S M K Pahi
Bidang sains dan matematik
LESSON 5.3 - Total internal reflection
The Critical Angle, c
The angle of incidence in an optically more dense
medium which results in angle of refraction of 90o in
an optically less dense.
LESSON 5.3
TOTAL INTERNAL REFLECTION
What is meant by ‘ Total Internal Reflection ‘
Determine the relationship between Refractive
index (n) and Critical angle (c)
The total reflection of a beam of light at the interface
of one medium and another medium of lower
refractive index
(optically less dense) , when the angle of incidence to
the second medium exceeds a specific critical angle.
Ray diagram to show how the Total Internal
Reflection happen ?
n = sin i
sin r
n=
(1) Angle of incidence ,i1 is small.
Produces a strong refracted ray and a
weak reflected ray.
n=
(2) Angle of incidence is increased as i2.
Produces a refracted ray and a reflected
ray whose intensity has increased
compared to the situation in (1)
1
sin c
Example 1
(3) Angle of incidence is increased to the
critical angle, c.
The refracted ray travels along the waterair boundary.
The diagram shows a light ray entering in a glass
prism.
[ Refractive index of glass = 1.51 ]
(4) Angle of incidence , i3 > c.
No refraction occurs.
All the light is reflected within the water .
Total internal reflection occurs.
(a) Determine the critical angle of the glass.
(b) Draw the ray light after it passes through a
point P until the direction of the ray of light
unchange.
The conditions for the occurrence of total internal
reflection.
(1) The light ray must be travel from an
optically denser medium to less dense
medium.
(2) The angle of incidence must be greater
than the critical angle.
1
S M K Pahi
Bidang sains dan matematik
LESSON 5.3 - Total internal reflection
Experiment to determine the critical angle of
glass.
Solution
A semi-circular glass bolock is placed on a sheet of
white paper.
The outline of the glass block is traced onto the paper
as ABC.
The glass block is put aside.
A normal ON is drawn.
The glass block is placed again on its outline.
A ray of light from the ray box is directed to glass
block.
The angle of incidence is increased until the refracted
ray travels along the length of the air- glass boundary
( refraction angle is 90o ).
By using a protractor the angle of incidence is
measured = c
The crtical angle of the glass block = c
Example 2
Figure shows a light ray AO travelling from medium X
to the air.
[The refractive index of medium X = 2.0 ]
Natural phenomena and Use of Total Internal
Reflection.
Mirages(fatamorgana)
Draw the ray light after it passes through the point O
when
(a) θ = 25o (b)θ = 30o (c) θ = 35o
Solution
In thetime when the weather is hot , the incidence ray
from the sun passes through a dense air layer to a
less dense air layer.
Finally , the ray of passes through the air layer close
to the road surface at an angle of incidence greater
than the critical angle.
Total internal reflection occurs at this layer.
The observer sees the image of the sky on the
surface of the road as a pool of water.
2
S M K Pahi
Bidang sains dan matematik
LESSON 5.3 - Total internal reflection
Fibre optics
Prism periscope
The periscope is built using two right –angled prisms
made of glass .
The crtical angle of the prism is 42o .
The angle of incidence is 45o is greater than the
critical angle.
Total internal reflection occurs.
The characteristics of the images are
(i) Virtual
(ii) Upright (iii) Same size as
the object.
Advantanges of the prism periscope compared to
mirror periscope,
(i) The image is brighter
(ii) No multiple images is formed (very clear)
The external wall of a fibre optic is less dense than
the internal wall.
When light rays travel from a denser internal wall to
aless dense external walls at an angle that exceeds
the critical angle , total internal reflection occurs.
The advantages of the fibre optics:
(i) Cheap
(ii) easily handled
(iii) More information can be transmitted
Binocular
A ray light experiences two total internal
reflections at each prism. The two prisms is to
invert the image (upside down and right-to-left.)
But the lenses in the binoculars also invert the
image and so the the prisms put it back the right
way again.
So the final image in binoculars is upright ,not
laterally inverted and magnified.
3
S M K Pahi
Bidang sains dan matematik
LESSON 5.3 - Total internal reflection
TUTORIAL 3
1
A ray of red light travelling in glass strikes the
glass-air boundry . Some light is reflected and
some is refracted. Which diagram shows the
paths of the rays?
2
One of the diagram below shows the path of a
beam of
light that is incident on a water-air surface with
angle of incidence greater than the critical angle.
Which one is it?
4
Which of the following shows total internal
reflection?
5
The diagram shows light ray XO experiencing
total internal reflection when travelling from the
glass to air.
Which statements about total internal reflection
are correct?
3
P - θ is more than the critical angle of glass
Q - The speed of light in the glass is higher
than in air
R - The refractive index of glass is greater
than air
Which of the following diagram correctly shows
the total internal reflection of ray of light?
[ Refractive index of medium X = 1.3
Refractive index of medium Y = 1.5 ]
A
B
C
D
4
P and Q
P and R
Q and R
P,Q and R
S M K Pahi
Bidang sains dan matematik
LESSON 5.3 - Total internal reflection
6
The diagram shows a semi-circular plastic block
is placed in a liquid.
A
C
OB
OD
B
D
OC
OE
9
A ray of light incident on one side of a
rectangular glass block. If the angle of refraction
in the glass block is 40o ,
which one of the following diagrams best
reprents this ray?
