EP025 Buku Tutorial 20222023

SULIT EP025

LIST OF SELECTED CONSTANT VALUES
SENARAI NILAI PEMALAR TERPILIH

Speed of light in vacuum c = 3.00 × 108 m s−1
Laju cahaya dalam vakum

Permeability of free space µ0 = 4π × 10−7 H m−1
Ketelapan ruang bebas

Permittivity of free space e0 = 8.85 × 10−12 F m−1
Ketelusan ruang bebas
e = 1.60 × 10−19 C
Electron charge magnitude
Magnitud cas elektron h = 6.63 × 10−34 J s

Planck constant me = 9.11 × 10−31 kg
Pemalar Planck = 5.49 × 10−4 u

Electron mass
Jisim elektron

Neutron mass mn = 1.674 × 10−27 kg
Jisim neutron = 1.008665 u

Proton mass mp = 1.672 × 10−27 kg
Jisim proton = 1.007277 u

Deuteron mass md = 3.34 × 10−27 kg
Jisim deuteron = 2.014102 u

Molar gas constant R = 8.31 J K−1 mol−1
Pemalar gas molar
NA = 6.02 × 1023 mol−1
Avogadro constant
Pemalar Avogadro k = 1.38 × 10−23 J K−1

Boltzmann constant g = 9.81 m s−2
Pemalar Boltzmann

Free-fall acceleration
Pecutan jatuh bebas

2 SULIT

SULIT EP025

LIST OF SELECTED CONSTANT VALUES
SENARAI NILAI PEMALAR TERPILIH

Atomic mass unit 1 u = 1.66 × 10−27 kg
MeV
Unit jisim atom
= 931.5 c2
Electron volt
Elektron volt 1 eV = 1.6 × 10−19 J

Constant of proportionality = ! = 9.0 ´ 109 N m2 C-2
for Coulomb’s law "#$!
Pemalar hukum Coulomb

Atmospheric pressure 1 atm = 1.013 ´ 105 Pa
Tekanan atmosfera

Density of water rw = 1000 kg m−3
Ketumpatan air

3 SULIT

SULIT EP025

LIST OF SELECTED FORMULAE

SENARAI RUMUS TERPILIH

F = Qq = k Qq 14. t = RC
4pe o r 2 r2
1.

E = F -t
qo
15. Q = Qoe RC

2.

kQ Q = Q çèæ1 - -t ö
r2 o ÷ø
e RC

E = 16.

3.

V W er = e
qo eo
= 17.

4.

V = kQ 18. Co = eo A
r d
5.

6. DU = qDV 19. C = erCo

U k æ q1q2 ö 20. I = dQ
ç r12 ÷ dt
= è ø

7.

kæççè q1q2 q1q3 q2q3 øö÷÷ 21. Q = ne
r12 r13 r23
U = + +

8. 22. V = IR

9. E = DV r = RA
d l
23.

10. C = Q 24. R = Ro [1+a(T -To )]
V

11. 1 = 1 + 1 + ... + 1 25. V = e - Ir
C C1 C2 Cn

26. R = R1 + R2 + ...+ Rn

12. C = C1 + C2 + ... + Cn

1 1 1 Q2 27. 1 = 1 + 1 + ... + 1
2 2 2 C R R1 R2 Rn
U = CV 2 = QV =

13.

4 SULIT

SULIT EP025

LIST OF SELECTED FORMULAE
SENARAI RUMUS TERPILIH

28. P = IV = I 2R = V2 41. f = BAcosq
R 42. F = Nf

29. 29. W = IVt df
dt
43. e = -

V1 = æççè R1 + R1 ...Rn ö÷÷øV
R2 +
30. 30. 44. e = Blv sinq

e1 = l1 e = -NA dB
e2 l2 dt
31. 31. 45.

32. B = µo I e = -NB dA
2p r dt
46.

33. B = µo I 47. e = NABw sinwt
2r

34. B = µonI e = -L æ dI ö
çè dt ø÷
48.

35. B = 1 µo nI L = Nf
2 I
49.

36. F = qvB sinq Lcoil = µo N 2 A
2r
50.

37. F = IlB sinq

F µ! I1I 2 51. µL =solenoid oN2A
l 2pd l
=
38.

U = 1 LI 2
2
39. t = NIAB sinq 52.

v = E 53. M = µo N1N2 A
B l
40.

5 SULIT

SULIT EP025

LIST OF SELECTED FORMULAE

SENARAI RUMUS TERPILIH

65. ym = (m + 1 ) l D
2

54. R = 2 f a

1 = 1 + 1 66. d sinq = ml
f u v
55.

hi v 67. d = 1
ho u N
m= = -

56. h
p
n1 n2 n2 - n1 68. l =
u v R
57. + =

1 = æ nmaterial -1÷ö æ 1 - 1 ö l= h
f ç nmedium ø ç R1 R2 ÷ 69. 2meV
è è ø
58. 70. A= Z+N

59. ym = mlD ( )71. Dm = Zmp + Nmn - mnucleus
d

ym = (m + 1 )lD 72. mnucleus = matom - Zme
2
73. Dm = (ZmH + Nmn ) - matom
60. d

Dy = lD 74. EB = Dmc2
d
61.

62. 2nt = ml 75. dN = -l N
dt

63. 2nt = (m + 1 )l 76. N = Noe-lt
2

64. ym = ml D 77. A = A e-lt
a o

T1 = ln2
l
78. 2

6 SULIT

ACKNOWLEDGEMENTS

Physics Unit KMKJ wish to thank everyone who has contributed in shaping and
writing this TUTORIAL BOOK EP025 PHYSICS 2. Special thanks go to those for
their many valuable suggestions and conscientiousness in completing this book.

