2019 fizbook 2

1

CHAPTER 1 : Electrostatics

 Electrostatics refers to the study of charge at rest. The unit of force is Newton (N). The system, which
Charge exists in the form of electron, proton or
atom of more / less electron (known as ion). consists of a test charge and only one point
charge, is called the ‘system of a point
A neutral atom has the same number of electron charge’.
and proton. This neutral atom can become a
charge, Q when it receives electrons (becoming a  If the test charge, q interacts with as many as N
negative charge) or donates its electrons point charge, then there are also N individual force
(becoming a positive charge). will interact upon q. Consequently, q will

negative charge experiences a single net force named the resultant
(electron)
force, FT which represented by the formula of
positive charge magnitude :
(proton)
 FT = Fx 2  Fy 2
 There are 4 basic properties of charge:
o there are 2 types of elementary charge, i.e.  and the formula of direction :
electron, q = e (negatively charge) and proton,
q = p (positively charge).  = tan-1   Fy 
o there are interactions between charges (2 like  Fx
charges repel each other while 2 different
charges attract each other). This system, which consists of a test charge and
o charge obeys the principle of conservation. more than one point charge, is called the ‘system
o charge is quantized (the value of charge is of point charges’.
discrete through a relationship of Q = Nq with
N = multiple factor and q = magnitude of basic  Electric field, E refers to the 3D space around a
charge, i.e. 1.6x10-19 ‘point charge’ where electrostatic force can be
C). experienced. The magnitude of electric field
around a point charge is represented by:
 Under this topic, 4 physical quantities will be E = kQ/r2
studied regarding to charge, i.e. electrostatic force
(F), electric field (E), electric potential energy (U) where r = the distance between the point charge to
and electric potential (V). a referred point in the field.

 Interaction between charges is caused by The unit of electric field is NC-1 or also can be
electrostatic force, F. This force is too strong written as Vm-1. This system, which consists of
compared with the gravitational attractive force. only one point charge (without test charge), is
called the ‘system of a point charge’.
This force obeys the Coulomb’s law, which states
that: “2 charges will repel/ attract with a force
which directly proportional to the product of the
magnitude of charges and inversely proportional to
the square of the distance of the charges”.

Charge which is being investigated is called ‘the
test charge’, q while the charge which interacts
upon the test charge is named ‘the point charge
(or fixed charge)’, Q.

Force between the test charge and each point
charge is called the ‘individual force’ with formula:

F = kQq/r2
where k = 9.0x109Nm2C-2

r = distance between the two charges.

2

Electric field is a vector quantity where the
direction for positively point charge is forming a
pattern directed outwards from the charge, while
for negatively point charge directed inwards to the
charge.

Besides, the patterns of electric field for  Electric potential energy, U refers to the work
done/ required to bring a test charge, q from
combinations of point charges are also being infinity to a point around a point charge, Q.

studied such as: The magnitude the potential energy (work done) at
o combination of 2 like charges (identical and the point is represented by:

non-identical magnitudes), U = kQq/r
o 2 different charges (identical and non-identical
where r = distance between the point charge to the
magnitudes), referred point.
o 2 parallel plates.
The system, which consists of a test charge and
The strength of electric field graphically shows by only one point charge, is called the ‘system of a
the number of line. The greater the number of line, point charge’. The unit of the potential energy is
the stronger the electric field is. Joule (J).

 If a point experiences as many as N electric fields

(which are produced by as many as N point

charges), then the point will experiences a net

electric field called the resultant electric field which

represented by the formula of magnitude :

 ET = Ex 2  Ey 2

and the formula of direction :

 = tan-1  Ey 
Ex

Electric potential energy is a scalar quantity where
the positive sign indicates that the work is done
upon the test charge, while the negative sign
indicates that the work is done by the test charge.

and for sure this system, which consists of more  If the point is surrounded by as many as N point
than one point charges (without test charge), is charges, then a net value of potential energy (total
called the ‘system of point work done/ needed by a test charge) must be
charges’. calculated through the formula of :

 Based on the concept, actually the test charge, q U = k qo  Q1  Q2  Q3  .... 
only experiences the electrostatic force, F r1 r2 r3
because it is located in the electric field of the
‘point charge’, Q through relationship: and for sure this system, which consists of more
F = qE than one point charges (within test charge), is
called the ‘system of point
It means that, without electric field, the charges’.
electrostatic force will never be produced.
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 A ‘test charge’, q that moves perpendicularly to
uniform electric field (which is produced by 2
parallel plates) will undergo projectile motion
towards the plate of different type of charge.
However, if it moves parallel with the electric field,
a linear path will be made also towards the plate of
different type of
charge.

Electric potential, V refers to the work per unit Furthermore, two points of different distance from
charge to bring a test charge, q from infinity to a
point around a point charge, Q. A unit charge the point charge, Q surely has different magnitude
refers the charge of magnitude 1 C.
of electric potential. Then, the difference values is
The magnitude of electric potential (work per unit called ‘potential difference, or
charge) at the point is represented by:
voltage.
V = kQ/r
 If the point is surrounded by as many as N point
where r = distance between the referred point to charges, then a net value of electric potential (total
the point charge. work done/ needed per unit of test charge) must
be calculated through the formula of :
The system, which consists of only one point
charge (without test charge), is called the ‘system V = k  Q1  Q2  Q3  .... 
of a point charge’. The unit of electric potential is r1 r2 r3
JC-1 or volt (V).
and for sure this system, which consists of more
The electric potential is a scalar quantity which
can be related with the electric potential energy than one point charges (without test charge), is
by: called the ‘system of point charges’. The
equipotential surface of this system do also exist
V = U/q but no longer in the spherical shape (depends on

 Moreover, all points around the point charge with the system itself).
the same distance from the charge have the same
value of electric potential.

