RAK Science Training March 2024

Engineering Optics

Waves, mirrors and lenses

March 2024

Outcomes + Agenda

05

06

07

08

01

02

03

04

Index

Starter

Light; its characteristics and
propagation

Engineering applications:
reflection, refraction

Reflection

Images formed in curved
mirrors

Refraction of light

Laws of refraction

30 minutes

Reflection ,curved

mirrors

15 minutes

Break

20 minutes

Refraction of light

30 minutes

Law of refractions

30 minutes

Applications-

lenses

10 minutes

Plenary

Training workshop activities

30 minutes

Light and its
propagation

30 minutes

Outcomes +

Agenda +Starter

At the end of the workshop, the participant is expected to be
able to:

Explain the nature of light.

Implement some practical

activities to enable the

student to better

understand the process of

refraction of light .

Identify some conceptual
errors related to reflection

and refraction .

Define the meaning of

reflection, refraction,

and total internal

reflection.

Employ some technological

applications in teaching
physics concepts in the

lesson .

Apply the laws of reflection

and refraction to solve
mathematical problems.

Learning outcomes

Everyone will now compete to design the best telescope that can

outperform Galileo’s Telescope.

Tools needed:

•Cardboards, about 24 inches long.

•Convex lenses with different sizes.

•Strong glue, scissors and pencil.

If the convex lenses are the same size, the telescope will not work.

The lenses are fixed on a 1 m long wooden ruler, use clay

(playdough) to adjust the distance between the lenses.

Activity: Shall we challenge Galileo?

20 min.

Scientists and light

20 min.

In your groups, select one of the scientists below and find out the
most important contributions to the development of light “optics”.
Discuss the findings with your colleagues.

Open Ended

select one of the scientists below and find out the most important contributions to the development of light “optics”.

Light is essential for photosynthesis and energy production in plants.

Many tools and devices that are used whether in examining or analyzing plants, soil

and water depend on different regions of the electromagnetic spectrum for the

scientific basis of their working methods, such as:

•Optical microscope

•Flame photometer

•Atomic Absorption

•Surveying and land leveling devices using laser

•Remote sensing equipment (agriculture)

Light, its properties and how it travels

Why do we study light?

Physicists are usually interested in knowing the components of matter

and the laws that describe the various interactions between them.

Several theories have emerged trying to explain the nature of light and

how it propagates.

Isaac Newton's research is the actual beginning of understanding the

nature of light, as Newton's interest in mechanics constituted a strong

motivation to explain the nature of light on a purely mechanical basis.

Light and the nature of its propagation

Light, its properties and how it travels

Many scientists have tried to provide models and theories

that explain the nature of light.

From Newton to Huygens to Maxwell and Einstein.

The theory of Einstein comprises of both photonic

theories (wave theory and particle theory).

Theories explaining the nature of light

Light, its properties and how it travels

1704

Wave-particle dualism / Louis

de Broglie

All matter, including light, exhibits
wave and particle properties at the

same time

1690

Quantum theory/Albert Einstein

Light exhibits both wave-like and particle-
like behavior at the same time. It can be
described as packets of energy called

photons.

1864

Electromagnetic wave theory/James

Maxwell

Light is an electromagnetic wave, made up of

electric and magnetic fields that oscillate together

1905

Wave Theory/Christian

Huygens

Light is a wave that propagates

through a medium called the aether

1924

Particle theory/Isaac

Newton

Light is made up of tiny particles

called particles

The most known theories about the
nature of light

1.

Light does not need a medium of

transmission as it travels in a vacuum.

2.

Light travels in straight lines

Properties of light

Light, its properties and how it travels

3.

Light has the property of independence of rays

When light rays intersect, none of them affects the other, but rather

continues in its direction.

This property is known as the principle of independence of light

rays.

4.

Light travels at a constant speed in a homogeneous medium:

The speed of light in a vacuum: 2.9979X 108

Properties of light

Light, its properties and how it travels

Calculate the distance light travels in a year.

Example (1)

5 min.

Multiple Choice

Calculate the distance light travels in a year.

• 9.5 x 10^15 m
• 9.5 x 10^14 m

• 9.5 x 10^13 m

• 9.5 x 10^12 m

•Reflection of light

•Refraction of Light

•Interference

•Diffraction

•Polarization

•Distraction

In this workshop ,we are going to discuss refraction and reflection of light.

Engineering applications on the
behavior of light

•The process of sight occurs by bouncing light

from the object to be viewed into the eye.

•From the above, we deduce that reflection of

light is: the bouncing of a light wave off a

reflective surface.