TOPIC 1: Electrostatics
PUAN HABIBAH BINTI SALLEH

TOPIC 2: Capacitors and Dielectrics
CIK NOOR AMALINA BINTI MOHD SHUKRI

TOPIC 3: Electric Current and Direct-Current Circuits
PUAN FARZANA BINTI HUSSIN
CIK SAHIRAH AKILAH BINTI MOHD SAH

TOPIC 4: Magnetism
PUAN SHAZRINA BINTI NGATEMIN

TOPIC 5: Electromagnetic Induction
ENCIK ZAHIDI BIN HASHIM

TOPIC 6: Geometrical Optics
CIK ANIS SAHIRA BINTI CHE RAMLI

TOPIC 7: Physical Optics
ENCIK EADY ESWADDY BIN CHE YAHYA

TOPIC 8: Wave Properties of Particle
CIK SALASIAH BINTI HAMZAH

TOPIC 9: Nuclear and Particle Physics
CIK SALASIAH BINTI HAMZAH

Copyright © 2022 Physics Unit KMKJ
Completed and updated: 22 December 2022

Topic INDEX Page
1 1-8
2 Title of chapter 9 - 13
3 Electrostatics 14 - 23
4 Capacitors and Dielectrics 24 - 31
5 Electric Current and Direct-Current Circuits 32 - 35
6 Magnetism 36 - 41
7 Electromagnetic Induction 42 - 49
8 Geometrical Optics 50 - 51
9 Physical Optics 52 - 58
Wave Properties of Particle
Nuclear and Particle Physics

TOPIC 1 : ELECTROSTATICS

1.1 Coulomb’s Law
1.2 Electric Field
1.3 Electric Potential
1.4 Charge in a uniform electric field

At the end of this topic, students should be able to:

COULOMB’S LAW

1. State Coulomb’s Law, = =
4 2 2

2. Sketch the electric force diagram.

3. Apply Coulomb’s Law for a system of point charges.

*Simple configuration of charges with a maximum four charges in 2D

ELECTRIC FIELD

4. Define and use electric field strength, ⃗ =

0

5. Use = for point charge.
2

6. Sketch the electric field strength diagram.

*Simple configuration of charges with a maximum four charges in 2D

7. Determine the electric field strength for a system of charges.

*Simple configuration of charges with a maximum four charges in 2D

ELECTRIC POTENTIAL
8. Define electric potential, =

0

9. Define and sketch equipotential lines and surfaces of:
a) an isolated charge; and
b) a uniform electric field.

1

10. Use = for a point charge and a system of charges.



*Simple configuration of charges with a maximum four charges in 2D.

11. Apply potential difference between two points:

= − , =
0

12. Apply the change in potential energy between two points in electric field:

=
13. Apply potential energy of a system of point charges:

= ( 1 2 + 1 3 + 2 3) up to maximum three charges.

12 13 23

CHARGE IN A UNIFORM ELECTRIC FIELD
14. Analyse the motion of a charge qualitatively and quantitatively in a uniform electric

field for each of the following case
a) stationary charge;
b) charge moving perpendicularly to the field;
c) charge moving parallel to the field; and
d) charge in dynamic equilibrium.

15. Use = for uniform electric field.



2

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 1
(ELECTROSTATICS)

SECTION A

1. Which one of the following is true about an electric field at a point?
A. It indicates the electric force per unit mass at that point
B. It indicates the total charge on a particle at that point
C. It indicates the electric force per unit charge at that point
D. It indicates the electric charge per unit mass of a particle at that point

2. Coulomb’s law states that the electrostatics force between two points charges is
inversely proportional to the __

A. sum of the charges
B. product between the charges
C. sum of their separation distance
D. square of their separation distance

3. A stationary charge particle will produce __

A. Electric field
B. Magnetic field
C. Gravitational field
D. Electromagnetic field

4. A stationary positive charge is placed in a uniform electric field. The direction of
electric force exerted on that stationary positive charge is ___

A. Towards the negative plate
B. Parallel to the negative plate
C. Perpendicular to the electric field
D. Opposite direction to the electric field

5. Which figure correctly shows the equipotential lines around a positive point
charge if the potential difference between successive lines are equal?

3

A. C.

B. D.

SECTION B
1.

FIGURE 1
FIGURE 1 shows three charges are arranged in a straight line. Calculate the
magnitude and direction of the Coulomb force on

a) 6.00µC charge.
b) 1.50µC charge.
c) -2.00µC charge.

(ANS: 46.8N to the left, 157N to the right, 111N to the left )
2.

FIGURE 2
4

FIGURE 2 shows three-point charges are located at the corners of an equilateral
triangle. Calculate the magnitude and direction of the net electric force on the
2.00 µC charge.

(ANS: 0.438N, 85.2° below +x-axis)
3.

FIGURE 3
FIGURE 3 shows two small metallic spheres, each of mass m=0.20 g, are
suspended as pendulums by light strings from a common point. The spheres are
given the same electric charge, and it is found that they come to equilibrium when
each string is at an angle of Ɵ = 5.0° with the vertical. If each string has length
L=30.0 cm, what is the magnitude of the charge on each sphere?

(ANS: 7.2nC)
4.

FIGURE 4
(a) Determine the electric field strength at a point 1.00 cm to the left of the

middle charge shown in FIGURE 4.
(b) If a charge of -2.00 µC is placed at this point, what are the magnitude and

direction of the force on it?
(ANS: (a)2x107N/C to the right, (b) 40.0N to the left)

5

5.

FIGURE 5
FIGURE 5 shows charge q1 = 7.00 µC is at the origin, and charge q2 = 5.00 µC is on
the x-axis, 0.3 m from the origin.
(a) Find the magnitude and direction of the electric field at point P, which has

coordinates (0, 0.400) m.
(b) Find the force on a charge of 2.00 x 10-8 C placed at P.

(ANS: (a) 2.71x105 N/C ,66.6°, (b) 5.42x10-3N)
6.

FIGURE 6
FIGURE 6 shows three-point charges are aligned along the x-axis. Determine the
electric field at the position x = +2.0 m, y= 0.

(ANS:24 N/C in the +x-direction)

7. Two charges Q1 =+6.0µC and Q2= -8.0µC are separated 1.2 m from each other.
(a) Calculate the potential at a point along the line joining the charges at a
distance 0.9m from Q1.
(b) Calculate the potential energy of a 3µC charged particle placed at that point.
(ANS:-180kV, -0.54J )

6

8.

FIGURE 7
FIGURE 7 shows two charges Q1 =+6.0µC and Q2= -8.0µC are separated 12 cm
from each other. What is the potential difference between points P and Q?

(ANS: -1080 kV)
9.

FIGURE 8
FIGURE 8 shows three charges, +q, +2q and -4q are arranged in each corner of an
equilateral triangle with sides 10 cm. Calculate the
(a) electric potential energy of the system, given that q=2µC
(b) work required to remove the charge +q from the system
(c) electric potential at the centre of the equilateral triangle.

(ANS: -3.6 J, 0.72 J, -4.15x105 V)
10.

FIGURE 9
7

FIGURE 9 shows two parallel plates X and Y with a separation distance of 20 cm.
The potential difference between the plate is 20 V.

(a) Sketch the electric field between the plates.
(b) Calculate electric field strength between the plates.
(c) If an electron is held at midpoint between the plates, determine the

magnitude and the direction of force exerted on the electron.