If a line/ surface is drawn to join all the points, then
a spherical area (surface) is formed. This surface
is known as the ‘equipotential surface’. It means
that, to transfer a test charge from one to any
other point within the surface, the work done is
zero.

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CHAPTER 2 : Capacitors & Dielectrics

 Capacitor is one of various electronic devices in In application, capacitance, C can be related with
an electric circuit. Basically, it consists of two potential difference across the capacitor, V and
conducting plates separated by an insulator known charge accumulated on the plate, Q through a
as dielectric material. Figure 1 shows a schematic relationship:
diagram of the symbol respectively neutral and
charged capacitor. C = Q/V

Figure 1 : +Q +  In an electric circuit, if there are more than one
capacitor, all of them can be connected through
- -Q three ways, either connected in :
 series,
Neutral capacitor V  parallel, or
 combination of series-parallel.
Charged capacitor
 For series and parallel connections, two
There are various types of capacitor but in this information must be known:
topic investigation only made upon the parallel o sketching the circuit including the voltage
plate capacitor. supplied and connection of all capacitors and
how to simplified into effective circuit,
 In this topic, based on the conceptual provided, 5 o three formula related that are the ‘effective
fields are being studied regarding to capacitor: capacitance’ CT , total charge QT as well as
o the property of capacitor known as the total voltage VT (refer Figure 2).
capacitance C,
o types of connection of capacitors in a circuit,  When a neutral capacitor is charged, negatively
o energy stored in a charged capacitor, charges (electrons) will transfer from one of the
o processes performed by a capacitor, plate (which is connected to the positive terminal
o the role played by the dielectric materials. of a dry cell) to the other plate.

 The main use of capacitor in the circuit is to store Consequently, the first plate will has less electrons
charges, Q on each plate. The quantity (becoming positively plate) while the second plate
(magnitude) of charge on each plate is the same will has more electrons (becoming negatively
but has different sign. plate).

These charges (brought by electrons from one This transformation leads to the production of the
plate to another) are stored during charging electric potential difference, V as well as the
process due to potential difference, V (supplied by electric field, E between the plates. At this time,
voltage of a dry cell/ power supply) across the the capacitor is said having the electric potential
plates. energy (in the form of electric field). The energy if
formulated by:
For every 1 unit of voltage (1 V) supplied, the
ability of a capacitor to store charge depends on U = ½ CV2
its physical property known as capacitance, C.
and exist as long as the electric field exist between
The magnitude of capacitance is fix (constant) and the plates.
depends on the physical conditions of the
capacitor. The magnitude of capacitance of a  Charging process refers to a process where a
parallel plate capacitor is represented by: neutral capacitor accumulates charge. Electrons at
one of the plate are transferring to the other plate.
C = A/d Discharging process refers to a process where a
charged capacitor reduces the charge (returns the
where A = area of each plate, electrons to the original plate). For each of the
d = separation between the 2 parallel process, four information must be known:
plates, o sketch of circuit diagram,
 = or o graphs (I vs t and Q vs t),
o equations (I and Q),
with o = 8.85x10-12C2N-1m-2 and r @  = o the time constant (refer FIGURE 3).
dielectric constant (depends on the type of
dielectric material).

5

 Time constant,  refers to the time taken by the more charge (increase the magnitude of
capacitor to store 63% of its maximum charge capacitance).
during charging process or remain 37% of its
maximum charge during discharging. When a voltage is supplied across the capacitor,
the molecules of the dielectric material will be
There are two main uses of the time constant: polarized and then the magnitude effective electric
o as an indicator to determine the percentage of field across the capacitor decreases. The
decrease in the electric field will cause the electric
charge stored in the capacitor at certain time. potential decreases.
o to control the time taken of the process (a
Since the capacitor still connected to the dry cell,
measure of how quickly the capacitor charges then this potential difference must remain
or discharges) since this process cannot be constant. Therefore, more charge must be stored
observed by our naked eyes. on each plate of the capacitor. Hence, the new
ratio of the quantity of charge stored per unit
The time constant is controlled by using proper potential difference is grater and it means the
value of the capacitance, C as well as the capacitance of the capacitor is now upgraded.
resistance, R of the circuit through relationship of:
Moreover, the dielectric material has a property
 = RC called the ‘dielectric constant’,  or r. The
constant shows the multiple factor of the
 Dielectric material refers to an insulator which capacitance.
placed between the two conductor plates to built a
capacitor. The main use of the dielectric material
is to increase the ability of the capacitor to store

6

Figure 2 :
a) Series connection :

VT = V1 + V2 + V3 + … + Vn
QT = Q1 = Q2 = Q3 = … = Qn

1 = 1 + 1 + 1 +…+ 1
CT C1 C2 C3 Cn

b) Parallel connection :

V = V1 = V2 = V3 = … = Vn
QT = Q1 + Q2 + Q3 + … + Qn
CT = C1 + C2 + C3 + … + Cn

Figure 3 :

a) Charging Process :

I C R
V

mA

R

t

 Current flowing through the circuit, I  Ioe RC

 Charge stored in the capacitor, Q  Qo 1  e t 
RC 

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b) Discharging process :

V  

CR



R
mA

I

t

 Current flowing in the circuit, I  Ioe RC

t

 Charge remain stored in the capacitor, Q  Qoe RC

8

CHAPTER 3 : Electric Current & Direct Current (DC)

 An electric current, I is the orderly flow of  Resistor is a most popular component in a
electrons in a conductor, which is induced by DC circuit. It is made of a conductor and
an electrostatic field produced by a voltage. used to resist the movement of electrons.

