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6490-6493
A transmitting antenna can most efficiently radiate waves having a wavelength of about the same size as the antenna Visible radiation emitted by atoms is, however, much longer in wavelength than atomic size 3 Infrared waves, with frequencies lower than those of visible light, vibrate not only the electrons, but entire atoms or molecules of a substance
1
6491-6494
Visible radiation emitted by atoms is, however, much longer in wavelength than atomic size 3 Infrared waves, with frequencies lower than those of visible light, vibrate not only the electrons, but entire atoms or molecules of a substance This vibration increases the internal energy and consequently, the temperature of the substance
1
6492-6495
3 Infrared waves, with frequencies lower than those of visible light, vibrate not only the electrons, but entire atoms or molecules of a substance This vibration increases the internal energy and consequently, the temperature of the substance This is why infrared waves are often called heat waves
1
6493-6496
Infrared waves, with frequencies lower than those of visible light, vibrate not only the electrons, but entire atoms or molecules of a substance This vibration increases the internal energy and consequently, the temperature of the substance This is why infrared waves are often called heat waves 4
1
6494-6497
This vibration increases the internal energy and consequently, the temperature of the substance This is why infrared waves are often called heat waves 4 The centre of sensitivity of our eyes coincides with the centre of the wavelength distribution of the sun
1
6495-6498
This is why infrared waves are often called heat waves 4 The centre of sensitivity of our eyes coincides with the centre of the wavelength distribution of the sun It is because humans have evolved with visions most sensitive to the strongest wavelengths from the sun
1
6496-6499
4 The centre of sensitivity of our eyes coincides with the centre of the wavelength distribution of the sun It is because humans have evolved with visions most sensitive to the strongest wavelengths from the sun EXERCISES 8
1
6497-6500
The centre of sensitivity of our eyes coincides with the centre of the wavelength distribution of the sun It is because humans have evolved with visions most sensitive to the strongest wavelengths from the sun EXERCISES 8 1 Figure 8
1
6498-6501
It is because humans have evolved with visions most sensitive to the strongest wavelengths from the sun EXERCISES 8 1 Figure 8 5 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5
1
6499-6502
EXERCISES 8 1 Figure 8 5 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5 0 cm
1
6500-6503
1 Figure 8 5 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5 0 cm The capacitor is being charged by an external source (not shown in the figure)
1
6501-6504
5 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5 0 cm The capacitor is being charged by an external source (not shown in the figure) The charging current is constant and equal to 0
1
6502-6505
0 cm The capacitor is being charged by an external source (not shown in the figure) The charging current is constant and equal to 0 15A
1
6503-6506
The capacitor is being charged by an external source (not shown in the figure) The charging current is constant and equal to 0 15A (a) Calculate the capacitance and the rate of change of potential difference between the plates
1
6504-6507
The charging current is constant and equal to 0 15A (a) Calculate the capacitance and the rate of change of potential difference between the plates (b) Obtain the displacement current across the plates
1
6505-6508
15A (a) Calculate the capacitance and the rate of change of potential difference between the plates (b) Obtain the displacement current across the plates (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor
1
6506-6509
(a) Calculate the capacitance and the rate of change of potential difference between the plates (b) Obtain the displacement current across the plates (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor Explain
1
6507-6510
(b) Obtain the displacement current across the plates (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor Explain FIGURE 8
1
6508-6511
(c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor Explain FIGURE 8 5 8
1
6509-6512
Explain FIGURE 8 5 8 2 A parallel plate capacitor (Fig
1
6510-6513
FIGURE 8 5 8 2 A parallel plate capacitor (Fig 8
1
6511-6514
5 8 2 A parallel plate capacitor (Fig 8 6) made of circular plates each of radius R = 6
1
6512-6515
2 A parallel plate capacitor (Fig 8 6) made of circular plates each of radius R = 6 0 cm has a capacitance C = 100 pF
1
6513-6516
8 6) made of circular plates each of radius R = 6 0 cm has a capacitance C = 100 pF The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s–1
1
6514-6517
6) made of circular plates each of radius R = 6 0 cm has a capacitance C = 100 pF The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s–1 Rationalised 2023-24 Physics 214 (a) What is the rms value of the conduction current
