s (a) s A photographic plate is placed directly in front of a small diffused source in the shape of a circular disc It takes 12 s to get a good exposure If the source is rotated by 60° about one of its diameters, the time needed to get the same exposure will be (b) 12 s (c) 24 s (d) 48 s (a) s 10 A point source of light moves in a straight line parallel to a plane table Consider a small portion of the table directly below the line of movement of the source The illuminance at this portion varies with its distance r from the source as 1 1 (c) /0, (a) /0, — (b) / or i (d) / • r r r r 11 Figure (22-Q1) shows a glowing mercury tube The intensities at point A, B and C are related as (b)A>C>B (d)B=CC>A (c)B= C> A separation between the source and the screen is increased by 1%, the illuminance will decrease (nearly) by (c) 2% (d) 4% (a) 0.5% (b) 1% A battery-operated torch is adjusted to send an almost parallel beam of light It produces an illuminance of 40 lux when the light falls on a wall m away The illuminance produced when it falls on a wall m away is close to (b) 20 lux (c) 10 lux (d) lux (a) 40 lux / I\ • C L • A B Figure 22-Q1 OBJECTIVE II The brightness producing capacity of a source (a) does not depend on its power (b) does not depend on the wavelength emitted (c) depends on its power (d) depends on the wavelength emitted A room is illuminated by an extended source The illuminance at a particular portion of a wall can be increased by (a) moving the source (b) rotating the source (c) bringing some mirrors in proper positions (d) changing the colour of the source Mark the correct options (a) The luminous efficiency of a monochromatic source is always greater than that of a white light source of same power (b) The luminous efficiency of a monochromatic source of wavelength 555 nm is always greater than that of a white light source of same power (c) The illuminating power of a monochromatic source of wavelength 555 nm is always greater than that of a white light source of same power (d) The illuminating power of a monochromatic source is always greater than that of a white light source of same power Mark the correct options (a) Luminous flux and radiant flux have same dimensions (b) Luminous flux and luminous intensity have same dimensions (c) Radiant flux and power have same dimensions (d) Relative luminosity is a dimensionless quantity Photometry 455 EXERCISES point on the table-top, directly below the source, is 15 lux Find the illuminance at a point on the table-top 80 cm away from the first point 12 Light from a point source falls on a small area placed perpendicular to the incident light If the area is rotated about the incident light by an angle of 60°, by what fraction will the illuminance change ? 13 A student is studying a book placed near the edge of a circular table of radius R A point source of light is suspended directly above the centre of the table What should be the height of the source above the table so as to produce maximum illuminance at the position of the book ? 14 Figure (22-E1) shows a small diffused plane source S placed over a horizontal table-top at a distance of 2'4 m with its plane parallel to the table-top The illuminance at the point A directly below the source is 25 lux Find the illuminance at a point B of the table at a distance of 1'8 m from A A source emits 45 joules of energy in 15 s What is the radiant flux of the source ? A photographic plate records sufficiently intense lines when it is exposed for 12 s to a source of 10 W How long should it be exposed to a 12 W source radiating the light of same colour to get equally intense lines ? Using figure (22.1), find the relative luminosity of wavelength (a) 480 nm, (b) 520 nm (c) 580 