 The electric current is equal to the ratio of
the charge, dq within a small period of time,
dt.
or I = dq
dt

If the magnitude and direction of the flow of
electric current do not change in time (known
as Direct Current (DC)), then:

I= Q
t

The direction of current flow is opposite of resistor symbol of resistor
that of electron flow.
 Metals are usually good conductors of Resistor has a property named ‘resistance,
electricity. In metal, there are many free R’ which measures the opposition to the flow
electrons moving randomly.
When a metal is connected to a voltage of current in the circuit. It is measured in
source, the electrons become accelerated in
the short distances between the collisions ohm, 
with the ions of the crystal lattice of the
metal. The magnitude of resistance, R while

During the collisions, their velocities change building a resistor depends on :
as part of their electric energy is transmitted  a constant depends on the types of
to the ions as heat. Then the electrons are
again accelerated and will again slow down material of the resistor called ‘resistivity,
as the result of collisions. ’.
The velocity of the electrons reaches a  length, l of the resistor.
permanent mean value vd known as the ‘drift  cross-sectional area, A of the resistor.
velocity’.
or R =  l 
A

When the resistor is applied in the circuit, it
obeys the Ohm’s law, which state that:
“At a given temperature, the current flowing
through a conductor is directly proportional
to the potential difference between the ends
of the conductor.”

VI
Or V = R I

The resistor which obeys the Ohm’s law is
called ‘ohmic resistor’, while ‘non-ohmic
resistor’ does not obey the Ohm’s law.

The change in temperature will affect the
rate of collision between these electrons and
the atoms in the conductor as well as the
resistance to the flow of the current.

9

The change of resistance, R is directly There are 2 main types of connection:
proportional to the change of temperature,  series.
T as well as the original value of the  parallel.
resistance, Ro.
or R = RoT  Resistors arranged in series :

where  = the temperature coefficient of  V = V1 + V2 + V3 + … + Vn
increase in the resistance.  I = I1 = I2 = I3 = … = In
 R = R1 + R2 + R3 + … + Rn
Note that this equation is valid for metal only.  Resistors arranged in parallel :
For semiconductor, if the temperature
increases, the resistance decreases. This is  V = V1 = V2 = V3 = … = Vn
because the number of free electron  IR = I1R1 = I2R2 = I3R3 = … = InRn
increases by the increase of temperature.  I = I1 + I2 + I3 + … + In

 Electrical energy, U can be transformed into   1    1    1    1   ...   1 
different types of energy, such as heat, light R  R1 R2 R3 Rn
or mechanical work. It is represented as:
U = VIt  In DC circuit, the uses of resistor are as

where V = potential difference across the follow:
load.  to control electric current (if the resistors

I = current flows through the load. are arranged in parallel).
t = time taken.  to distribute voltage (if the resistors are

The unit of electrical energy is joule, J. arranged in series).

 The rate of work performed (or energy used)
by the load is called the ‘electrical power’, P
and represented as:
P = VI

The unit of electrical power is watt, W.

 Direct current refers to electric current, which
has constant magnitude as well as direction
of current flow.

 Current flows from a point of higher potential
to another point of lower potential. This
potential difference is supplied and remained
by using a source (example: battery).

A battery is supplying the so-called
‘electromotive force (e.m.f.), ’. It refers to
the amount of energy per unit charge
(voltage) passing through the circuit. The
voltage produces electric field so that
electrons can be forced to move in one
direction to flow current.

The e.m.f,  can be formulated as:
 = I(R + r)

where I = current flows in circuit.
R = resistance in the circuit.
r = internal resistance of the battery.

 In DC circuit, if there are more than one
resistor, then the total resistance contributed
by all the resistance must be calculated. The
value is depending on the connection of the
resistors.

10

 Ohm’s law is used to analyze voltage and  In a DC circuit, there are also some types of
current is a circuit. However, it can be used if circuit design also to do measurement, such
the circuit consists of only one cell (battery). as:
 potentiometer :
 If the circuit consists of one cell or even - to determine internal resistance of
more than one cell, then the more flexible cell.
laws called ‘Kirrchoff’s laws’ are take place. - To determine e.m.f. of unknown cell.

I1 1 r1 VAP = VXY
 wheatstone bridge:
I3 R3
X - to determine the resistivity of resistor.
Y
I2 r2 R2 RX = Ra
2 R Rb

 It can be divided into two laws but must be

must together:
 Kirrchoff’s 1st law (or Kirrchoff’s current

law) states that:
“The algebraic sum of the current at a

junction of a circuit is zero, since electric
charges do not stay at a junction”.

 or Iin  Iout

 Kirrchoff’s 2nd law (or Kirrchoff’s voltage

drop law) states that:
“For a closed loop, the algebraic sum of

the voltages drops is equal to the
algebraic sum of the e.m.f.s.”

 or   IR

 In a DC circuit, there are some devices to do

measurement, such as:
 voltmeter (arranged in parallel to the

component) to measure voltage.
 ammeter (arranged in series to the

component) to measure current.

voltmeter ammeter

11

CHAPTER 4 : Magnetic Field

 Magnetic field, B refers to a three  There two types of magnetic force:
dimensional field (region) around a magnetic o Magnetic force due to moving charge
body or a current-carrying conductor where across the magnetic field, which
the force can be experienced.
represented as follow:
The magnetic field strength is called the F = qvB sin
‘magnetic flux density’. It is a vector quantity
with SI unit of Tesla, T. where q = magnitude of charge.
v = velocity of the particle.
Based on the above definition, there are two  = angle between the direction
main sources of magnetic field:
 magnet bar (directed North to South). of v and B
 current-carrying conductor (right hand

grip).

Earth has a week magnetic field caused by
the electrical current flowing in its core. It
directed from geographical South Pole to the
North.

Note that the charge is finally
undergoing circular motion.