(ANS: 100Vm-1, 1.6x10-17 N to the plate-X)
11.

60 mm 80V

20 mm

0V

FIGURE 10

FIGURE 10 shows a section of the deflection system of a cathode ray oscilloscope.

An electron traveling at a speed 1.5107 m s−1 enters the space between two
parallel plate 60 mm long. The electric field between the plates is 4.0 103V m−1.

(a) Sketch the path of the electron in between plates and after emerging from
the space between the plates.

(b) Find the magnitude and direction of the acceleration of the electron in
between the plates.

(c) Calculate the vertical and horizontal component of the electron velocity
when it emerges from the space between the plates. Find the angle of
deflection of the electron beam.

(ANS: 7.03x1014ms-1, vx=1.5x107ms-1, vy=2.81x106ms-1, 10.6°)

8

TOPIC 2 : CAPACITOR AND DIELECTRICS

2.1 Capacitance and capacitors in series and parallel
2.2 Charging and discharging of capacitors
2.3 Capacitors with dielectrics

At the end of this topic, students should be able to:

CAPACITANCE AND CAPACITORS IN SERIES AND PARALLEL
1. Define and use capacitance, =



2. Determine the effective capacitance of capacitors in series and parallel.
3. Use energy stored in a capacitor, = 1 2 = 1 = 1 2

2 2 2

CHARGING AND DISCHARGING OF CAPACITORS
4. State physical meaning of time constant and use =
5. Sketch and explain the characteristics of Q-t and I-t graph for charging and

discharging of a capacitor.
6. Use:

−

a) = for discharging; and

−

b) = (1 − ) for charging.

CAPACITORS WITH DIELECTRICS

7. Define and use dielectric constant, =


8. Describe the effects of dielectric on a parallel plate capacitor.

9. Apply capacitance of air-filled parallel plate capacitor, =


10. Determine capacitance with dielectric, =

9

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 2
(CAPACITORS AND DIELECTRIC)

SECTION A

1. The parallel metal plates of the capacitors separated by ___
A. insulators
B. conductors
C. insulators and conductors
D. resistors

2. The charge on capacitor plates is directly proportional to ___

A. current
B. potential differences
C. electric field intensity
D. resistance

3. The capacitance of a parallel plate capacitor increases when a dielectric material is
inserted between the plates because ___

A. excess charges are stored in the dielectric material
B. the dielectric material reduces the potential difference between the plates.
C. the charges have moved from positive plate to negative plate.
D. the dielectric material increases the electric field strength between the

plates.

4. A simple capacitor is made by placing two oppositely charged conducting plates
in parallel to each other at a distance, d. If the distance between the plates is
increases, what will happen to the capacitor?

A. Increase the charge on its plates.
B. Decrease the charge on its plates.
C. The capacitance increases.
D. The capacitance decreases.

10

SECTION B
1.

FIGURE 1

FIGURE 3 shows combination of five capacitors C1 = 3 µF, C2 = 11 µF, C3 = 12 µF,
C4 = 6 µF, and C5 = 9 µF.

(a) Calculate the effective capacitance of the circuit.

(b) If V1 = 12 V, calculate the total charge Q supplied.
(ANS: 6 µF, 72 µC)

2. A 15 V battery is connected to three capacitors in series. The capacitors have the

following capacitances: 4.5 µF, 12 µF and 32 µF. Find the voltage across the 32 µF

capacitor.
(ANS: 1.39 V)

3. Why electrical energy can still be stored in a capacitor even though the net
(a) charge is zero?
How to increases the capacitance of air-filled capacitor without changing its
(b) dimension?

4.

FIGURE 2
11

FIGURE 2 shows an open circuit which consists of a capacitor C1 = 15 µF without
charge and capacitor C2 = 5 µF with 50 µC of charge. S switch is connected to a at
time, t = 0 s.

(a) What is the time constant,  during charging for capacitor, C1?
(b) Sketch a graph for charge, Q1 induced in C1 against time, t and graph of

current I produced by the battery against time, t.
(c) Calculate the charge induced in C1 at time, t = 10 s.
(d) What is the total charge that can be store in C1? By referring to suitable

equations, explain how this value can be influenced by the dielectric
constant 1 on the capacitor.
(e) Capacitor C1 is let to be fully charged and then S switch is shift to b. After
equilibrium is achieved, what is the potential difference across capacitor C2?

(ANS: 7.5 s, 66.3 µC, 90 µC, 7 V)

5. A capacitor of 2.0 µF is charged using a 1.5V battery. The charged capacitor is then
discharged through a 60kΩ resistor.

(a) What is the time constant of the discharged circuit?
(b) Calculate the time taken for the charge on the capacitor to decrease to 1 and



1 of its initial value.

100

(ANS: 0.12 s, 0.12 s, 0.55 s)

6.
(a) Calculate the value of capacitance for the two pieces of aluminium plane
having area of 1 m2 and separated at 1 cm away in vacuum.

(b) Parallel plate capacitor in question (a) is filled with material having dielectric
constant value of 5 and potential difference of 10V is applied. Calculate

i. the new capacitance value of the capacitor
ii. the induced charge on the surface of dielectric
iii. the energy stored in the capacitor

(ANS: 885 pF, 4.43 x 10-9 F, 4.43 x 10-8 C, 2.21 x 10-7 J)

7. A 24 µF capacitor is charged to 180 µC. Calculate the additional energy required
to charge the capacitor to 300 µC.
(ANS: 1.2 x 10-3 J)

12

8. Consider a parallel plate capacitor with a capacitance value of C=100 µF, plate
area, A = 0.18 m2; and dielectric constant, r = 7.0.
(a) Calculate the separation distance between the plate.
(b) State a way to increase the capacitance value without increasing the area
size of the capacitor plate.
(ANS: 1.12 x 10-7 m)

9.

FIGURE 5
FIGURE 5 shows a circuit which is used to charge a capacitor of 50 µF which is
initially without charge. The circuit consists of a voltage source of 12 V, resistor of
800 kΩ, switch S and galvanometer G.