1
6515-6518
0 cm has a capacitance C = 100 pF The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s–1 Rationalised 2023-24 Physics 214 (a) What is the rms value of the conduction current (b) Is the conduction current equal to the displacement current
1
6516-6519
The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s–1 Rationalised 2023-24 Physics 214 (a) What is the rms value of the conduction current (b) Is the conduction current equal to the displacement current (c) Determine the amplitude of B at a point 3
1
6517-6520
Rationalised 2023-24 Physics 214 (a) What is the rms value of the conduction current (b) Is the conduction current equal to the displacement current (c) Determine the amplitude of B at a point 3 0 cm from the axis between the plates
1
6518-6521
(b) Is the conduction current equal to the displacement current (c) Determine the amplitude of B at a point 3 0 cm from the axis between the plates FIGURE 8
1
6519-6522
(c) Determine the amplitude of B at a point 3 0 cm from the axis between the plates FIGURE 8 6 8
1
6520-6523
0 cm from the axis between the plates FIGURE 8 6 8 3 What physical quantity is the same for X-rays of wavelength 10–10 m, red light of wavelength 6800 Å and radiowaves of wavelength 500m
1
6521-6524
FIGURE 8 6 8 3 What physical quantity is the same for X-rays of wavelength 10–10 m, red light of wavelength 6800 Å and radiowaves of wavelength 500m 8
1
6522-6525
6 8 3 What physical quantity is the same for X-rays of wavelength 10–10 m, red light of wavelength 6800 Å and radiowaves of wavelength 500m 8 4 A plane electromagnetic wave travels in vacuum along z-direction
1
6523-6526
3 What physical quantity is the same for X-rays of wavelength 10–10 m, red light of wavelength 6800 Å and radiowaves of wavelength 500m 8 4 A plane electromagnetic wave travels in vacuum along z-direction What can you say about the directions of its electric and magnetic field vectors
1
6524-6527
8 4 A plane electromagnetic wave travels in vacuum along z-direction What can you say about the directions of its electric and magnetic field vectors If the frequency of the wave is 30 MHz, what is its wavelength
1
6525-6528
4 A plane electromagnetic wave travels in vacuum along z-direction What can you say about the directions of its electric and magnetic field vectors If the frequency of the wave is 30 MHz, what is its wavelength 8
1
6526-6529
What can you say about the directions of its electric and magnetic field vectors If the frequency of the wave is 30 MHz, what is its wavelength 8 5 A radio can tune in to any station in the 7
1
6527-6530
If the frequency of the wave is 30 MHz, what is its wavelength 8 5 A radio can tune in to any station in the 7 5 MHz to 12 MHz band
1
6528-6531
8 5 A radio can tune in to any station in the 7 5 MHz to 12 MHz band What is the corresponding wavelength band
1
6529-6532
5 A radio can tune in to any station in the 7 5 MHz to 12 MHz band What is the corresponding wavelength band 8
1
6530-6533
5 MHz to 12 MHz band What is the corresponding wavelength band 8 6 A charged particle oscillates about its mean equilibrium position with a frequency of 10 9 Hz
1
6531-6534
What is the corresponding wavelength band 8 6 A charged particle oscillates about its mean equilibrium position with a frequency of 10 9 Hz What is the frequency of the electromagnetic waves produced by the oscillator
1
6532-6535
8 6 A charged particle oscillates about its mean equilibrium position with a frequency of 10 9 Hz What is the frequency of the electromagnetic waves produced by the oscillator 8
1
6533-6536
6 A charged particle oscillates about its mean equilibrium position with a frequency of 10 9 Hz What is the frequency of the electromagnetic waves produced by the oscillator 8 7 The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0 = 510 nT
1
6534-6537
What is the frequency of the electromagnetic waves produced by the oscillator 8 7 The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0 = 510 nT What is the amplitude of the electric field part of the wave
1
6535-6538
8 7 The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0 = 510 nT What is the amplitude of the electric field part of the wave 8
1
6536-6539
7 The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0 = 510 nT What is the amplitude of the electric field part of the wave 8 8 Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is n = 50
1
6537-6540
What is the amplitude of the electric field part of the wave 8 8 Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is n = 50 0 MHz
1
6538-6541
8 8 Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is n = 50 0 MHz (a) Determine, B0,w, k, and l
1
6539-6542
8 Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is n = 50 0 MHz (a) Determine, B0,w, k, and l (b) Find expressions for E and B
1
6540-6543
0 MHz (a) Determine, B0,w, k, and l (b) Find expressions for E and B 8
1
6541-6544
(a) Determine, B0,w, k, and l (b) Find expressions for E and B 8 9 The terminology of different parts of the electromagnetic spectrum is given in the text
1
6542-6545