nm and (d) 600 nm The relative luminosity of wavelength 600 nm is 0.6 Find the radiant flux of 600 nm needed to produce the same brightness sensation as produced by 120 W of radiant flux at 555 nm The luminous flux of a monochromatic source of W is 450 lumen/watt Find the relative luminosity at the wavelength emitted A source emits light of wavelengths 555 nm and 600 nm The radiant flux of the 555 nm part is 40 W and of the 600 nm part is 30 W The relative luminosity at 600 nm is 0'6 Find (a) the total radiant flux, (b) the total luminous flux, (c) the luminous efficiency A light source emits monochromatic light of wavelength 555 nm The source consumes 100 W of electric power and emits 35 W of radiant flux Calculate the overall luminous efficiency A source emits 31'4 W of radiant flux distributed uniformly in all directions The luminous efficiency is 60 lumen/watt What is the luminous intensity of the source ? A point source emitting 628 lumen of luminous flux uniformly in all directions is placed at the origin Calculate the illuminance on a small area placed at (1'0 m, 0, 0) in such a way that the normal to the area makes an angle of 37° with the X-axis 10 The illuminance of a small area changes from 900 lumen/m to 400 lumen/m when it is shifted along its normal by 10 cm Assuming that it is illuminated by a point source placed on the normal, find the distance between the source and the area in the original position 11 A point source emitting light uniformly in all directions is placed 60 cm above a table-top The illuminance at a Figure 22-El 15 An electric lamp and a candle produce equal illuminance at a photometer screen when they are placed at 80 cm and 20 cm from the screen respectively The lamp is now covered with a thin paper which transmits 49% of the luminous flux By what distance should the lamp be moved to balance the intensities at the screen again ? 16 Two light sources of intensities cd and 12 cd are placed on the same side of a photometer screen at a distance of 40 cm from it Where should a 80 cd source be placed to balance the illuminance ? ANSWERS OBJECTIVE I (d) (c) (c) (b) (c) (c) (b) 10 (c) EXERCISES (c) 11 (d) (a) OBJECTIVE II (c), (d) (b), (c), (d) (a), (b), (c), (d) (b), (c) W 10 s 0-14 (b) 0.68 (c) 092 (d) 0.66 200 W 66% (a) 70 W (b) 39730 lumen (c) 568 lumen/W 456 240 lumerVW 150 cd 40 lux 10 20 cm 11 3'24 lux Concepts of Physics 12 it will not change 13 R/✓2 14 6.1 lux 15 24 cm 16 80 cm APPENDIX A Units and Dimensions of Physical Quantities Quantity Displacement Mass Time Area Volume Density Velocity Acceleration Force Work Energy Power Momentum Gravitational constant Angle Angular velocity Angular acceleration Angular momentum Moment of inertia Torque Angular frequency Frequency Period Young's modulus Bulk modulus Shear modulus Surface tension Coefficient of viscosity Pressure Wavelength Intensity of wave Temperature Specific heat capacity Stefan's constant Heat Thermal conductivity Current Charge Current density Electrical conductivity Dielectric constant Electric dipole moment Electric field Potential (voltage) Electric flux Capacitance Electromotive force Resistance Permittivity of space Permeability of space Magnetic field Magnetic flux Magnetic dipole moment Inductance Common Symbol s m, M t A V p u, u a F W E, U, K P p G 0, co a L I t co v T Y B rl S Ti P, p X I T c a Q K I q, Q j a k p E V cl) C SI Unit METRE (m) KILOGRAM (kg) SECOND (s) m2 m3 kg/m m/s m/s newton (N) joule (J)(= N—m) joule (J) watt (W)(= J/s) kg—m/s i\T—m 2acg radian radian/s radiants kg—m 2/s kg—m N—m radian/s hertz (Hz) s N/m N/m N/m N/m N—s/m N/m , Pa m W/m KELVIN (K) J/kg—K W/m 24i4 J W/m—K AMPERE Dimension L M T L2 L3 Mad3 L/T DT ML/T ML2/T ML2/T ML2/T ML/T