 Pattern of magnetic field is represented by o Magnetic force due to current flows in a
the so-called ‘magnetic field lines’. The conductor across the magnetic field,
properties of the magnetic field lines: which represented as follow:
o The field lines never cross or split each F = ILB sin
other.
o There are no two or more of field lines at where I = magnitude of current
the same point. flowing through the
conductor.
 There is no specific equation of magnetic
field of a current-carrying conductor. The L = length of the conductor.
formula depends on the shape of the  = angle between the direction
conductor itself.
of I and B.
Example equations of magnetic field, B for
several symmetrical conductor are as follow: The direction of magnetic force can be
o Magnetic field at the centre of the coil determined by using ‘Fleming Left-Hand
Rule’.
with N turns and radius R :
B = oNI  If two long straight wire carrying current are
2R located side by side, interaction will happen
and described as follow:
o Magnetic field on the axis of a solenoid o If the currents flow in the same direction,
which has number of turns per meter, n: the wires will attract each other.
B = onI o If the currents flow in the opposite
direction, the wires will repel each other.
o Magnetic field at a long straight wire:
B = oI 12
2r

No matter what interaction it is, the This is the main working principle of a
magnitude of force per unit length is the galvanometer.
same:
 When a charge is moving across a uniform
F1 = F2 = I1L   oI2  magnetic field, then magnetic force will
2d produced which deflect the original direction
of the charge.

If the magnetic is large, then the charge will
undergo a circular motion and contributes
the centripetal force, FC.

Therefore, 1 Ampere is defined as : FC = FB
“The DC current which, when flowing
through two parallel infinitely long straight mv2
conductors of negligible circular cross-
section, placed one meter apart in free or qvB =
space, will produce a force of magnitude
2 x10-7 N on every meter of their lengths”. r

 If a current flows in a coil of N turns in a Therefore, the radius of the circle:
radial magnetic field, a pair of magnetic
forces produced and generate total constant mv
torque and represented as follow:
r=
  = NIAB
qB
where A = area of the coil.
and the period of the motion :

2m

T=

qB

Note : It shows that the period is not
depends on the velocity

13

CHAPTER 5 : Electromagnetic Induction

 In laboratory, experimentally shows that  There are two laws explaining the production
there is a magnetic field, B surrounding a of induced e.m.f :
current-carrying conductor. o Faraday’s law states that :
“The magnitude of the e.m.f. induced in
On the other hand, can a magnetic field a circuit is directly proportional to the
produces current in a conductor? Current rate of change of magnetic flux linkage
flows if there is electromotive force (e.m.f.). through the circuit.
or   d
E.m.f. normally supplied by a source (such dt
o Lenz’s law states that :
as battery, accumulator, power supply, ect.) “The induced current flow in such a
direction that is opposes the change that
Actually, e.m.f. not only supplied by a produces it.”
or  = -  d 
source. It also can be produced through a  dt 
process called ‘induction’. or  = - d (NBA cos)
dt
Electromagnetic induction refers to
Note :
phenomena, which occur when there is a  Induced e.m.f,  = -ve (against the

change in magnetic flux,  through a increment of d)
 Induced e.m.f,  = +ve (against the
conductor and thus produces the so-called
‘induced e.m.f.’ in the conductor. It leads to reduction of d)
the production of current named ‘induced
current’. The direction of induced current can be
determined by using ‘Right-Hand Grip’ rule.
 There are several phenomena which
induced e.m.f. is produced, such as:  Based on the general equation, the formula
o Relative motion between magnet bar of induced e.m.f. of above phenomena are
as follow:
and a coil. o Relative motion between magnet bar
o Interaction between two neighboring and a coil:
 = - NA cos dB 
circuits.  dt 
o The movement of a mobile straight rod where dB = Bf  Bi
dt t
with constant velocity v across a uniform

magnetic field.
o Revolution of a revolving rotor across a

uniform magnetic field.

The production of induced e.m.f in all above
phenomena is due to the rate change of
magnetic flux in the conductor.

 Magnetic field flux through an area A normal
to a magnetic field B is defined as :
 = NBA cos

where N = number of loop.
B = magnetic field strength.
A = area of surface.
 = angle between magnetic field

line and the normal line.

Thus, the change in the flux :
 = (NBA cos)

The flux is changed if at least one of the
factors changes.

The SI unit for magnetic flux is Tm2 or
normally known as Webber (Wb).

14

o Interaction between two neighboring  Inductor is an electronic device (in the form
circuits: of a coil or solenoid) which undergoes
 = - NA cos dB  induction and used to store energy.
 dt 
where dB = on  dI  symbol of inductor
dt  dt 
 Inductor has a constant value known as
o The movement of a mobile straight rod ‘inductance’. There are two types of
of length L with constant velocity v inductance:
across a uniform magnetic field:  self-inductance, L
 = -BLv  mutual inductance, M.

The SI unit of inductance is Henry, H.

 Self-inductance, L is the property of a coil or
solenoid which can induce an e.m.f. (named
back e.m.f.) in the component itself due to
the rate change of current (self-induction
process).

The back e.m.f is represented as follow:

 = - L dI 

 dt 

o Revolution of a revolving rotor across a The magnitude of the self-inductance, L
uniform magnetic field: depends on the form of the inductor:
 = NBAsin(t)  L in the form of a coil:

L = N

I
 L in the form of a solenoid:

L = on2lA

 During the process of building up the current,
self-induction would have taken place and
the applied external voltage would have
done work to overcome this self-induced
e.m.f. which opposes the applied voltage.

The work done represents the total energy
stored in the inductor as follow:

U = 1 LI2

2

The unit of energy is joule, J. This amount of
energy is stored by the inductor in the form
of magnetic field.