(a) What is the time constant of the charging circuit?
(b) At t = 0 s, switch S is closed, and the capacitor is let to charge until saturated.

i. What changes will you observe on the deflection of galvanometer
pointer during the charging process?

ii. Sketch a graph of current, I against time, t.
(ANS: 40 s)

13

TOPIC 3 : ELECTRIC CURRENT AND DIRECT-CURRENT CIRCUITS

3.1 Electrical Conduction
3.2 Ohm’s Law and Resistivity
3.3 Variation of Resistance with Temperature
3.4 Electromotive Force (EMF), Internal Resistance and Potential Difference
3.5 Resistors in Series and Parallel
3.6 Kirchhoff’s Rules
3.7 Electrical Energy and Power
3.8 Potential Divider
3.9 Potentiometer

At the end of this topic, students should be able to:

ELECTRICAL CONDUCTION
1. Describe microscopic model of current.

*emphasise on the flow of free electrons in a metal
**include concept of drift velocity
2. Define electric current, =



3. Use electric current, = , =



OHM’S LAW AND RESISTIVITY
4. State and use Ohm’s Law.
5. Define and use resistivity, =



VARIATION OF RESISTANCE WITH TEMPERATURE
6. Explain the effect of temperature on electrical resistance in metals.
7. Use R=RO[1+α(T-TO)]

*α is at temperature 20°C

ELECTROMOTIVE FORCE (EMF), INTERNAL RESISTANCE AND POTENTIAL
DIFFERENCE
8. Define emf, ε and internal resistance, r of a battery.
9. State factors that influence the internal resistance.
10. Explain the relationship between emf of a battery and potential difference across

the battery terminals.
11. Use terminal voltage, V = ε - Ir

14

RESISTORS IN SERIES AND PARALLEL
12. Determine the effective resistance of resistors in series and parallel.

KIRCHHOFF’S RULES
13. State and apply Kirchhoff’s Rules.

*maximum two closed circuit loops.
**use calculator to solve the simultaneous equations.

ELECTRICAL ENERGY AND POWER

14. Use power, P = IV, P = I2R and = 2 (known as power loss).



15. Use electrical energy, W = IVt

POTENTIAL DIVIDER

16. Explain principle of potential divider.

17. Use equation of potential divider, 1 = ( 1 )

1+ 2+…..

*maximum three resistors

POTENTIOMETER
18. Explain principle of potentiometer and its applications.
19. Use related equations for potentiometer, 1 = 1

2 2

15

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 3
(ELECTRIC CURRENT AND DIRECT-CURRENT CIRCUITS)

SECTION A

1. The amount of charge flowing through cross-sectional area of a wire per unit of
time is called _____.

A power
B current
C voltage
D resistance

2. The resistance of a wire depends on the following factors EXCEPT _____.

A volume
B length
C cross sectional area
D type of material

3. The electrical resistance in metal conductor increases when its temperature
increased is due to the increase in its _____.

A drift velocity of the electron
B mean free time between collisions
C amplitude of crystal lattice vibrations
D number of free electrons per unit volume

4. Electromotive force (emf). Is defined as the energy provided by the source to each
unit charge that flows through the _____.

A total external resistance only
B external and internal resistances
C internal resistance of a source only
D terminal potential difference of the circuit

5. The terminals of a battery are connected across two resistors in parallel. The
resistances of the resistors are not the same. Which of the following statements is
correct?

16

A. The current in the larger resistor is greater.
B. The potential difference across the larger resistor is greater.
C. The potential difference across each resistor is the same.
D. The power delivered to the larger resistor is greater.

SECTION B

1. If current of 80.0 m A exist in a metal wire,

(a) how many electrons flow past a given cross section of the wire in 10.0 min?
(b) In what direction do the electrons travel with respect to the current?

(ANS: 3 x 1020 electrons )

2. An electric heater carries a current of 13.5 A when operating at a voltage of
1.20 x 102 V. What is the resistance of the heater?
(ANS: 8.89 Ω)

3. A potential difference of 8 V is supplied across a metal wire with uniform cross
sectional area of 0.08 mm2 and length of 0.5 m. Determine the resistivity of the wire
if the electric current flow is 1.2 A.
(ANS: 1.07 x 10-6 Ωm)

4. A bird stands on a high voltage transmission wire with its feet 5.00 cm apart. The
wire is made of aluminium with diameter 1.20 cm and carries a current of 55.0 A.
[Resistivity of aluminium: 2.65 x 10-8 Ωm]

(a) Calculate the resistance of the wire between the bird’s feet.
(b) Calculate the potential difference between the bird’s feet.

(ANS: 1.17 x 10-5 Ω, 6.44 x 10-4 V)

5. A wire of 25 Ω resistance is melted. The melt is used to make a new wire that is
three times longer than the original wire. Calculate the new wire resistance of the
wire.
(ANS: 225 Ω)

6. While taking photographs in Death Valley on a day when the temperature is 58.0
°C, Bill Hiker finds that a certain voltage applied to a copper wire produces a
current of 1.0 A. Bill then travels to Antartica and applies the same voltage to the

17

same wire. What current does he register there if the temperature is -88.0 °C?

Assume no change occurs in the wire’s shape and size.

( = 3.9 × 10−3℃−1) (ANS: 2.3 A)

7. The heating element of an oven is made from a coil of nichrome wire. The oven is
connected to a 240 V power supply with a current of 1.99 A flowing through the
coil at initial temperature of 30 °C. When the oven reaches the operating
temperature, the current is 1.77 A. Calculate the final temperature of the coil if the
temperature coefficient of resistivity of nichrome is 4.0 x 10-4 ℃-1.
(ANS: 340.74 °C)

8. A copper wire has a resistance of 25 Ω at 20°C. When the wire is carrying a current,
heat produced by the current causes the temperature of the wire to increase by
27°C. (Given the temperature coefficient of resistivity for copper is
6.80 x 10-3 °C-1)
(a) Calculate the change in the wire’s resistance
(b) If its original current was 10.0 mA and the potential difference across wire
remains constant, what is its final current?
(ANS: 4.59 x 10-3 Ω, 8.45 x 10-3 A)

9. A 6.0 V battery has an internal resistance of 10.0 Ω. The battery is then uses to
light a menthol of 120.0 Ω which is connected in series to a resistor of 40.0 Ω and
the potential difference across the battery is measured once again. What is the
reading of the voltmeter?
(ANS: 5.65 V)

10. A cell has a terminal voltage of 1.35 V when it is connected to a 0.9 Ω external

resistor. When the resistance is increased to 2.4 Ω, the terminal voltage is 1.44 V.

Calculate the internal resistance of the cell.
(ANS: 0.1 Ω)

11.

FIGURE 1
18

FIGURE 1 shows a battery connected to a resistor, R. The current flow is 2 A
when R is 2 Ω and 1 A when R is 5 Ω. Determine the emf, ε of the battery and its
internal resistance. R.