L3/MT T -1 T -2 ML2/T ML2 ML2/T T -1 T -1 T M/LT M/LT M/LT M/T M/LT M/LT L M/T K L2/T K M/T 3K ML2/T ML/T 3K I IT coulomb C) A/m 1/S1—m (# mho/m) I 2T 3/ML3 C—m Wm (= N/C) volt (V)(= J/C) LIT ML/IT ML2/IT lag v-m mL3trr 12T 4/ML2 ML2/IT R farad (F) volt (V) ohm (0) co C 2/N-m (= F/m) I 2T 4/ML3 E I-to B cps 1.i L ML2/ 2T mil2T N/A tesla (T)(= Wb/m 2) WIT weber (Wb) ML2/IT 11,2 N—m/T henry (H) ML2/I 2T APPENDIX B Universal Constants (as revised in 1986) Unit Uncertainty in the last two digits 6.67259 x 10 -11 N-m 7/kg 85 m/s exact 36 Quantity Symbol Value Constant of gravitation G Speed of light in vacuum c 2.99792458 x 10 Avogadro constant NA 6.0221367 x 10 23 mol -1 Gas constant R 8.314510 J/K-mol 70 Boltzmann constant k 1.380658 x 10 -23 8.617385 x 10 -6 J/K eV/K 12 73 Stefan-Boltzmann constant a 5.67051 x 10 -8 WM 2-K 19 Wien's displacement law constant b 2.897756 x 10 -8 m-K 24 Charge of proton e 1.60217733 x 10 -18 C 49 54 13 Mass of electron m„ 9.1093897 x 10 -31 5.48579903 x 10 -4 kg u Mass of proton m, 1.6726231 x 10 -27 1.007276470 kg u 10 12 Mass of neutron m„ 1.6749286 x 10 -27 1.008664904 kg u 10 14 Permeability of vacuum No 471 x 10 -7 = 12.566370614 x 10 -7 N/A exact Permittivity of vacuum po c Eo exact = 8.854187817 x 10 -12 C 2/N-m F/m Faraday constant F 96485.3029 C/mol 29 Planck constant h 66260755 x 10 -34 4.1356692 x 10 -16 J-s eV-s 40 12 Rydberg constant R 1.0973731534 x 10 in -1 13 13.605698 eV 40 5.29177249 x 10 -11 m 24 Ground state energy of hydrogen atom Bohr radius (10 Astronomical Constants Quantity Value Unit Mass of the sun 1.99 x 10 3° kg Radius of the sun 6.95 x 10 Mass of the earth 5.98 x 10 24 Mean radius of the earth 6.37 x 10 Mass of the moon 7.36 x 10 22 Radius of the moon 1.74 x 10 Mean earth-sun distance 1.50 x 10 11 kg kg In Mean earth-moon distance 3.84 x 10 Escape speed from the earth 11.2 km/s Escape speed from the moon 2.38 lun/s INDEX A Aberration 400 chromatic 398 monochromatic 398 spherical 34 Acceleration 101, 167 angular 34 average 102 centripetal 36, 210 due to gravity variation in 214 34 instantaneous 142 of centre of mass 102 radial 101 tangential 419, 426 Accommodation 230 Amplitude Angle 362 of incidence 390 of minimum deviation 362 of reflection 362 of refraction 101, 167 Angular acceleration relation with torque 171 232 Angular frequency 174 Angular impulse 173 Angular momentum 101, 166 Angular position Angular simple harmonic motion 234 167 Angular speed 101 Angular velocity 167 of a rigid body 312, 337 Antinode 261 Archimedes' principle Aspirator pump 267 Astigmatism in images 400 427 in vision Atmosphere 260 pressure of unit of pressure 260 B Banking of roads Barometer Beats Bending of cyclist on a circular path Bernoulli equation of fluid flow Brahe, Tycho Brewster's law Bulk modulus Buoyancy 104 260 341 172 265 203 376 281 261 C Capillary, rise of liquid in Cavendish Centre of mass definition motion of 289 204 139 142 105 Centrifugal force Centripetal acceleration 102 Centripetal force 103 CGS unit Chromatic aberration 398, 400 Circular motion 101 Coefficient of kinetic friction 86 of restitution 148 of static friction 87 of viscosity 290 Coherent sources 335, 370 Collision 145 elastic 147 inelastic 147 Colour 361 Coma 399 Compressibility 281 Concave lens 394 mirror 385 Conservation of angular momentum 173 of energy 122 of linear momentum 144 Conservative forces 121 Contact angle 288 Continuity, equation of 264 Continuous spectra 437 Convex lens 394 mirror 385 Coulomb's law 57 Critical angle, in refraction 389 Critical velocity 293 Cross product 16 Curvature, in images 400 Cyclist, motion on a circular path 172 D Damped harmonic motion Decibel Diffraction by circular aperture by single slit by straight