 Mutual induction is the process where an
e.m.f. is induced in a coil (or solenoid) when
the current in a neighboring coil (or solenoid)
is changing (Refer phenomenon 2).

15

 The induced e.m.f is represented as follow:  The magnitude of the mutual-inductance, M
depends on the form of the inductor:
 M in the form of a coil:

M2 = N22
I1

 M in the form of a solenoid:

M2 = oN1N2A
L1

2 = - M2 dI1 
dt

16

CHAPTER 6 : Geometrical Optics

 Optics refers to the field of study of light. Light is The position and the properties of image due to
one of seven groups of electromagnetic wave and these all types of surface can be determined by
has its own range of frequency that differs with using either the ray diagram or formula of
other e.m. waves. reflection:

 Why does the word ‘geometrical optics’ is used in 1/f = 1/u + 1/v
this topic? The word ‘geometrical optics’ is used
because in this topic two phenomena regarding to where f = focal length,
light (reflection and refraction) are studied with its u = object distance,
aim is to determine the properties of image v = image distance.
produced. One of the methods to determine the
properties is by using graphical method known as The magnification of image:
the ‘ray diagram’. To use this method, a geometry M = v/u.
set (such as metre rule, protractor and a pair of
compasses) because to draw the diagram, the  For convex mirror, three basic information must be
scale as well as the shape of the medium surfaces known:
must be drawn perfectly to make sure the position o all parallel incident rays which incident on the
of the image produced is exactly at the right place. convex mirror will be diverged.
o the focal point of the convex mirror is located
 There are three possible types of image property: behind the mirror which means that f is
o real-virtual, negatively assigned.
o upright-inverted, o the properties of image are fixed no matter
o magnified-diminished-same size as the where the object is located in front of the
object. convex mirror :
 virtual (located behind the mirror),
Beside graphical method, the properties of image  upright,
also can be determined by using mathematical  diminished.
method that based on formula (dependst on the
sign conventions). However, the position of the image does
depend on the object distant.
 Reflection of light refers to the return of all or part
of light rays when incident on the boundary of a normal
medium. The reflection of light happens on all line
types of media especially mirror. In order to
determine the properties of image due to C
reflection, two laws of reflection must be obeyed
especially if the ray diagram is used:  For concave mirror, three basic information must
o incident angle = reflected angle, be known:
o incident ray, reflected ray and normal line all o all parallel incident rays which incident on the
lie on the same plane. concave mirror will be converged.
o the focal point of the concave mirror is located
 To simplify the investigation of reflection, two in front the mirror which means that f is
types of mirror are studied : plane mirror and positively assigned.
spherical mirror (convex mirror and concave o the position and the properties of image are
mirror). variable and surely depend on the object
distance.

 Refraction of light refers to the change in the
direction suffered by wave front of light as it
passes obliquely from one medium to another in
which its speed of propagation is changed. The
refraction of light happens on all the transparent
media especially glass.

17

 In order to determine the properties of image due o the properties of image are fixed no matter
to refraction, two laws of refraction must be where the object is located in front of the
obeyed especially if the ray diagram is used: concave glass:
o incident ray, refracted ray and normal line all  virtual (located in front the glass),
lie on the same plane,  upright.
o ratio: However, the position of the image does
sin i / sin r = n2 / n1 = c / v = 1 / 2 depend on the object distant.

with n2 = refractive index of refracted  For convex glass, three basic information must be
medium, known:
o all parallel incident rays which incident on the
n1 = refractive index if incident convex glass will be converged.
medium. o the radius of curvature of the convex glass is
located behind the glass which means that r is
This statement is known as the ‘Snell’s law’. positively assigned.
o the position and the properties of image are
n2 > n1 n2 < n1 variable and surely depend on the object
distant.
The frequency of light never changed when
passing through different media.  Besides, the relationship between radius of
curvature and focal length is as follow :
 To simplify the investigation of refraction, three r = 2f
types of glass are studied: plane glass, single
spherical glasses (convex glass and concave  Thin lens refers to a glass consisting of two
glass) and thin lenses. surfaces where the thickness of the lens is
relatively small compared the radius of curvature
The position and the properties of image due to of the two surfaces.
these all types of surface (excluding thin lenses)
can be determined by using either the ray diagram There are several types of lens: biconvex lens,
or formula of refraction: biconcave lens, meniscus convex lens, meniscus
concave lens, plano-convex lens and plano-
n1/u + n2/v = (n2 – n1)/r concave lens.

where n1 = refractive index of the medium where Since a lens has two surfaces, the incident ray will
the object is located. undergo twice refraction. Every surface has
respective focal point. It seems that a lens has two
r = radius of curvature. focal points (and focal lengths). Therefore, the
actual focal length, f of the lens must be
 For plane glass, two basic information must be determined by using a special formula known as
the ‘lens maker’s equation’:
known:
o the radius of curvature of the plane mirror is 1/f = ((n2 / n1) – 1)(1/r1 + 1/r2)

located at infinity, which means that r = . where n2 = refractive index of the lens,
o the properties of image are fixed no matter n1 = refractive index of medium surround
the lens.
where the object is located in front of the
n1
plane mirror:
 virtual (located behind the mirror), n2
 upright.
Moreover, this formula also can be used to identify
However, the position of the image does the lens material. When the focal length of the lens
is determined, then the position as well as the
depend on the object distant. properties of the image can now be determined,
whether by using ray diagram or a formula known
 For concave glass, three basic information must as the ‘lens formula:
be known:
o all parallel incident rays which incident on the 1/f = 1/u + 1/v

concave glass will be diverged. with magnification, M = v/u
o the radius of curvature of the concave glass is

located in front the glass which means that r

is negatively assigned.