[ The critical angle of glass is 42o ]
10
The diagram shows a light ray, P, directed into a
glass block. The critical angle of the glass is 42o.
In which direction does the light move from point
Q?
Which of the following is correct?
A
B
C
D
7
Density of the plastic block is less
than density of the liquid
Refractive index of the plastic block
is less than refractive index of the
liquid
Critical angle of the plastic block is
less than critical of the liquid
Angle of incidence is less than
critical angle of the liquid
The diagram shows a ray of light passing
through medium to medium N.
Which of the following is correct?
A
B
The angle of reflection is 55o
The critical angle of medium M less than
C
Density of medium M less than the density
of medium N
35o
8
The figure shows a ray of light AO traveling in a
liquid strikes the liquid-air boundary.
[ The critical angle of the liquid = 45o ]
In which direction does the light move from O ?
5
S M K Pahi
Bidang sains dan matematik
LESSON 5.3 - Total internal reflection
11
The diagram shows a light ray , M, directed into
a glass block. The critical angle of the glass is
42o.
In which diagram does the light move from point
O?
12
The figure shows a ray of light is incident in air
to the surface of Prism A and B.
15
The diagram shows a light ray travelling from
air into a plastic block with an angle of incidence
,X. What is the critical angle of the plastic?
16
The diagram shows a light ray travelling from air
into a glass prism.
Which comparison is correct ?
A
B
C
13
The critical angle is
A
B
C
D
14
Density of prism A < density of prism B
Critical angle of prism A < critical angle of
prism B
Refractive index of prism A < refractive
index of prism B
the smallest angle of incidence in
optically more dense medium
the smallest angle of incidence in
optically less dense medium
the greatest angle of incidence in optically
more dense medium
the greatest angle of incidence in optically
less dense medium
What is the critical angle of the glass?
A
C
E
Which of the following shows the correct critical
angle , c of the semi- circular glass block ?
6
40o
60o
80o
B
D
50o
70o
S M K Pahi
Bidang sains dan matematik
LESSON 5.3 - Total internal reflection
17
A
C
E
18
44.5o
48.8o
54.3o
B
D
46.9o
49.2o
The refractive index of plastic block is 13 .
5
What is the value of the cosine of the critical
angle of the plastic?
A
19
21 The diagram shows a cross- section of a fibre
optic cable.
The refractive index of water is 1.33.
What is the critical angle of the water.
5
12
B
C
13
12
D
E
13
5
Which comparison is correct ?
A
B
C
12
13
22
5
13
Density of P < density of Q
Density of P >density of Q
Density of P = density of Q
The diagram shows a long block of glass over
an object O. Light from O reaches the top
surface of the glass at X , Y and Z.
The figure shows a ray of light AO traveling in
medium X strikes the medium X-air boundary.
[ The refractive index of medium X = 1.12 ]
(a) What is the name given to the bending of
light at X?
…………………………………………………
(b) At Z light is ……………. ……………
reflected.
(c)
In which direction does the light move from O ?
20
…………………………………………………
(d) Explain why light is reflected as shown at
Z?
A OE
B OD
C OC
D OB
Which of the following not applies the principle
of total internal reflection?
A
B
C
D
Give the name of the angle marked R.
…………………………………………………
Prism binocular
Mirror periscope
Optical fibre
Road mirage
…………………………………………………
…………………………………………………
7
S M K Pahi
Bidang sains dan matematik
LESSON 5.3 - Total internal reflection
23
A ray of light is incident at an angle of 60o at
mid-point O of the plane face AB of a
semicircular glass block as shown in Figure(a).
ray directed towards O which undergoes
total internal reflection at the surface AB.
24
(a)
(i) Calculate the angle of refraction
of this ray
at O, given that the refractive index of
the glass is 1.5.
(ii)
(b)
The diagram show a ray of light XOYZ is
incident at angle of 600 to an ice block.
Draw the path of this ray from O on
Figure(a) and continue its path until it
has emerged into the air.
(i) Calculate the critical angle for
the glass-air boundry.
(ii)
(a) Mark the critical angle of ice with ”c” in the
figure above.
(b) Determine the value of the critical angle ,
c.
On Figure(b) below draw the the path
of a ray which travels through the
glass to O in such way it strikes the
surface AB at an angles of incidence
equal to the the critical angle and
continues the path of this ray after it
has struck the surface AB at O.
(c)
Calculate the refractive index of ice.
(d) Explain how the direction of ray of light XO
can be changed to ensure the total internal
reflection will occur ?
(c) On Figure(c) draw the complete path of a
.............................................................................
8
S M K Pahi
Bidang sains dan matematik
LESSON 5.3 - Total internal reflection
.............................................................................
(e) What happen to the critical angle when
the ice block is replaced by a substance
which has the refractive index 1.8 ?
………………………………………………………
………………………………………………………
25
The diagram shows a ray of light XO is incident
to a glass prism PQR.
[The refractive index of glass is 1.5]
(a) Why is the ray of light XO entering the
prism in
a straight line?
.............................................................................
.............................................................................
(b) Determine the critical angle of the glass
prism.
(c)
By using certain calculations, draw the
complete path of a ray started from Y until
the direction of the path of ray unchanged.
9