edge Fraunhofer Fresnel of light Of sound waves Dimension Dispersion angular without deviation Dispersive power Displacement Distortion in images Doppler effect Dot product 242 334 373 371 374 370 371, 373 370 342 434 434 435 434 32 400 343 15 Efflux, speed of Elastic collision Elastic limit Elastic potential energy Elasticity Electromagnetic force Energy conservation principle kinetic mechanical of a spring potential surface Equation of continuity Equilibrium neutral rotational stable unstable Erg Escape velocity Ether Eye 266 146 282 282 279 56, 57 122 118 122 125 122 286 264 172 172 172 172 217 361 419 F Farsightedness Field, gravitational Fizeau measuring speed of light Floatation Flow critical velocity equation of continuity irrotational lines of of a fluid Reynolds number steady streamline tube of Fluid flow of pressure in viscosity of Flux luminous radiant Focal length of a lens of a spherical mirror Focus of a lens of a spherical mirror Force centrifugal centripetal conservative due to contact due to spring electromagnetic frictional gravitational 426 210 444 445 261 293 264 264 263 263 293 263 263 264 263 258 290 449 449 394 386 394 385 56 105 103 121 58 58 57 58, 85 56, 204 Concepts of Physics 460 149 impulsive 70 inertial 122 nonconservative 58, 85 normal 59 nuclear 70 pseudo 168 torque of 59 weak 229 Force-constant 242 Forced oscillation Foucault, measuring speed of light 445 31 Frame of reference 65 inertial 65 noninertial 370 Fraunhofer diffraction 67 Free-body diagram 232 Frequency 334 and pitch of sound 232 angular 313, 338 fundamental 314 harmonic 313, 337 natural 314, 338 overtone 314 resonant 371, 373 Fresnel 369 biprism 371 diffraction 58 Friction 85, 88 laws of kinetic 85 90 rolling 85, 87 static 365 Fringe 313, 338 Fundamental frequency G 424 Galilean telescope 438 Gamma ray Geometrical optics 362 Geostationary satellites 217 Gravitation, law of 56, 204 Gravitational constant G 204 Gravitational 210 field due to a point mass 211 due to a sphere 213 due to a spherical shell 212 218 mass potential due to a point mass 207 due to a sphere 209 due to a spherical shell 208 124, 206 potential energy 36, 210 Gravity, acceleration due to H Harmonic motion Hooke's law Horsepower Huygens construction of wavefront principle 229 280 119 360 363 362 363 and laws of reflection 364 and laws of refraction 258, 266 Hydrostatics 427 Hyperopia I 450 Illuminance 450 Illuminating power Image 398 defects of 386 virtual Impulse 149 of a force 174 of a torque 149 Impulsive force 361, 365 Index of refraction 146, 148 Inelastic collision 72 Inertia Inertial 70 force 65 frame 218 mass Instantaneous 34 acceleration 32 speed velocity 33 Intensity 334 and loudness of sound in double slit experiment 366 in single slit diffraction 372 of sound 333 Interference constructive 310 destructive 310 of light, double slit experiment 365 of sound 335 of waves 309 365 fringes from coherent sources 335 from thin films 368 International system of units Inverse square law in photometry 451 J Joule, unit of energy K Kelvin, unit of temperature Kepler's laws Kinematics Kinetic energy and work of a rotating body Kinetic friction 203, 217 31, 167 118 118 175, 182 85 L Lambert's cosine law Laser Lens concave converging 451 362 394 394 394 convex diverging maker's formula power of sign convention for Lenses in contact Light corpuscle theory of diffraction of interference of linearly polarized polarization of speed of unpolarized visible range wave theory of Line spectra Linear momentum Liquid pressure in flow of viscosity of Luminosity Luminous intensity 394 394 395 396 394 397 360 371 365 374 375 361, 444 375 361 360 437 144 258 263 290 449 450 M Magnification angular by a lens by a spherical