18

 For a system that consists of more than two
lenses, two process of refraction occurred. The
image produced by the 1st lens acts as the object
for the 2nd lens. The final magnification equals the
product of individual magnification of the both
lenses:
M = M1M2
where M1 = magnification by lens 1,
M2 = magnification by lens 2.

19

CHAPTER 2 : Physical Optics

 Optics refers to the field of study of light. Light is  The patterns of diffraction produced are also
one of seven groups of electromagnetic wave
and has its own range of frequency that differs depending on the setting of the optical devices
with other e.m. waves.
made. In this topic, 2 types of diffraction pattern
Why the word ‘physical optics’ is used in this
topic? The word ‘physical optics’ is used are studied respectively through
because in this topic, two more phenomena o a single slit,
related to light (that are interference and o a device called the ‘diffraction grating’.
diffraction) are being studied with its aim is to
draw and explain the patterns produced from And surely, for every case, 4 basic things must
that phenomena where the ‘physical’ property of
light, i.e. wave must be applied. be known:
o schematic diagram of the optical devices,
 Interference of light refers to a phenomenon o the drawing of the interference pattern,
occurred when two or more light waves o the pair of equation (for constructive @
overlapped in the same space. In order to
produce the pattern of interference, two maximum and destructive @ minimum),
conditions must be obeyed: o the explanations about the pattern.
o the waves must be coherent, which have
the same frequency (or wavelength) and These all information is summarized in TABLE
fixed phase different. 1 and FIGURE 2. Besides, the investigation on
o the principle of superposition is applied. the spectrum of light using a diffraction grating is
also made.
There are 2 types of interference:
o constructive interference (which is related  The phenomenon of diffraction also is relating to
the sharpness of an image. A sharp image is
to the bright image) that occurred if the two said to have high resolution. The resolution
waves are inphase. (sharpness) of an image depends on the
o destructive interference (which is related to spreading angle (or angle of diffraction),  of
the dark image that occurred if the two light which means that the diffraction with bigger
waves are antiphase.  will produce higher blur and thus producing an
image of less clear. This angle moreover, is
 The patterns of interference produced depend directly proportional to the magnitude of the
on the setting of the optical devices made. In wavelength,  of the light used. As a conclusion,
this topic, 4 types of interference pattern are a clearer image is coming from a shorter
studied respectively through the: wavelength of light.
o double slits,
o thin films of different media,  TABLE 2 below shows the main differences
o air wedge, between the pattern of interference and
o interference pattern known as the ‘Newton’s diffraction :
rings’.
Interference Diffraction
For every case, 4 basic things must be known :
o schematic diagram of the optical devices, The thickness of all The thickness between
o the drawing of the interference pattern, fringes is the same. bright and dark fringes
o the pair of equation (for constructive and is obviously different.
All bright fringes have The intensity is higher
destructive), the same level of for bright fringes that
o the explanations about the pattern. intensity.
are closer to the
These all information is summarized in TABLE centre.
1 and FIGURE 1. Besides, the changing upon
the pattern (such as the number of fringes
observed, the thickness of fringes, ect.) when
one of the physical factors is changed, is also
investigated.

 Diffraction of light (leads to make an image
unclear @ blur) refers to a phenomenon of the
spreading of light over its geometrical region as
they pass through an obstacle or an aperture
whose the size of which are comparable to its
wavelength (a  ). If the width of the aperture
(or slit) is wide enough (a >> ), then the
diffraction is said no happen.

20

FIGURE 1 : Schematic diagram of the setting of the optical devices & Interference patterns.

a) Young Double Slit : m m’

dQ 4 3
R
3 2

y 2
1 (2nd dark)
1
0 (1st dark)
0

O0
1

21

2

© Physics Teaching
Courseware

b) Thin Film : c) Air Wedge :

Thin film of m= 0 1 2 3 4 5 6 7 …
refractive index n
m' = 0 1 2 3 4 5 6 7 8 …
© Physics Teaching
Courseware 1st bright fringe

1st dark fringe

21

FIGURE 2 : Schematic diagram of the setting of the optical devices & Diffraction patterns.
a) Single Slit :

2 m=3
S2 m=2
m=1

b) Diffraction Grating : m=0 m=2
m=1 m=3
© Physics Teaching
Courseware

22

Table 1 : Formula for Interference and Diffraction

Apparatus Formula Pattern

Young Double Slit Bright Dark Symmetrical fringes.
Central bright fringe,
Thin Film mD m' 1 D
(1n2n1) ym = ym’ =  2 m = 0.

Thin Film d d Either bright or dark.
(1n2n3) where m = 0, 1, 2, … For dark, tmin refers to m = 1.
where m’ = 0, 1, 2, …
Single Slit Either bright or dark.
2nt = m  1  2nt = m’ For bright, tmin refers to
Diffraction Grating  2 where m’ = 0, 1, 2, …
m = 1.
where m = 0, 1, 2, …
Symmetrical fringes.
2nt = m 2nt = m' 1  The thickness of dark fringes
where m = 0, 1, 2, …  2
is much narrower.
- where m’ = 0, 1, 2, … 1st dark fringe refers to
a sinm’ = m’
or m = 1.
Symmetrical fringes.
m' D The thickness of bright
ym’ = fringes is much narrower.
Central bright fringe,
a
where m’ = 1, 2, … m = 0.

d sinm = m -
where m = 0, 1, 2, …

23

CHAPTER 8 : Quantization of Light

 Light is one of the electromagnetic waves. The energy is represented as :
As wave, light undergoes reflection, E = hf
refraction, interference and diffraction.
or E = hc/
However, there are some cases such cases
as black body radiation and photoelectric where h = planck constant (6.626 x10-34 Js).
effect, explanation based on classical theory
(light as a wave) are failed. The explanation  Photoelectric effect is a process of emitting
cannot be proved by experiment. electrons (known as photo electrons) from a
metal surface when irradiated with light or
In order to overcome the problem, quantum other electromagnetic radiations.
theory takes place by describing light is
discrete just like a particle.