(ANS: 6 V, 1 Ω)

12. Calculate the effective resistance and total current flow from the battery for the
circuit in FIGURE 2 below.

FIGURE 2

(ANS: 8.94 Ω, 1.68 A)

13. Calculate the effective resistance in the FIGURE 3 below and determine the
current flow through the 1 Ω resistor when the potential difference across points
a and b is 120 V.

FIGURE 3

(ANS: 2.446 Ω, 49.06 A)

14. FIGURE 4 shows a circuit with ξ1 = 20 V, ξ2 = 10 V, ξ3 = 12 V, R1 = 8 Ω, R2 = 10 Ω,
R3 = 10 Ω and R4 = 8 Ω. Calculate current I1, I2 and I3 that flow in the circuit.

19

FIGURE 4
(ANS: 0.64 A, 0.485 A, -0.159 A)

15. Determine the current I1, I2, I3 and I4 labeled in the FIGURE 5 and FIGURE 6.
a)

2V

I2
FIGURE 5
b)

20

FIGURE 6

(ANS: 0.65 A, 0.42 A, 0.25 A, 0.25 A)

16. A filament bulb A is rated 240 V, 100 W and another bulb B is rated 240 V, 60 W.

(a) Find the ratio of the resistances of the filaments at their normal working

temperature.
(b) If each of the bulbs are connected in turns to a 120 V supply, what is the

power dissipated from each bulb?
(ANS: 0.6, 25 W, 15 W)

17. A cell of e.m.f 1.5 V and internal resistance 1.0 Ω maintains a constant current of
0.5 A in an external circuit. When an electric charge of 2.0 C flows in the external
circuit, calculate the

(a) thermal energy dissipated from the cell.
(b) energy dissipated from the external circuit.
(c) total energy supplied by the cell.

(ANS: 1.0 J, 2.0 J, 3.0 J)

18.

FIGURE 7
21

FIGURE 7 shows two resistors are connected in series with a battery.
Calculate the potential difference across points A and B.

(ANS: 2 V)
19.

2.0 V, 2.0 Ω

l Q
P
G
1.0 V, 1.0 Ω

1.0 Ω
FIGURE 8

FIGURE 8 shows a potentiometer PQ which has a slide wire of length 100 cm and
resistance 6.0 Ω. The 1.0 V and 2.0 V batteries have internal resistance 1.0 Ω and
2.0 Ω respectively.

(a) What is the balanced length, l?
(b) If the resistor 1.0 Ω is changed to 2.0 Ω, determine the new balanced

length of the wire.
(ANS: 0.33 m, 0.44 m)

20.
2.0 V

l Y
X

G

1.0 Ω switch
ɛ,r

FIGURE 9

22

FIGURE 9 shows a potentiometer with a slide wire XY of length 100 cm is
connected to a battery of e.m.f. 2.0 V and is used to determine the e.m.f. ɛ and the

internal resistance r of another battery.When the switch is opened, the balanced
length is 60.0 cm and when the switch is closed, the balanced length is 32.0 cm.
Determine the value of

(a) emf ɛ of the battery.
(b) internal resistance of the battery.

(ANS: 1.2 V, 0.875 Ω)

23

TOPIC 4: MAGNETISM

4.1 Magnetic field
4.2 Magnetic field produced by current-carrying conductor
4.3 Force on a moving charged particle in a uniform magnetic field
4.4 Force on a current carrying conductor in a uniform magnetic field
4.5 Forces between two parallel current-carrying conductors
4.6 Torque on a coil
4.7 Application of motion of charged particle

At the end of this topic, students should be able to:

MAGNETIC FIELD
1. Define magnetic field.
2. Identify magnetic field sources.

*example: i. bar magnet and current-carrying conductor (straight wire, circular coil and
solenoid)
ii. earth magnetic field

3. Sketch magnetic field lines for:
(a) bar magnet and current-carrying conductor (straight wire, circular coil and
solenoid) and
(b) the Earth magnetic field.

MAGNETIC FIELD PRODUCED BY CURRENT-CARRYING CONDUCTOR
4. Sketch resultant magnetic field diagram at a point

*limited to two current carrying straight wires and 2D.

5. Determine direction of  by using right hand rule.
B

6. Determine the magnitude of magnetic field by using:

(a) B =  I for a long straight wire.
2r

(b) B =  NI at the center of the circular coil.
2R

24

(c) B = nI at the center of a solenoid.

(d) B = 1   nI at the end of a solenoid.
2

FORCE ON A MOVING CHARGED PARTICLE IN A UNIFORM MAGNETIC FIELD

7. Explain and use magnetic force,  =    .
F qv B

8. Determine the direction of force.

9. Describe circular motion of a charge in a uniform magnetic field.

10. Use relationship FB = FC .

FORCE ON A CURRENT CARRYING CONDUCTOR IN A UNIFORM MAGNETIC

FIELD
 

11. Use magnetic force, F = Il  B .

12. Determine the direction of force.

FORCES BETWEEN TWO PARALLEL CURRENT-CARRYING CONDUCTORS
13. Explain magnetic force per unit length of two parallel current-carrying conductors.
14. Apply magnetic force per unit length, F = 0 I1I 2 .

l 2d

TORQUE ON A COIL

15. Use torque,  =  where N = number of turns.
NIA  B

16. Explain briefly the working principles of a moving coil galvanometer.

APPLICATION OF MOTION OF CHARGED PARTICLE
17. Explain the motion of a moving charged particle in magnetic field and electric field

for v, B and E perpendicular to each other.
18. Use velocity, v = E in a velocity selector (e.g. Bainbridge mass spectrometer)

B

25

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 4
(MAGNETISM)

SECTION A

1. Which one of the following statements is NOT TRUE about magnetism?

A The north pole of the permanent magnet is attracted to the south pole.
B All permanent magnets are surrounded by a magnetic field.
C The direction of the magnetic field is indicated by the north of a compass.
D When a permanent magnet is cut into two pieces, one piece will be a north

pole and the other piece will be a south pole.

2. The magnitude of magnetic force on a current-carrying conductor is equal to __

A qE B qv x B

C ILxB D NIA x B

3. A neutron is entering a uniform magnetic field. What will happen to its motion?

A Moving in a parabolic path.
B Moving in a circular path.
C Accelerated.
D Undeflected.