(b) Find expressions for E and B 8 9 The terminology of different parts of the electromagnetic spectrum is given in the text Use the formula E = hn (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum
1
6543-6546
8 9 The terminology of different parts of the electromagnetic spectrum is given in the text Use the formula E = hn (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation
1
6544-6547
9 The terminology of different parts of the electromagnetic spectrum is given in the text Use the formula E = hn (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation 8
1
6545-6548
Use the formula E = hn (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation 8 10 In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2
1
6546-6549
In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation 8 10 In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2 0 × 1010 Hz and amplitude 48 V m–1
1
6547-6550
8 10 In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2 0 × 1010 Hz and amplitude 48 V m–1 (a) What is the wavelength of the wave
1
6548-6551
10 In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2 0 × 1010 Hz and amplitude 48 V m–1 (a) What is the wavelength of the wave (b) What is the amplitude of the oscillating magnetic field
1
6549-6552
0 × 1010 Hz and amplitude 48 V m–1 (a) What is the wavelength of the wave (b) What is the amplitude of the oscillating magnetic field (c) Show that the average energy density of the E field equals the average energy density of the B field
1
6550-6553
(a) What is the wavelength of the wave (b) What is the amplitude of the oscillating magnetic field (c) Show that the average energy density of the E field equals the average energy density of the B field [c = 3 × 108 m s–1
1
6551-6554
(b) What is the amplitude of the oscillating magnetic field (c) Show that the average energy density of the E field equals the average energy density of the B field [c = 3 × 108 m s–1 ] Rationalised 2023-24
9
1-4
Chapter Nine RAY OPTICS AND OPTICAL INSTRUMENTS 9 1 INTRODUCTION Nature has endowed the human eye (retina) with the sensitivity to detect electromagnetic waves within a small range of the electromagnetic spectrum Electromagnetic radiation belonging to this region of the spectrum (wavelength of about 400 nm to 750 nm) is called light It is mainly through light and the sense of vision that we know and interpret the world around us
9
2-5
1 INTRODUCTION Nature has endowed the human eye (retina) with the sensitivity to detect electromagnetic waves within a small range of the electromagnetic spectrum Electromagnetic radiation belonging to this region of the spectrum (wavelength of about 400 nm to 750 nm) is called light It is mainly through light and the sense of vision that we know and interpret the world around us There are two things that we can intuitively mention about light from common experience
9
3-6
Electromagnetic radiation belonging to this region of the spectrum (wavelength of about 400 nm to 750 nm) is called light It is mainly through light and the sense of vision that we know and interpret the world around us There are two things that we can intuitively mention about light from common experience First, that it travels with enormous speed and second, that it travels in a straight line
9
4-7
It is mainly through light and the sense of vision that we know and interpret the world around us There are two things that we can intuitively mention about light from common experience First, that it travels with enormous speed and second, that it travels in a straight line It took some time for people to realise that the speed of light is finite and measurable
9
5-8
There are two things that we can intuitively mention about light from common experience First, that it travels with enormous speed and second, that it travels in a straight line It took some time for people to realise that the speed of light is finite and measurable Its presently accepted value in vacuum is c = 2
9
6-9
First, that it travels with enormous speed and second, that it travels in a straight line It took some time for people to realise that the speed of light is finite and measurable Its presently accepted value in vacuum is c = 2 99792458 × 108 m s–1
9
7-10
It took some time for people to realise that the speed of light is finite and measurable Its presently accepted value in vacuum is c = 2 99792458 × 108 m s–1 For many purposes, it suffices to take c = 3 × 108 m s–1
9
8-11
Its presently accepted value in vacuum is c = 2 99792458 × 108 m s–1 For many purposes, it suffices to take c = 3 × 108 m s–1 The speed of light in vacuum is the highest speed attainable in nature
9
9-12
99792458 × 108 m s–1 For many purposes, it suffices to take c = 3 × 108 m s–1 The speed of light in vacuum is the highest speed attainable in nature The intuitive notion that light travels in a straight line seems to contradict what we have learnt in Chapter 8, that light is an electromagnetic wave of wavelength belonging to the visible part of the spectrum
9
10-13