 Black body radiation refers to the radiation
(ranges between Infra Red, IR to Ultra Violet,
UV) of a body due to its temperature. An
example of ideal black body is a small hole
(which seems black). Radiation from the hole
is investigated.

There are contradictions between classical  When the e.m. radiation irradiates on the
theory (especially based on Rydberg theory) target metal (acts as a cathode), free
with the experimental result. According to the electrons absorb photon (energy) and
classical theory, the intensity of a black body escape from the metal (ionization process)
is directly proportional to the frequency and has kinetic energy to reach the anode.
(inversely proportional to the wavelength of
light). Without power supply, current (known as
photoelectric current) will flow in the circuit
At long wavelengths, classical theory is in with minimum value, Io.
agreement with the experimental data. At
short wavelength, however, major Power supply is used to increase the kinetic
disagreement exists between classical energy of photoelectrons, so that more
theory and experimental data. electrons can reach to the anode to increase
o According to the quantum theory (Planck the current.
theory), the intensity of a black body
depends on the number of photon. Photon  The process can be explained by using
has single discrete energy and depends on Einstein equation :
the frequency (or wavelength). E = Wo + Kmax

where Wo = work function of metal.
Kmax = maximum kinetic energy

of photoelectrons.

Im

Io

VS 0

24

 The graph shows the experimental result. If the metal. Work function refers to the
the power supply is overturned, the current minimum energy needed to release an
still flow but the magnitude is decreases electron from the atom of the metal (it is a
(lower than Io). This is because the kinetic constant which depends on the types of
energy of the electrons is being reduced. metal used) and represented as :
The greater the reverse voltage supplied, the
smaller the current flows. Wo = hfo = hc/o

Stopping voltage, Vs is the minimum reverse where ho = threshold frequency
voltage needed to stop the motion of o = threshold wavelength.
electrons (thus, no more ‘photoelectric
current’ flows in the circuit). At this moment,  According to the classical wave theory, an
the kinetic energy of electrons is balanced by electron needs time to absorb sufficient
the potential energy supplied by the voltage : energy for it to escape from the metal
surface. Hence, there would be a time lapse
Kmax = eVs before ‘photoelectrons’ are emitted. Hence,
the frequency of the light needn’t exceed a
 The effect is only happen if the energy of certain minimum value. However,
photon is greater than the work function of experimental observations show otherwise.

25

CHAPTER 9 : Wave Properties of Particle

 Wave-particle duality is the phenomenon potential energy to be totally converted into
where under certain circumstances a particle kinetic energy, U = K where U = eV and
exhibits wave properties, and under other K = ½ mv2) to reach deeded velocity. The
conditions, a wave exhibits properties of wavelength produced is represented by :
particle.
= h
As wave, it undergoes interference and 2m K
diffraction because it has wavelength.
However, the photoelectric effect (the ability or also can be written as :
of photon to eject electrons from a metal h
surface) as well as the explanation on the
black body radiation suggests that =
electromagnetic waves may have properties 2m eV
of particles.
 The moving electrons then incident on a
 The basic property of particle is mass. This crystal lattice which acts as the diffraction
is because wave does not have mass. When grating (because separation between planes
a particle is moving, it has momentum of crystal, d  wavelength of electron, )
(p = mv). Can a moving particle such as an through suitable angle (known as glancing
electron be considered exhibits wave angle) to make sure the diffraction pattern is
properties? Can electron produce clear.
interference or diffraction pattern? Does it
have wavelength? A particle will show duality Experimentally shows that the pattern
if the wavelength can be determine. produced by electron is almost the same as
the pattern produced by X-ray. Therefore the
 The theory of de Broglie states that : “If diffraction pattern of electron can be
electromagnetic radiation - which treated as analyzed by using Bragg equation (equation
a wave, can also demonstrate corpuscular of X-ray diffraction):
(particle) properties, thus indicating its dual
nature, then surely particles of matter must 2dsin = m.
also have a dual nature and demonstrate
wave characteristics”.

 The wavelength of particle is known as de
Broglie wavelength and represented by:
 = h/mv

where m = mass of the particle,
v = velocity of the particle,
h = plack constant = 6.63 x10-34Js.

It means that a particle can only show its
wave property if it is moving with high speed
(v  c) to make sure the wavelength
produced is in e.m. wavelength range.

 In order to produce diffraction pattern,
electrons which is initially at rest, must be
accelerated by a high voltage (supplies

26

CHAPTER 10 : Nuclear & Particle Physics

An atom consists of a nucleus, which is or m = ((A  Z)mn  ZMp )  MN )
surrounded by electrons. The nucleus itself 1.660566x10 27
consists of nucleons (refers to protons and
neutrons). which measured in u.

Actually, the mass lose is converted into nuclear
forces that bind the nucleons to form a nucleus
based on the Einstein’s principle of equivalence
of mass and energy, which states that :

E = mc2

where E = energy.
m = mass.
c = speed of light = 2.99792x108 ms-1.

The properties of proton and neutron are as The process of formation of a nucleus involves
follow : the merging of nucleons. If the newly formed
nucleus is to be stable, it must emit some energy.

Nucleon Proton (p) Neutron (n) The energy equals the magnitude of the energy
necessary to split the nucleus into its free
Charge +e 0 nucleons. It is related to the mass defect and
Mass 1.673 x10-27 1.675 x10-27 represented as follow :

kg kg E = mc2

1.007276 u 1.008665 u or E = ((A – Z)mn + Zmp) – MN)c2
measured in J
The mass of nucleon is more suitable measured
in the unit of u (1 u = 1.660566 x10-27 kg).