4. If the north pole of bar magnet is brought near the north pole of the other
magnet, the force between them is __

A Repulsive
B Attractive
C Combine
D No longer effective

26

SECTION B
1.

d

FIGURE 1

FIGURE 1 shows two long and parallel conducting wires separated by a distance
d and carrying current, I. Sketch a resultant magnetic field diagram around the
axis of the wires for the following condition.

a) If the direction of both the current is the same
b) If the direction of both the current is opposite with each other.

2. a) Calculate the magnetic field at a point 2.0 cm from a long straight wire
b) carrying a current of 10 A.
c)
The magnetic field at a point 3.0 cm from a long straight wire is 4.0 10−4 T
d) . Calculate the amount of current flows into it.

3. A flat circular coil has 10 turns with radius of 5.0 cm. Determine the current
must flows inside the coil if a flux density of 2.0 10−4 T is produced at its
centre.

A solenoid of length 1.5 m and 2.6 cm in diameter carries a current of 18 A.
The magnetic field inside the solenoid is 2.3 mT. Calculate the length of the
wire forming the solenoid.

(ANS: 110−4 T, 60 A,1.592 A,12.5m )

20 cm

4A 6A
FIGURE 2

27

FIGURE 2 shows two wires carrying current of 4.00 A and 6.00 A in the direction
indicated.

a) Find the direction and magnitude of the magnetic field at a point
midway between the wires.

b) Find the direction and magnitude of the magnetic field at a point
midway between the wires if the current 4 A is in the opposite direction.

(ANS: 4 10−6 T (out of page), 2 10-5 T (out of page) )

4. A coil of 3 turns with a resistance of 4 Ω connected to a 12 V battery. The radius of
the loop is 1.8 cm.

a) Calculate the amount of current flowing through the loop
b) Determine the magnetic field strength due to each turn at the centre of

the coil.
c) Calculate the net magnetic field strength at the centre of the coil.

[Given: 0 = 4 10−7 H m-1]

(ANS: 3 A,1.04710-4 T, 3.14110-4 T )
5.

P 5.0 cm

5.0 cm

x I 2 = 4.0A

I1 = 3.0A
R

FIGURE 3

FIGURE 3 shows two long straight wires are oriented perpendicular to the page.
The current in one wire is I1 = 3.0A pointing into the page and current in the other

28

wire is I2 = 4.0A pointing out of page. Determine the magnitude and direction of
the net magnetic field intensity at point P.

(ANS: 8.9310-6 T,-63.10 )

6. Calculate the magnitude of the force on a proton travelling 5.0 107 ms−1 in the
uniform magnetic flux density of 1.5Wbm−2 , if:

a) the velocity of the proton is perpendicular to the magnetic field.
b) the velocity of the proton makes an angle 500 with the magnetic field.

(Given the charge of the proton is +1.60 10−19 C )

(ANS: 1.2 10−11 N , 9.19 10−12 N )

7.

v

AB

FIGURE 4

An electron at point A in FIGURE 4 has a speed v of 2.50 106 ms−1 . Determine

a) the magnitude and direction of the magnetic field that will cause the
electron to follow the semicircular path from A to B.

b) the time required for the electron to move from A to B.
(Given charge of electron, e = 1.60 10−19 C and mass of electron, me = 9.1110−31 kg)

(ANS: 2.610−4T , into the page)

8. Two charged particles with different speeds move one at a time through a region
of uniform magnetic field. The particles move in the same direction and experience
equal magnetic forces. If particle 1 has four times the charge of particle 2, calculate

the ratio of the speeds, v1 .
v2

(ANS: ¼)

29

9. A wire of 100 cm long is placed perpendicular to the magnetic field of
1.20 Wb m-2.

a) Calculate the magnitude of the force on the wire when a current of 15 A
is flowing.

b) For the same current in (a), determine the magnitude of the force on the

wire when its length is extended to 150 cm.
c) If the force on the wire in part (b) is 0.6 N and the current flows is 12 A,

calculate the magnitude of magnetic field supplied.

(ANS: 18 N, 27 N, 0.033 T)

10. Two long straight parallel wires are placed 0.25 m apart in a vacuum. Each wire
carries a current of 2.4 A in the same direction.

a) Sketch a labelled diagram to show clearly the direction of the force on
each wire.

b) Calculate the force per unit length between the wires.
c) If the current in one of the wires is reduced to 0.64 A, calculate the current

needed in the second wire to maintain the same force per unit length
between the wires as in (b).

(ANS: 4.6110−6 Nm−1,9.0A)

11. A 50 turns rectangular coil with sides 10 cm x 20 cm is placed vertically in a
uniform horizontal magnetic field of magnitude 2.5 T. If the current flows in the
coil is 7.3 A, determine the torque acting on the coil when the plane of the coil is:

a) perpendicular to the field,
b) parallel to the field,
c) at 750 to the field.

(ANS: 0 Nm, 18.25 Nm, 4.72 Nm)

12. a) A rectangular coil of 10 cm x 4.0 cm in a galvanometer has 50 turns and a
magnetic flux density of 5.0 x 10-2 T. The resistance of the coil is 40 and a
potential difference of 12 V is applied across the galvanometer, calculate the
maximum torque on the coil.

b) A moving coil meter has 50 turns coil measuring 1.0 cm by 2.0 cm. It is held
in a radial magnetic field of flux density 0.15 T and its suspension has a

torsional constant of 3.0 10−6 N m rad-1. Determine the current is required
to give a deflection of 0.5 rad.

(ANS: 310−3 Nm , 1.0410−3 A)

30

13. An electron with kinetic energy of 8.0 10−16 J passes perpendicular through a
uniform magnetic field of 0.40 10−3T. It is found to follow a circular path.
Calculate
a) the radius of the circular path.
b) the time required for the electron to complete one revolution.
(Given e / m = 1.761011Ckg −1, me = 9.1110−31 kg)
(ANS: 0.595 m, 8.9210−8 s)

14. An electron moving at a steady speed of 0.50 106 ms−1 passes between two flat,
parallel metal plates 2.0 cm apart with a potential difference of 100 V between
them. The electron is kept travelling in a straight line perpendicular to the electric
field between the plates by applying a magnetic field perpendicular to the
electron’s path and to the electric field. Calculate
a) the intensity of the electric field.
b) the magnetic flux density needed.
(ANS: 5000Vm−1,0.01T )

31

TOPIC 5 : ELECTROMAGNETIC INDUCTION

5.1 Magnetic Flux
5.2 Induced Emf
5.3 Self-Inductance
5.4 Energy Stored in Inductor
5.5 Mutual Inductance
5.6 Back Emf in DC Motor

At the end of this topic, students should be able to:

MAGNETIC FLUX
1. Define and use magnetic flux, ∅ = ⃗ ∙ =
2. Use magnetic flux linkage, = ∅

INDUCED EMF
3. Explain induced emf by using Faraday’s experiment.

