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physics course exercises
Liceo Scientifico Belfiore - Mantova
reflection and refraction
of light
in accordo con il
Ministero dell’Istruzione, Università, Ricerca
e sulla base delle
Politiche Linguistiche della Commissione Europea
percorso formativo a carattere
tematico-linguistico-didattico-metodologico
scuola secondaria di secondo grado
teachers
Luigi Togliani and Claudio Borghi
reflection and refraction of light
Indice Modulo
Strategies - Before



Prerequisites
Linking to Previous Knowledge and Predicting con questionari basati su
stimoli relativi alle conoscenze pregresse e alle ipotesi riguardanti i contenuti
da affrontare
Italian/English Glossary
Strategies – During



Video con scheda grafica
Keywords riferite al video attraverso esercitazioni mirate
Conceptual Map
Strategies - After

Esercizi:
 Multiple Choice
 Matching
 True or False
 Cloze
 Flow Chart
 Think and Discuss

Summary per abstract e/o esercizi orali o scritti basati su un questionario
e per esercizi quali traduzione e/o dettato

Web References di approfondimento come input interattivi per test orali e
scritti e per esercitazioni basate sul Problem Solving
Answer Sheets
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reflection and refraction of light
1
Strategies Before
Prerequisites
Trigonometry
Geometrical
optics
basic concept of
goniometric functions
light ray model
rectilinear propagation of
light
theorems about rightangled triangles
Reflection and
refraction of light
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reflection and refraction of light
2
Strategies Before
Linking to Previous Knowledge and Predicting

Do you know the definitions of sine, cosine and tangent of an angle?

Do you know the relationships between the sides of a right-angled triangle
and the goniometric functions of the angles?

Do you know the light ray model?
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reflection and refraction of light
3
Strategies Before
Italian/English Glossary
Angolo
Angle
Angolo di apertura di un prisma
Apex angle of a prism
Angolo limite
Critical angle
Coseno
Cosine
Indice di rifrazione
Index of refraction
Interfaccia
Interface
Luce monocromatica
Monochromatic light
Mezzo
Medium
Normale
Normal
Ottica geometrica
Optical geometry
Raggio incidente
Incident ray
Raggio riflesso
Reflected ray
Raggio rifratto
Refracted ray
Riflessione
Reflection
Riflessione totale
Total internal reflection
Rifrazione
Refraction
Seno
Sine
Superficie di incidenza
Incidence surface
Tangente
Tangent
Vuoto
Vacuum
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reflection and refraction of light
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Strategies During
Keywords
1) Circle the optical concepts or phenomena:
impact – incidence – ray – reflection – concentration – osmosis – refraction
– dispersion – depth – altitude – critical angle
2)

Completion:
The incident ray, the reflected ray, the ……………ray and the …………….. to the
surface at the point of the incidence lie in the same …………….

Light can travel through ….………..

A light ray passing from one …………… medium to another is partially reflected
and partially ……………..

The speed of light is lower than c in every ............

When an incident ray meets a surface between two mediums, the ..............
ray belongs to the medium from which it comes.