In an atom, electrons show its chemical or E =  ((A  Z)mn  ZMp ) MN ) 931.494
properties (through donations, receptions or 1.660566x10
sharing of electrons between atoms), while the 27
nucleus shows its physical properties.
measured in MeV

Such physical properties of a nucleus are known This energy is called the ‘nuclear binding energy’.
as atomic number, Z and Mass Number, A. The This energy actually contributed by all nucleons
atomic number, Z refers to the number of proton in the nucleus.
in the nucleus, while the mass number, A refers
to the sum of the number proton and neutron (A = The magnitude of binding energy contributed by
Z + N). each nucleon is called ‘the binding energy per
nucleon, En’ and represented mathematically by
By knowing the number of protons and neutrons
in a nucleus, it should have no problem in the following equation :
determining the mass of an atomic nucleus.
m c 2
However, the mass of a nucleus is smaller than
the sum of the masses of its components. The En =
difference between the sum of the masses of the
components and the mass of a nucleus is called A
the nucleus ‘mass defect’, m. It can be
calculated mathematically as follow : where A = mass number (the number of

m = ((A – Z)mn + Zmp) – MN) nucleon).

which measured in kg. The binding energy per nucleon of a nucleus is a
measure of the stability of the nucleus.

Nuclei which are more stable have higher value
of binding energy per nucleon (contribute more
defect mass). It is assumed that the mean
nucleon binding energy is  8 MeV.

27

 Radioactivity is a type of fission reaction, which Properties   
occurs spontaneously. It refers to the decay particle particle radiation
process of unstable nuclei (radioactive) to form a Charge
new nucleus with energy in the form of radiation Deflection by E +2e- e- neutral
is released. This random event cannot be
predicted. and B Yes Yes No
Penetrating
This chapter can be divided into two subtopic : Low Medium High
o Nuclear radiations, power
o Radioactive decay process. High Medium Low
Ionizing power

 Generally, there are three types of nuclear  The deflections of radiation respectively in
electric and magnetic field are described as
radioactive decay that emit three types of follow :

radiations : 
o Alpha decay,
o Beta decay, E
o Gamma decay. 



 In alpha () decay, the nucleus of heavy

radioactive element emits an alpha particle (also

known as alpha radiation). General equation of

an alpha decay process is :

A X  YA4 + 4 He
Z 2
Z2

 In beta () decay, the nucleus emits a beta

particle (also known as beta radiation) that has

high velocity. There are two types of beta 

   radiation, i.e. negatron 01 and positron 01 . B

General equation respectively of negatron and 

positron decay process :

A X  ZA1Y + 01 + 
Z

where  is called ‘antineutrino’

A X  ZA1Y + 01 + 
Z

where  is called ‘neutrino’

Neutrino is an elementary particle that exists to  Radioactivity is the spontaneous and random
account the missing energy in positron decay, emission of radiations from a radioactive element
while anti-neutrino is an elementary particle that through decaying its unstable nucleus. Note : 1
exists to account the missing energy in negatron nucleus decays  1 radiation (alpha or beta or
decay. If the two elementary particles meet gamma) emits.
together, they will disappear.

 In gamma () decay, a photon (gamma ray) is

emitted when the excited nucleus changes from a

higher level energy state to a lower level. General

equation of gamma decay process :

A X * (excited state)  A X + 
Z Z

 The comparison between the three radiation are
tabled as follow :

28

 Light nucleus are more stable and N = Z. Heavier  The graph describes the radioactivity process. It
nucleus are stable if N > Z. More neutrons are can be represented by the following formula :
needed to overcome the increase of electric N = No et
repulsion between protons in heavy nucleus as
well as to increase the binding energy in the where No = initial number of radioactive
nucleus. Nevertheless, nuclides with Z > 83 are elements (or nucleus).
unstable (radioactive). Examples : Uranium-238,
Thorium-232, Radium-226, Rubidium-87. N = number of radioactive
elements at that instant (the
 If heavy nucleus is undergoing natural number of nuclei remain at
radioactivity, a daughter nucleus is produced time t from initial).
which is also radioactive and a chain of
radioactive transformations is formed.  One more physical term related with radioactivity
is ‘half-time, T1/2. It defined as the time taken for
 The process of radioactive decay is involving
radioactive elements. According the law of half of the initial number of radioactive elements
radioactive decay : “The decay rate is directly
proportional to the number of nucleus present at to undergo decay. It is represented as follow :
that instant.”
T1/ 2 = ln2
or - dN  N 
dt

where -dN = the number of radioactive
nucleus decayed

= Nfinal – Ninitial
N = the number of radioactive

nucleus at that instant.

 The decay rate is also known as ‘activity’, A. It is
defined as the disintegrations (decay) per second
by the radioactive nucleus and is measured in
Becquerel (Bq).

Note : 1 Bq = 1 decay per second. Half-life actually is a constant (depends on type
of radioactive element). It also indicates the level
Another unit for activity is Curie (Ci). of stability of radioactive elements. A radioactive
Note : 1 Ci = 3.7 x1010 Bq element is more stable if it has longer half life.

Hence : dN =-N  The radioactivity process has many uses. Such
the uses are :
A= o as object dating : to estimate the archeology
dt age of a specimen.
o as tracers : to detect oil leakage or
where  is known as the decay constant (of unit investigate metabolic pathways.
s-1). It indicates the probability of a nucleus to o as a thickness gauge : to control the
thickness of sheets during manufacture.
decay per unit time and defines the speed of o as sterilization : for sterilizing medical
instruments and for food by killing bacteria.
radioactive decay.

END OF SYLLABUS

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