mirror lateral transverse Magnifier Magnifying power of a compound microscope of a Galilean telescope of a simple microscope of a terrestrial telesceope of an astronomical telescope Malus, law of Mass centre of gravitational inertial Maxwell Mechanical energy Michelson, measuring speed of light Microscope compound simple Minimum deviation, angle of Mirror spherical Modes of vibration 314, Moment of inertia of a disc 176, of a hollow cylinder of a hollow sphere of a rectangular plate of a ring 176, of a rod of a solid cylinder of a solid sphere 421 395 388 388 388 420 422 425 421 424 423 375 139 218 218 360 122 447 421 420 390 385 337 171 180 177 177 176 179 176 177 178 461 Index Momentum angular conservation of angular conservation of linear linear Motion in a straight line in a plane of a cyclist on circular path oscillatory projectile with constant acceleration Musical scale Myopia 173 173 144 144 31 31 37 172 229 38 35 345 426 N 313, 337 Natural frequency 420 Near point 426 Nearsightedness Newton's corpuscle theory of light 360 Newton's law of gravitation 56, 204 Newton's laws of motion 64 first law 66 second law 56, 68 third law 312, 337 Nodes 122 Nonconservative forces 303 Nonmechanical waves 58, 85 Normal force Object real virtual Optical fibre Optical instrument Optical path Optics, geometrical Organ pipes Oscillation damped forced simple harmonic Overtones 386 386 389 419 367 385 337 229 242 242 229 314, 337 P 178 Parallel axes theorem 386 Paraxial rays Pascal 259 law of pressure 258 unit of pressure 367 Path, optical Pendulum 108 conical 237 physical 235 simple 235 time period of 237 torsional 179 Perpendicular axes theorem Phase difference in interference 309, 335, 365 Phase in SHM Photoelectric effect Photometer Photometry Physical pendulum Pitch Plane mirror Plane wave Planets and satellites Poisseuille equation Poisson's ratio Polarization of a wave Polarization of light Polaroids 121, Potential energy change in rigid body motion elastic 124, gravitational of a spring Potential, gravitational Power delivered by a force delivered by a torque horsepower transmitted by a wave unit of Presbyopia Pressure amplitude in sound wave atmospheric definition of excess, inside a drop excess, inside a soap bubble unit of variation with height Prism angle of minimum deviation Projectile horizontal range of maximum height of motion of time of flight of Proportional limit in elasticity Pseudo force 232 360 451 449 237 334 385 330 216 291 281 317 375 376 124 123 282 206 125 207 119 175 119 308 119 427 331 260 258 286 288 258 258 390 391 38 39 39 38 39 282 70 Q Quantities derived fundamental Quinke's apparatus 2 336 R Radial acceleration Radian Radiant flux Radius of curvature of spherical mirrors of thin lenses Radius of gyration Rainbow Range, of projectile Rayleigh criterion 102 449 385 393 180 440 39 374 Real image Real object Reflection and Huygens' principle of light, laws of 362, phase change at 336, Refraction and Huygens' principle at plane surface at spherical surface laws of Refractive index Resolution limit of Resolving power of a microscope of a telesceope Resonance 242, Restoring force Reynolds number Rigid body, rotation of Rigidity modulus Roemer, measuring speed of light Rolling Rolling friction Rotation angular acceleration angular velocity axis of kinematics of of a rigid body relation with torque 386 386 363 385 369 364 389 391 362 361 374 425 425 316 229 293 166 281 444 181 91 167 167 166 167 166 169 S Satellites geostationary motion of Scalar Scalar product SHM, see simple harmonic motion Shear modulus strain stress Sign convention for refraction at a spherical surface for spherical mirrors for thin lenses Significant digits Simple harmonic motion