When an incident ray meets an incidence ……………. between two mediums, it
can …………… the second medium.
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reflection and refraction of light
5
Strategies During
Conceptual Map
Complete the conceptual map using the following words:
total internal
reflection
θ1 = θ2
critical
angle
Snell’s law
Incidence on a
surface between
two mediums
Rays of light travelling in a straight line
reflection and
refraction
refraction
reflection
If n2 > n1 it is possible that the
transmitted ray does not exist
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reflection and refraction of light
6
Strategies After
Multiple Choice
1. A ray of light forms an angle of 40° with the surface of a mirror. The value of
the angle of reflection is:
a.
b.
c.
d.
40°
50°
0°
none of these
2. Two mirrors are perpendicular (see figure). The
1st mirror reflects the ray CA; the reflected ray
meets the 2nd mirror in E. The new ray ED
E
D
a. is not parallel to CA
b. may be perpendicular to AE
c. is perpendicular to AE
d. none of these
A
B
C
3. See the figure of item 2. If BÂC = 70° then the value of AÊD is
a.
b.
c.
d.
70°
150°
130°
none of these
4.- How many images given by the two mirrors AB and BC (BA is perpendicular
to BC) can you see of the object in the figure?
a.
b.
c.
d.
2
3
4
none of these
B
A
5.- A ray of light comes from medium 1 to medium 2 (see figure). The ray of
reflection and the ray of refraction are perpendicular. If γ = 30° then
a.
b.
c.
d.
β = 30°
n2/n1 is around 1,4 according to Snell’s law
n2/n1 is around 1,9 according to Snell’s law
none of these
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1
α
β
2
γ
C
reflection and refraction of light
6.- When light passes from medium 1 to medium 2 the ratio of the indices of
refraction is n2/n1 = 1.6. If the value of the angle of refraction is 20° then the
value of the angle of reflection is about:
a.
b.
c.
d.
29°
31°
33°
none of these
7.- A ray of light passes from water (index of refraction 1.33) to air. If the angle
of incidence is 45° then
a.
b.
c.
d.
the angle of refraction is about 70°
the angle of refraction is about 32°
there is not refraction but total internal reflection
none of these
8.- The speed of light in vacuum is about 3,0·108 m/s . The speed of light in
glass with index of refraction 1.5 is
a.
b.
c.
d.
3.0·108 m/s because the speed of light is always constant
2.0·108 m/s
undefined because data are not enough
none of these
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reflection and refraction of light
7
Strategies After
Matching
Match the words on the right with the correct explanation on the left:
1. Angle of reflection
2. Index of refraction
3. Critical angle
4. Refraction
5. Total internal reflection
6. Image
a. Speed of light in a vacuum / speed of
light in medium
b. A phenomenon that happens when a
ray of light strikes a medium boundary
with an angle of incidence greater than
a certain angle
c. The angle which the reflected ray
makes to the normal
d. When on object stands in front of a
mirror
e. An angle above which total internal
reflection occurs
f. A phenomenon that happens when a
ray of light changes its direction when
it passes from a medium to another
one
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reflection and refraction of light
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Strategies After
True or False
State if the following sentences are true (T) or false (F).
1.- Light may pass through matter, but can’t pass through vacuum.
T
F
2.- The speed of light has a finite value but it can’t be measured.
T
F
3.- Light may be only reflected by a reflective surface like a mirror.
T
F
4.- A mirror may create images that can’t be collected by a screen.
T
F
5.- A ray of light passes from water to air. The angle of incidence
may be 50°.
T
F
6.- Two plane mirrors may form 5 images of an object.
T
F
7.- The index of refraction is always a number greater than 1.
T
F
8.- When a ray of light passes from water (index of refraction 1.33)
to glass (index of refraction 1.50) it can’t be totally reflected.
T
F
9.- When a ray of light passes through a prism you may observe
the dispersion of light.
T
F
10.- A ray of light passes from medium 1 (n1=2.6) to medium 2
(n1=1.3). According to Snell’s law: 1=30° and 2=60°.
T
F
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reflection and refraction of light
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Strategies After
Cloze
Complete the text using the words or the expressions listed below.
The phenomenon of refraction is the ...............[1] of light rays when they are
passing through a surface between one ................[2] material and another. It
is described by Snell's law:
where θ1 is the angle between the ray and the ................[3] in the first
medium, θ2 is the angle between the ray and the .................[4] in the second
medium, and n1 and n2 are the ................[5].
A ...............[6] is an optical and meteorological phenomenon that causes a
spectrum to appear in the sky when the Sun shines on droplets of water in the
Earth's atmosphere. It usually takes the form of a single ...............[7]. The
colour of the ................[8] is ............... [9] on the upper side of the
............[10] and ............... [11] on the inner side. The ..............[12] is
caused by light being ...............[13] while entering the droplet.
___________________________________________________________
arc – bending – indices of refraction – normal – rainbow – red – refracted
– transparent – violet
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reflection and refraction of light
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Strategies After
Flow Chart
Complete the following flow chart referring to a ray of light emitted by
an optical source to a plane surface. You can use the terms listed below:
the ray is refracted – the ray is totally reflected
start
a ray of
light
input
plane
crosses the surface
between medium 1
and medium 2
false
output
true
output
end
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reflection and refraction of light
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Strategies After
Think and Discuss
The following activity can be performed in a written or oral form. The teacher
will choose the modality, depending on the ability (writing or speaking) that
needs to be developed.
The contexts in which the task will be presented to the students are:
- the student is preparing an article about reflection and refraction of light
- the student is preparing a report about experimental activities regarding
reflection and refraction of light
The student should:
1) Choose one of the following topics:



Images with a plane mirror
The refraction of light with a half cylindrical dioptre
The dispersion of light with a prism
2) Prepare an article or a debate, outlining the main points of the argument, on
the basis of what has been studied.
3) If the oral activity is the modality chosen by the teacher, the student should
present his point of view on the topics to the whole class and a debate could
start at the end of his presentation.
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reflection and refraction of light
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Strategies After
Summary
Reflection is the change in direction of a wavefront at an interface between two
different media so that the wavefront returns into the medium from which it
originated. In particular we observe the reflection of light. A mirror provides the
most common model for specular light reflection. Reflection is principally
described by the law of reflection, which states that the angle of incident equals
the angle of reflection. Specular reflection forms images. Reflection from a flat
surface forms a mirror image, which appears to be reversed from left to right
because we compare the image we see to what we would see if we were rotated
into the position of the image.
Refraction is the change in direction of a wave due to a change in its speed.
Refraction of light is the most commonly observed phenomenon, but any type of
wave can refract when it interacts with a medium, for example when sound
waves pass from one medium into another or when water waves move into
water of a different depth. Refraction is described by Snell's law, which states
that for a given pair of media and a wave with a single frequency, the ratio of
the sines of the angle of incidence θ1 and angle of refraction θ2 is equivalent to
the ratio of phase velocities (v1 / v2) in the two media, or equivalently, to the
opposite ratio of the indices of refraction (n2 / n1):
The critical angle is the angle of incidence above which total internal
reflection occurs. The angle of incidence is measured with respect to the
normal at the refractive boundary (see diagram illustrating Snell's law). Consider
a light ray passing from glass into air. The light emanating from the interface is
bent towards the glass. When the incident angle is increased sufficiently, the
transmitted angle (in air) reaches 90 degrees. It is at this point no light is
transmitted into air. The critical angle θc is given by Snell's law,
.
Rearranging Snell's Law, we get incidence
.
To find the critical angle, we find the value for θi when θt = 90° and thus
sin θt = 1. The resulting value of θi is equal to the critical angle θc .
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reflection and refraction of light
Now, we can solve for θi, and we get the equation for the critical angle:
If the incident ray is precisely at the critical angle, the refracted ray is tangent to
the boundary at the point of incidence. If for example, visible light were
traveling through acrylic glass (with an index of refraction of 1.50) into air (with
an index of refraction of 1.00), the calculation would give the critical angle for
light from acrylic into air, which is
.
Light incident on the border with an angle less than 41.8° would be partially
transmitted, while light incident on the border at larger angles with respect to
normal would be totally internally reflected.
If the fraction n2 / n1 is greater than 1, then arcsine is not defined—meaning
that total internal reflection does not occur even at very shallow or grazing
incident angles.
So the critical angle is only defined when n2 / n1 is less than 1.
1) Answer the following questions. The questions could be answered
in a written or oral form, depending on the teacher’s objectives.
a. What does the law of reflection state?
b. What is a mirror image?
c. When can you see the phenomena of reflection and refraction at the same
time?
d. How can you define the phenomenon of refraction?
e. What is the relationship between the angle of incidence and the angle of
refraction?
f. Why the angle of refraction is lower than the angle of incidence if the index of
refraction of the second medium is greater than the index of refraction of the
first medium?
g. Why is it possible that the refracted ray does not exist?
h. When does the critical angle exist?
i. How can you calculate the critical angle?
j. What happens when it occurs the phenomenon of the total internal reflection?
2) Write a short abstract of the summary (max 150 words) highlighting
the main points of the video.
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reflection and refraction of light
Web References
Reflection, refraction and dispersion of light are treated in their different aspects,
experimental and theoretical, in these sections, also with pictures, diagrams,
tables and examples:
Reflection:
http://en.wikipedia.org/wiki/Reflection_(physics)
Refraction:
http://en.wikipedia.org/wiki/Refraction
Total internal reflection:
http://en.wikipedia.org/wiki/Total_internal_reflection
Dispersion:
http://en.wikipedia.org/wiki/Dispersion_(optics)
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reflection and refraction of light
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Activities Based on Problem Solving
a) At the interface between two materials a light ray is at an angle of 41.00o
with the interface on a side with an index of refraction of 2.15. If the light is
at an angle of 42.44o on the other side of the interface, what is the index of
refraction on this side?
b) A prism with an apex angle of 60.0° is constructed of glass with an index of
refraction of 1.41. The prism is illuminated with a narrow beam of collimated
and monochromatic light, whose angle of incidence is of 45.0°. What is the
angle δ between the direction of the emergent ray and the direction of the
incident ray?
c) A light ray hits a surface at an angle of 38.00o. The material on the other
side of the surface has an index of refraction of 1.56 and the light is making
an angle of 55.57o with the surface when it exits on this side. What is the
index of refraction on the incident side of the interface?
d) Will light traveling from glass to air reach the air if it approaches at a 38o
angle to the (flat) surface? Assume that the index of refraction of glass for
the used light is 1.51.
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reflection and refraction of light
Answer Sheets
Keywords:
1) incidence – ray – reflection – refraction – dispersion – critical angle
2) refracted – normal – plane – vacuum – transparent – refracted – medium –
reflected – surface – enter
Conceptual Map:
Rays of light travelling in a straight line
Incidence on a surface
between two mediums
reflection and
refraction
reflection
refraction
Snell’s law
If n2 > n1 it is possible that the
transmitted ray does not exist
θ1 = θ2
critical angle
total internal
reflection
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reflection and refraction of light
Multiple Choice:
1b – 2b – 3d – 4b – 5d – 6c – 7b – 8b
Matching:
1c – 2a – 3e – 4f – 5b – 6d
True or False:
1F -2F - 3F - 4T - 5F - 6T - 7F - 8T - 9T - 10F
Cloze:
[1] bending; [2] transparent; [3] normal; [4] normal; [5] indices of refraction;
[6] rainbow; [7] arc; [8] rainbow/arc; [9] red; [10] rainbow/arc; [11] violet;
[12] rainbow;[13] refracted
Flow Chart:
the ray is totally reflected (output on the left)
the ray is refracted (output on the right)
Activities Based on Problem Solving
a)
b)
c)
d)
2.20
30.0°
1.12
No, the angle of incidence is greater than the critical angle of 42o.
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