4. State and use Faraday’s Law, = − ∅



5. State and use Lenz’s Law to determine the direction of induced current.
6. Apply induced emf in:

i. a straight conductor, =

ii. a coil, = − , = −



iii. a rotating coil, =

SELF-INDUCTANCE

7. Define self-inductance.

8. Apply self-inductance, = − for coil and solenoid, where:
( )

i. = ∅



ii. = 0 2
2

iii. = 0 2


ENERGY STORED IN INDUCTOR
9. Apply the energy stored in an inductor, = 1 2

2

32

MUTUAL INDUCTANCE
10. Define mutual inductance.
11. Use mutual inductance, = 0 1 2 between two coaxial solenoids.



BACK EMF IN DC MOTOR
12. Explain back emf and its effect on DC motor.

33

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 5
(ELECTROMAGNETIC INDUCTION)

SECTION A

1. Electromagnetic induction occur when __

A a current is induced in the coil.
B there is a magnetic flux in the coil.
C there is a change in magnetic flux.
D an e.m.f. is induced in a magnetic flux coil.

2. An e.m.f. will be induced in a straight conductor if __

A the conductor cuts across a constant magnetic flux.
B the conductor moves parallel to a constant magnetic flux.
C the conductor is stationary across a constant magnetic flux.
D a constant magnetic flux is placed parallel to the conductor.

3. Self inductance in a solenoid depends on the following factors EXCEPT the __

A current.
B number of turns.
C solenoid’s length.
D cross-sectional area.

SECTION B

1. (a) An equilateral triangle 20.0 cm on each side is placed in a uniform magnetic
field of 10.0T which makes an angle of 60o with the plane of the coil. Calculate
the magnetic flux through the triangle.
(ANS:  = 0.15 Wb )

(b) A 15.0 cm long solenoid has 200 turns. The solenoid has a diameter of 4.0
cm and carries 10.0 A current. Calculate the magnetic flux through the circular
cross-sectional area of the solenoid.

(ANS:  = 2.11x10-5 Wb )

34

2. A coil of 50 turns and cross-sectional area 0.8 cm2 lying in a magnetic field
which changes from 2.0 x 10-3 T to 8.0 x 10-3 T in 0.50 s.
(a) Calculate the induced e.m.f. generated.
(b) If its resistance is 20 what current will flow in the coil?
(c) Sketch a diagram (including a galvanometer) to show the current
direction.
(ANS:  = 4.8 x 10-5 V, I = 2.4 mA)

3. A conducting rod of 10 m length is moving perpendicularly in a uniform
magnetic field of 15.0 T with velocity of 20 cm s-1.
(a) Calculate the induced e.m.f. generated.
(b) If its resistance is 10  what current will flow in the rod?
(c) Sketch a diagram (including a galvanometer) to show the current
direction.
(ANS: ε = 0.3 V, I = 0.03 A)

4. A coil in an electric generator with magnetic field 1.96 T is rotating at 20
revolutions per minute and has 102 turns with an area of 100 cm2.
(a) What is the maximum voltage?
(b) If its resistance is 1.5  what is the maximum current will flow in the rod?
(c) Explain the direction of the current flown.
(ANS: εmax = 4.18 V, Imax = 2.79 A)

5. (a) When the current in a coil is changing at a rate of 200 A s-1, the back e.m.f
induced is 25V. Calculate the self-inductance of this coil.
(ANS: L = 0.625 H)

(b) A solenoid containing 150 turns with the length of 20 cm and cross-
sectional area of 5cm2. Calculate the inductance of the solenoid.

(ANS: L = 7.07x10-5 H)

6. Primary coil of a cylindrical core with a length with a length of 25 cm and
radius 1.5 cm has 100 turns. If the secondary coil has 50 turns, calculate :
(a) its mutual inductance.
(b) the induced e.m.f. in the secondary coil if the current flowing in the
primary coil is changing at the rate of 4.5 A s-1.
(ANS: M = 17.8 μH, ε = 79.9 μV)

35

TOPIC 6 : GEOMETRICAL OPTICS

6.1 Reflection at a Spherical Surface
6.2 Refraction at a Spherical Surface
6.3 Thin Lenses

At the end of this topic, students should be able to:

REFLECTION AT A SPHERICALSURFACE
1. State radius of curvature, = 2 for spherical mirror
2. Sketch ray diagrams with a minimum of two rays to determine the characteristics

of image formed by spherical mirrors
3. Use mirror equation, 1 = 1 + 1 for real object only.



*sign convention for focal length, f and radius of curvature, R:
i. positive f and R for concave mirror
ii. negative f and R for convex mirror

4. Apply magnification, = ℎ = −

ℎ

REFRACTION AT A SPHERICALSURFACE

5. Use 1 + 2 = 2− 1 for spherical surface.


*sign convention for radius of curvature, R:

i. positive R for convex surface

ii. negative R for concave surface

THIN LENSES

6. Use thin lens equation, 1 = 1 + 1 for real object only.



*sign convention for focal length, f:

i. positive f for convex lens

ii. negative f for concave lens

7. Use lens maker’s equation, 1 = ( − 1) ( 1 − 1 )
1 2

*nair = 1

8. Apply magnification, = ℎ = −

ℎ

9. Use the thin lens formula for a combination of two convex lenses

36

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 6
(GEOMETRICAL OPTICS)

SECTION A

1. When an object is closer to a convex mirror than the mirror’s focal point, ___
A The magnification is less than one
B The image distance is greater than the object distance
C The magnification is equal to one
D The image is real

2. The image of an object located 10 cm from a concave spherical mirror of radius 10
cm is ___
A real, inverted and magnified
B real, inverted and diminished
C real, inverted and the same size
D virtual, upright and magnified

3. To locate the position of an image formed by a lens using ray diagram, one needs
to ___
A have rays coming from multiple points of the object and find an intersect
point
B have rays coming from one point of the object and find an intersect point
C have a ray going parallel to the axis
D have a ray pass through the edge of the lens without bending

4. State the characteristic of the image if the value of magnification is +0.25.
A Upright, diminished
B Upright, same size
C Inverted, diminished
D Inverted, magnified

5. If the image formed by a convex lens is real and magnified, its magnification can
be ___
A +0.5
B -0.5
C +5.0
D -5.0

37

SECTION B

1. During a magic show, an upright image three times the size of a girl is produced

by aspherical concave mirror of radius of curvature 50 cm. How far is the girl

standing in front of the mirror?
(ANS: 16.7 cm, in front of mirror )

2. a) An upright image is produced by a spherical mirror at a distance of 30 cm
from the centre of curvature of this mirror. The magnification is 4.

i) State the type of spherical mirror used
ii) Sketch the ray diagram to show how the image is produced
iii) Calculate the object distance from the mirror and the focal length of

themirror

(ANS: 4.5 cm, 6 cm )
b) Can the mirror in (a) be used by a dentist to check the teeth? Explain your

answer.