For many purposes, it suffices to take c = 3 × 108 m s–1 The speed of light in vacuum is the highest speed attainable in nature The intuitive notion that light travels in a straight line seems to contradict what we have learnt in Chapter 8, that light is an electromagnetic wave of wavelength belonging to the visible part of the spectrum How to reconcile the two facts
9
11-14
The speed of light in vacuum is the highest speed attainable in nature The intuitive notion that light travels in a straight line seems to contradict what we have learnt in Chapter 8, that light is an electromagnetic wave of wavelength belonging to the visible part of the spectrum How to reconcile the two facts The answer is that the wavelength of light is very small compared to the size of ordinary objects that we encounter commonly (generally of the order of a few cm or larger)
9
12-15
The intuitive notion that light travels in a straight line seems to contradict what we have learnt in Chapter 8, that light is an electromagnetic wave of wavelength belonging to the visible part of the spectrum How to reconcile the two facts The answer is that the wavelength of light is very small compared to the size of ordinary objects that we encounter commonly (generally of the order of a few cm or larger) In this situation, as you will learn in Chapter 10, a light wave can be considered to travel from one point to another, along a straight line joining Rationalised 2023-24 Physics 222 FIGURE 9
9
13-16
How to reconcile the two facts The answer is that the wavelength of light is very small compared to the size of ordinary objects that we encounter commonly (generally of the order of a few cm or larger) In this situation, as you will learn in Chapter 10, a light wave can be considered to travel from one point to another, along a straight line joining Rationalised 2023-24 Physics 222 FIGURE 9 1 The incident ray, reflected ray and the normal to the reflecting surface lie in the same plane
9
14-17
The answer is that the wavelength of light is very small compared to the size of ordinary objects that we encounter commonly (generally of the order of a few cm or larger) In this situation, as you will learn in Chapter 10, a light wave can be considered to travel from one point to another, along a straight line joining Rationalised 2023-24 Physics 222 FIGURE 9 1 The incident ray, reflected ray and the normal to the reflecting surface lie in the same plane FIGURE 9
9
15-18
In this situation, as you will learn in Chapter 10, a light wave can be considered to travel from one point to another, along a straight line joining Rationalised 2023-24 Physics 222 FIGURE 9 1 The incident ray, reflected ray and the normal to the reflecting surface lie in the same plane FIGURE 9 2 The Cartesian Sign Convention
9
16-19
1 The incident ray, reflected ray and the normal to the reflecting surface lie in the same plane FIGURE 9 2 The Cartesian Sign Convention them
9
17-20
FIGURE 9 2 The Cartesian Sign Convention them The path is called a ray of light, and a bundle of such rays constitutes a beam of light
9
18-21
2 The Cartesian Sign Convention them The path is called a ray of light, and a bundle of such rays constitutes a beam of light In this chapter, we consider the phenomena of reflection, refraction and dispersion of light, using the ray picture of light
9
19-22
them The path is called a ray of light, and a bundle of such rays constitutes a beam of light In this chapter, we consider the phenomena of reflection, refraction and dispersion of light, using the ray picture of light Using the basic laws of reflection and refraction, we shall study the image formation by plane and spherical reflecting and refracting surfaces
9
20-23
The path is called a ray of light, and a bundle of such rays constitutes a beam of light In this chapter, we consider the phenomena of reflection, refraction and dispersion of light, using the ray picture of light Using the basic laws of reflection and refraction, we shall study the image formation by plane and spherical reflecting and refracting surfaces We then go on to describe the construction and working of some important optical instruments, including the human eye
9
21-24
In this chapter, we consider the phenomena of reflection, refraction and dispersion of light, using the ray picture of light Using the basic laws of reflection and refraction, we shall study the image formation by plane and spherical reflecting and refracting surfaces We then go on to describe the construction and working of some important optical instruments, including the human eye 9
9
22-25
Using the basic laws of reflection and refraction, we shall study the image formation by plane and spherical reflecting and refracting surfaces We then go on to describe the construction and working of some important optical instruments, including the human eye 9 2 REFLECTION OF LIGHT BY SPHERICAL MIRRORS We are familiar with the laws of reflection
9
23-26
We then go on to describe the construction and working of some important optical instruments, including the human eye 9 2 REFLECTION OF LIGHT BY SPHERICAL MIRRORS We are familiar with the laws of reflection The angle of reflection (i