amplitude and circular motion angular angular frequency of characteristics of composition of two damped energy consideration in equation of frequency of phase of time period of SI units 217 216 12 15 281 280 279 392 386 394 21 229 230 233 234 232 231 238 242 233 230 232 232 231 462 Single slit, diffraction by 371 389 Snell's law 345 Sonic boom 316 Sonometer 329 Sound 329 audible frequencies 330 displacement wave 330 infrasonic 333 intensity of 335 interference of 334 loudness of Newton's formula for speed 332 334 pitch 330, pressure wave 335 quality of 331 speed of 339 speed determination in lab 336 standing waves 330 ultrasonic Spectrometer 438 436 Spectrum absorption 437 band 437 continuous 437 emission 437 infrared 438 line 437 pure and impure 436 ultraviolet 438 Speed average 32 instantaneous 32 of escape 217 Speed of light 60,361,444 Fizeau's method 444 Foucault's method 445 Michelson's method 447 Spherical aberration 398 Spherical mirror 385 Spring-force 58 Spring potential energy of 125 Standing wave 311, 336 Static friction 85,87 Stationary wave 311,336 in an organ pipe 337 on a string 314 Stokes' law 291 Strain 280 Streamline 263 Stress 279 Strings, vibration of 314 Superposition of waves 309 Surface energy 286 Surface of a liquid 284 Surface tension 284 excess pressure due to 286 Concepts of Physics T Telescope astronomical Galilean terrestrial Tension Terminal velocity Thin film, interference from Thin lens Time period of SHM of simple pendulum Torque about a line about a point and angular acceleration and angular momentum of a force of several forces Torricelli Torsional constant Torsional modulus Torsional pendulum Total internal reflection Tube of flow Turbulent flow Tycho Brahe Vision, defects of 423 423 424 424 58, 68 292 368 394 229 231 235 169 169 169 171 174 169 170 260 237 281 237 389 263 263 203 U Ultrasonic sound Uniform circular motion Units, SI 330 102 V Variable mass system, motion of rocket Vector addition of component of a scalar product vector product Velocity average instantaneous of escape Venturi tube Vibration of air columns Vibration of string laws of normal mode Virtual image Virtual object Viscosity 144 12 13 14 15 16 33 33 33 217 267 337 314 316 315 386 386 290 - 426 W Watt 119 Wave difference between travelling and standing 312 diffraction of 342 displacement 330 equation of 304 interference of 309 mechanical 303 motion 303 nonlinear 309 nonmechanical 303, 308 plane 330 polarization of 317 power transmitted in 308 pressure 330 progressive 304 pulse on string 304 reflection of 310 reflection of sound 336 sinusoidal 305 sound 330 speed of sound 331 speed on string 307 spherical 330 standing 311, 336 stationary 311, 336 superposition of 309 transmission of 310 transverse and longitudinal 318 travelling 304 velocity on string 307 Wavefront 330, 362 Weightlessness 217 Work 118 by constant force 119 by internal forces 121 by gravitational force 119 by spring-force 119 Work-energy theorem 118 X X-ray 438 Y Young, Thomas Young's double hole experiment Young's double slit experiment Young's modulus determination in laboratory 360 365 365 280 283 ... dimensions of : (a) volume of a cube of edge a, (b) volume of a sphere of radius a, (c) the ratio of the volume of a cube of edge a to the volume of a sphere of radius a ? Introduction to Physics. .. get the order of magnitude of that 10 number Thus, the diameter of the sun is of the order of 10 m and that of a hydrogen atom is of the order of 10-10m More precisely, the exponent of 10 in such... quantities 1.7 ORDER OF MAGNITUDE In physics, we coma across quantities which vary over a wide range We talk of the size of a mountain and the size of the tip of a pin We talk of the mass of our galaxy