3. An upright image twice the size of an object is formed by a spherical mirror. If the
distance between the image and the object is 30 cm, find the focal length of the

mirrorand state what type of spherical mirror it is.
(ANS: 20 cm)

4. An object of height 5 cm is 30 cm from a convex mirror of radius of curvature
40 cm. Calculate the

a) image location.
b) height of the image

(ANS: -12 cm, 2 cm)

5. A converging spherical mirror of radius of curvature 20 cm is used as a shaving

mirror. Determine the distance of an object from the mirror if an upright image
three times the height of the object is produced. Draw a ray diagram to illustrate
your answer.

(ANS: 6.67 cm)

6. A convex spherical mirror of focal length 50 cm is used as a rear mirror of a vehicle.

An object is 200 cm behind the rear mirror. Find the position of the image and state
itscharacteristics. Draw a ray diagram to illustrate your answer.

(ANS: -40 cm )

38

7. A point object is located 5.0 cm from a big block of glass with a spherical concave
surface of radius of curvature 20.0 cm. The refractive index of the glass is 1.50.
Show the image is approximately 6.7 cm from the concave surface.
(ANS: -6.67 cm )

8. One end of a glass rod is convex with a radius of curvature 2.5 cm. A point light
source is 6.0 cm from the convex end of the glass rod. Find the position of the
image formed by the refraction of light at the convex glass surface.
(Given refractive index of glass is 1.50)
(ANS: 45 cm )

9.

FIGURE 1
FIGURE 1 shows a goldfish is swimming inside a spherical plastic bowl of water,
with an index of refraction of 1.33. If the fish is 20.0 cm from the wall of the 40.0
cm radius bowl, wheredoes it appear to an observer outside the bowl?

(ANS: -17.7 cm )
10. An object 1.0 cm tall is 1.50 m to the right of a convex spherical surface whose

radius of curvature is 0.50 m. The medium to the right of the surface is air (index
of refraction is 1), and the medium to the left has an index of refraction equal
to 1.67. Find theposition of the image. Is it real or virtual?

(ANS: 2.5 cm )
11.

FIGURE 2
39

FIGURE 2 shows a coin 2 cm in diameter is embedded in a solid glass ball of

radius 30 cm. The index of refraction of the ball is 1.5 and the coin is 20 cm from

the surface. Find the position of the image of the coin.
(ANS: -17.14 cm )

12. The surfaces of a lens are of radii of curvature 15.0 cm and 10.0 cm. Calculate the
focal length of the lens if the lens is (given the refractive index of lens =1.5)

a) a converging meniscus
b) A diverging meniscus

(ANS: 60 cm, -60 cm )

13. A double convex lens has faces of radii 18 and 20 cm. When an object is 24 cm
away from the lens, a real image is formed 32 cm from the lens. Determine the

a) focal length of the lens
b) refractive index of the lens material

(ANS: 13.71 cm, 1.69 )

14. A convex lens of focal length 20.0 cm is used to project the image of a bright object
onto a screen. The height of the image formed on the screen is 50 times the height
ofthe object. Calculate the distance of the object from lens. How should the object
distance be changed so that an image can be formed on a screen placed further

away from lens?
(ANS: 20.4 cm )

15. One of the lenses of a student’s spectacles is a diverging meniscus with radii of
curvature 5.0 cm and 8.0 cm. The refractive index of the material of the lens is 1.60.

a) An object is at a distance of 1 m from lens. Where is the image location?
b) If the student put on the spectacles when he dives into water of

refractive index 1.33, where would the image for the same distance
object be formed by lens ?

(ANS: -18.18 cm, -39.64 cm )

16. A plano convex lens made up of glass of refractive index 1.5 has a focal length of

25 cm. Calculate the radius of curvature of the convex surface.
(ANS: 12.5 cm )

17. A spider with a diameter of 2 cm hangs from the ceiling. The distance between the
spider and the wall is 200 cm. A thin lens is placed so that an image formed on the
wall is half the size of the spider.

40

a) State the type of lens used.
b) Determine the position of the lens from the wall.

(ANS: 66.7 cm )

18. The objective and eyepiece of the microscope are both converging lenses and have
focal length of 2 cm and 2.5 cm respectively. The lenses are separated at a distance
6 cm. The sample of specimen is 4 cm in front of the objective. Determine:

a) The position of the final image

b) The overall magnification of the microscope

c) State the characteristics of the final image formed
(ANS: 4 cm, -10 cm, -5 )

41

TOPIC 7 : PHYSICAL OPTICS

7.1 Huygens’ Principle
7.2 Constructive and Destructive Interference
7.3 Interference of Transmitted Light Through Double-Slits
7.4 Interference of Reflected Light in Thin Film
7.5 Diffraction by a Single Slit
7.6 Diffraction Grating

At the end of this topic, students should be able to:

HUYGENS’S PRINCIPLE
1. State Huygens’s Principle (e.g. spherical and plane wavefronts).
2. Sketch and explain the wave front of the light after passing through a single slit

and obstacle using Huygens’s Principle.

CONSTRUCTIVE AND DESTRUCTIVE INTERFERENCES
3. Define coherence.
4. State the conditions for interference of light.
5. State the conditions of constructive and destructive interference.

*emphasise on the path difference and its equivalence to phase difference.

INTERFERENCE OF TRANSMITTED LIGHT THROUGH DOUBLE_SLITS

6. Use:

i. ym = mD for bright fringes (maxima); and
d

 m + 1 D for dark fringes (minima), where m = 0, ±1, ±2, ±3, … .
ii. ym =  2
d

*bright fringes: m = 0, central or 0th order max, m = 1, first bright or 1st order max

dark fringes: m = 0, first dark or 0th order min, m = 1, 2nd dark or 1st order min

7. Use: ∆ = and explain the effect of changing any of the variables.



*Δy: separation between two consecutive dark or bright fringes

42