First :Reflection of light

1.

Regular/Specular Reflection

•All reflected rays are parallel

•This reflection occurs when rays fall on

a smooth polished surface such as a

mirror.

Types of reflection

First :Reflection of light

2.

Diffuse Reflection

•Reflected rays: random directions (non-

parallel).

•The reflective surface is not polished nor

smooth (rough).

Types of reflection
First :Reflection of light

The reflection process takes place according to laws that regulate this phenomenon. What

are these laws?

“The incident and reflected ray ,as well as the

axis perpendicular to the reflecting surface from

the point of incidence all lie in one plane

perpendicular to the reflecting surface.”

First law of reflection
First :Reflection of light

Angle of incidence = angle of reflection

𝜃i=𝜃r

First :Reflection of light

The second law of reflection

The figure shows two mirrors with an angle of

1200 .

A beam of light fell on the mirror (M1) at an

angle of 650with the normal.

Find the direction of the ray reflected from

mirror (M2).

Exercise (2)

5 min.

Multiple Choice

What is the angle for the ray deflected from mirror M2?

• 55

• 65

• 45

• 35

In your group, think if the two laws

of reflection apply in the case of

irregular reflection?

Think

3 min.

“image” you

“real” you

Plane mirrors
First :Reflection of light

•If the angle is between the two mirrors is 900,the

reflected rays return to the light source so that

they are parallel to their original path (Retro-

Reflection Phenomenon)

•We notice that each of the two rays was reflected

three times until it bounced parallel to the original

ray.

Applications on the second law for reflection

First :Reflection of light

Curved mirrors are mirrors whose surface consists

of a small part of a sphere. Images are formed in

these mirrors according to the law of reflection, but

the nature of the image in this case is different,

and curved mirrors are divided into two types.

•Concave mirrors

•Convex mirrors

Images formed by reflection in
curved mirrors

M

M

Origin axisY

Concave
mirror

Convex
mirror

Nq

Nq

Secondary axisY

Q

Q

The location and nature of the images formed by curved mirrors

can be determined by drawing two of three rays that can be

easily drawn and are shown, respectively, as follows:

1.

A ray passing through the center of curvature is reflected

back on itself.

2.

A ray parallel to the original axis and reflected at the focus.

3.

A ray passing through the focus is reflected parallel to the

original axis.

Images formed by reflection in
curved mirrors

When the mirror is convex ,where its

focus is virtual ,all images formed of the

object are virtual images, and the

following figure shows one of these

cases.

Images formed by reflection in
curved mirrors

All images formed arevirtual images

F

C

Use the following simulation to study the characteristics of the

images formed in curved mirrors (convex and concave), then

summarize the most important characteristics in the table:

Technology activity

Object position

Characteristics

The object is very far away

The object is far more than twice the focal length

The object is twice as far away from focal length( At the center of curvature)

The object is at a greater distance than the object focal length and smaller than twice the focal length

The object is placed at less than the focal length

5 min.

Open Ended

https://phet.colorado.edu/sims/html/geometric-optics/latest/geometric-optics_all.html

Using the above link, briefly describe the characteristics of each object position.

B

M

B

M

B

M

B

MB

Object position

The drawing

Image properties

The object is very far away
As small as possible / real

at the focus

The object is atmore than twice the

focal length

Real / inverted /miniature

Between the focus and the center

of curvature

The obejct is tat wice as far away
from focal length (At the center of

curvature)

Real / inverted / equal to the body

at the center of curvature

The object is at a greater distance than the object’s focal length and smaller than twice the focal length

Real/inverted/magnified

At a farther distance from the

center of the curvature

The object is at less than the focal

length

Virtual / moderate / magnified

You see inside the mirror

Images created by concave mirrors

Break

It is the change in the path of light when

it moves from one transparent medium

to another transparent medium.

Second :Refraction of light

Think - Share - Discuss

Interpret: The speed of light in air 3.00 x
108m/s But this speed decreases to
approximately 2 x 108m/s when light enters the
glass.

What causes refraction of light?

Second :Refraction of light

5 min.

What causes refraction of light?

Second :Refraction of light

Multiple Choice

What causes the refraction of light?

• If light falls from a less dense medium to a more dense medium, it will be refracted near the normal.

  If light falls from a medium with greater density to a medium with less density, it will be refracted away from the normal.

  The angle q2Known as the angle of refraction.

• When light enters inside the glass the light is absorbed by the atom A which causes the electrons to vibrate and move.