9
24-27
9 2 REFLECTION OF LIGHT BY SPHERICAL MIRRORS We are familiar with the laws of reflection The angle of reflection (i e
9
25-28
2 REFLECTION OF LIGHT BY SPHERICAL MIRRORS We are familiar with the laws of reflection The angle of reflection (i e , the angle between reflected ray and the normal to the reflecting surface or the mirror) equals the angle of incidence (angle between incident ray and the normal)
9
26-29
The angle of reflection (i e , the angle between reflected ray and the normal to the reflecting surface or the mirror) equals the angle of incidence (angle between incident ray and the normal) Also that the incident ray, reflected ray and the normal to the reflecting surface at the point of incidence lie in the same plane (Fig
9
27-30
e , the angle between reflected ray and the normal to the reflecting surface or the mirror) equals the angle of incidence (angle between incident ray and the normal) Also that the incident ray, reflected ray and the normal to the reflecting surface at the point of incidence lie in the same plane (Fig 9
9
28-31
, the angle between reflected ray and the normal to the reflecting surface or the mirror) equals the angle of incidence (angle between incident ray and the normal) Also that the incident ray, reflected ray and the normal to the reflecting surface at the point of incidence lie in the same plane (Fig 9 1)
9
29-32
Also that the incident ray, reflected ray and the normal to the reflecting surface at the point of incidence lie in the same plane (Fig 9 1) These laws are valid at each point on any reflecting surface whether plane or curved
9
30-33
9 1) These laws are valid at each point on any reflecting surface whether plane or curved However, we shall restrict our discussion to the special case of curved surfaces, that is, spherical surfaces
9
31-34
1) These laws are valid at each point on any reflecting surface whether plane or curved However, we shall restrict our discussion to the special case of curved surfaces, that is, spherical surfaces The normal in this case is to be taken as normal to the tangent to surface at the point of incidence
9
32-35
These laws are valid at each point on any reflecting surface whether plane or curved However, we shall restrict our discussion to the special case of curved surfaces, that is, spherical surfaces The normal in this case is to be taken as normal to the tangent to surface at the point of incidence That is, the normal is along the radius, the line joining the centre of curvature of the mirror to the point of incidence
9
33-36
However, we shall restrict our discussion to the special case of curved surfaces, that is, spherical surfaces The normal in this case is to be taken as normal to the tangent to surface at the point of incidence That is, the normal is along the radius, the line joining the centre of curvature of the mirror to the point of incidence We have already studied that the geometric centre of a spherical mirror is called its pole while that of a spherical lens is called its optical centre
9
34-37
The normal in this case is to be taken as normal to the tangent to surface at the point of incidence That is, the normal is along the radius, the line joining the centre of curvature of the mirror to the point of incidence We have already studied that the geometric centre of a spherical mirror is called its pole while that of a spherical lens is called its optical centre The line joining the pole and the centre of curvature of the spherical mirror is known as the principal axis
9
35-38
That is, the normal is along the radius, the line joining the centre of curvature of the mirror to the point of incidence We have already studied that the geometric centre of a spherical mirror is called its pole while that of a spherical lens is called its optical centre The line joining the pole and the centre of curvature of the spherical mirror is known as the principal axis In the case of spherical lenses, the principal axis is the line joining the optical centre with its principal focus as you will see later
9
36-39
We have already studied that the geometric centre of a spherical mirror is called its pole while that of a spherical lens is called its optical centre The line joining the pole and the centre of curvature of the spherical mirror is known as the principal axis In the case of spherical lenses, the principal axis is the line joining the optical centre with its principal focus as you will see later 9
9
37-40
The line joining the pole and the centre of curvature of the spherical mirror is known as the principal axis In the case of spherical lenses, the principal axis is the line joining the optical centre with its principal focus as you will see later 9 2
9
38-41
In the case of spherical lenses, the principal axis is the line joining the optical centre with its principal focus as you will see later 9 2 1 Sign convention To derive the relevant formulae for reflection by spherical mirrors and refraction by spherical lenses, we must first adopt a sign convention for measuring distances