  These electrons emit light rays towards the atom B where light is absorbed again, which allows slowing down of light rays.

• Both answers are correct

The angle of refraction depends on:

Characteristics of the two media

Angle of incidence, according to the relationship:

sin 𝜃2
sin 𝜃1

= constant

where

v1:The speed of light in the first medium

V2: The speed of light in the second medium

Second :Refraction of light

v2
v1

=

Index of refraction (n):

Where (n) :
-has no unit
-n >1 because v is always less than c.

Index of refraction

𝑛 = 𝑙𝑖𝑔ℎ𝑡 𝑠𝑝𝑒𝑒𝑑 𝑖𝑛 𝑎𝑖𝑟 𝑜𝑟 𝑣𝑎𝑐𝑢𝑢𝑚

𝑙𝑖𝑔ℎ𝑡 𝑠𝑝𝑒𝑒𝑑 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚

𝑣

Second :Refraction of light

=

𝑐

When a wave travels from the first
medium to the second medium, the
wavelength changes while the frequency
remains constant.

𝜆1𝑛1 = 𝜆2𝑛2

Index of refraction
Second :Refraction of light

The first law:the incident ray, the refracted
ray, and the normal to the interface of two
media at the point of incidence all lie on the
same plane.

Laws of refraction
Second :Refraction of light

The second law (Snell’s law):

𝑛1 𝑠𝑖𝑛 𝜃1 = n2sin 𝜃2

Special case:

If light falls from air with index of refraction (n1=1) to

the medium with index of refraction(n2=n), then:

Laws of refraction
Second :Refraction of light

Using Snell’s law, track the path of the light

rays in the two figures (A) and (B) ,and

explain:

1- In which of the two figures is the ray

refracted approaching the normal?

2- In which of the two figures is the angle of

refraction greater than the angle of

incidence?

Exercise (3) - Individually

B

A

5 min.

A light ray traveling through the air, fell on

a glass surface n=1.52 at an angle of 30

degrees, as in the figure, find the angle of

refraction.

Question

5 min.

Multiple Choice

A light ray traveling through the air, fell on a glass surface n=1.52 at an angle of 30 degrees, as in the figure, find the angle of refraction.

• 19.2

• 31.5

• 9.2

• 12.9

A light ray traveling through the air, fell on

a glass surface n=1.52 at an angle of 30

degrees, as in the figure, find the angle of

refraction.

Question

5 min.

Calculate the speed of light emitted at a

plastic disc with index of refraction n=1.55

and wavelength of light in air = 780 nm.

Calculate the wavelength of light inside

the plastic disc.

Question

5 min.

Multiple Choice

Calculate the speed of light emitted at a plastic disc with index of refraction n=1.55 and  wavelength of light in air = 780 nm.

• 1.24 x 10^8 m/s

• 1.94 x 10^5 m/s

• 1.94 x 10^8 m/s

• 1.24 x 10^5 m/s

Multiple Choice

Calculate the wavelength of light inside the plastic disc with index of refraction n=1.55 and  wavelength of light in air = 780 nm.

• 405 nm

• 503 nm

• 305 nm

• 803 nm

Calculate the speed of light emitted at a

plastic disc with index of refraction n=1.55

and wavelength of light in air = 780 nm.

Calculate the wavelength of light inside

the plastic disc.

Question

5 min.

A ray of light fell from the water (n1=1.33) at an

angle(θ1=600) on a glass surface (n2=1.52)

Find:

1- The direction of the reflected beam (Θr = ?)

2- The direction of the refracted ray (Θ2= ​?)

Question

5 min.

Multiple Choice

What are the values for Θ_r and Θ₂ ?

• Θ_{r = 60}°

  Θ_{2 = 49.27}°

• Θ_{r = 40}°

  Θ_{2 = 49.27}°

• Θ_{r = 60}°

  Θ_{2 = 69.27}°

A ray of light fell from the water (n1=1.33) at an

angle(θ1=600) on a glass surface (n2=1.52)

Find:

1- The direction of the reflected beam (Θr = ?)

2- The direction of the refracted ray (Θ2= ​?)

Question

5 min.

The first law: the incident ray, the
refracted ray, and the normal to the
interface of two media at the point of
incidence all lie on the same plane.

Total Internal Reflection

• The angle of incidence (in the denser medium)

corresponding to the largest possible angle of refraction (90 degrees) is called the critical angle.

• If the angle of incidence exceeds the critical angle,

the ray is refracted within the same medium of
incidence ,this is known as total internal reflection.

• The critical angle Θc by substituting Θ2 with 90o in

Snell’s law:

n2>n1

1

2

2

1

2

1

2

2

1

1

sin

sin

90sin

sin

sin

sin

n
n

n

n

n

n

n

n

c

c

c

=

=
=
=










Total Internal Reflection

If light falls from inside sea
water(n1=1.33) to the air outside (n2=1).

Calculate the critical angle.

Solution:

Question

Sinθc=1÷1.33=0.75188

θc=sin-1(0.75188)=48.70

1

2

sin
n
n

c =

5 min.

When hit by light rays, convex and concave
lenses reflect light differently.

Images Formed by Refraction

Use the following simulation to study the characteristics of the

images formed in curved mirrors (convex and concave), then

summarize the most important characteristics in the table:

Technology activity – In pairs

Object position

Characteristics

The object is very far away

The object is far more than twice the focal length

The body is twice as far away from focal length( At the center of curvature)

The object is at a greater distance than the object focal length and smaller than twice the focal length

The object is placed at less than the focal length

5 min.

Open Ended

Use the following simulation to study the characteristics of the images formed in curved mirrors (convex and concave), then summarize the most important characteristics in the table: https://phet.colorado.edu/sims/html/geometric-optics/latest/geometric-optics_all.html

• Using the following figure, we find that

there is a relationship between the
position of the object S, the location of
the image S’ and focal length f. The
similarity of the two triangles FP'Q',
FOA we find that:

• The similarity of the two triangles OP’Q’

and OPQ we find that:

• By comparing (1) and (2) we find that:

General law - Mirrors and Lenses

)1(
'

'

'

''

f

fs

y
y

FO
FP

OA

QP

−
=

=

)2(
'

'

'

''

S
S

y
y

PO

OP

PQ

QP

=

=

f

S

S

Sf

S

f
S

f

fS

S
S

1

'
1

1

'
1

1

1

1
'

'

'

=

+

−

=

−

=
−
=

Although the previous equation was derived for the lens, we can derive it for the
diverging lens, as well as for the convex and concave mirror.

When using this law, the following must be taken into account:

1.

Focal length f is positive in the case of the concave mirror and the convex lens, and it is negative in the case of the convex mirror and the concave lens.

2.

Distance of the object S is positive if the body is real, and it is negative if the object is virtual.

3.

Distance of the image S’ is positive if the image is real and negative if the image is virtual.

4.

All distances S’-S- f are measured from the center of the mirror or lens.

General law - Mirrors and Lenses

Place an object of length 5cm 40cm away

from a concave mirror with a focal length

of 15cm.

Calculate the distance and length of the

image as well as the magnification in the

mirror

cm

y

y

S
S

y
y
m

cm

S

S

f

S

f

S

S

35
40
24
'

40
24

5

'

'

'

24'

..........
600
25

40
1

15
1

1

1

'

1

1

'

1

1

=

=

=

=

=

=

=

−

=

−

=

=

+

Question

5 min.

Multiple Choice

Place an object of length 5cm 40cm away from a concave mirror with a focal length of 15cm.

Calculate the distance and length of the image.

• Distance = 24 cm

  Length = 5 cm

• Distance = 14 cm

  Length = 5 cm

• Distance = 24 cm

  Length = 3 cm

• Distance =14 cm

  Length = 3 cm

Place an object of length 5cm 40cm away

from a concave mirror with a focal length

of 15cm.

Calculate the distance and length of the

image as well as the magnification in the

mirror

cm

y

y

S
S

y
y
m

cm

S

S

f

S

f

S

S

35
40
24
'

40
24

5

'

'

'

24'

..........
600
25

40
1

15
1

1

1

'

1

1

'

1

1

=

=

=

=

=

=

=

−

=

−

=

=

+

Question

5 min.

The magnification of the lens or mirror can be
expressed in the equation below:

Magnification of Lenses and Mirrors

S
S

y
y
m
'

' =
=

Digital Platforms Evaluation- Science Teachers
2024

https://forms.office.com/r/7Rfka8HNgP

Exit card

• Something new I learned today. . . . . . . . .

• Something I would love to know more

about. . . .

• One of the benefits I gained from today's

training. . . . .

3 min.

Open Ended

Please complete the exit ticket

Poll

Please rate today's training session out of 5

• 1

• 2

• 3

• 4

• 5

References

• https://www.pbslearningmedia.org/collection/universe/topic/waves/
• Principles of Optics: 60th Anniversary Edition 7th Edition
• https://www.bartleby.com/subject/science/physics/concepts/mirrors-

and-lenses

Thanks