Total Internal Reflection
Radiation & Matter 4:
Total Internal Reflection
AIM
The aim of this unit is to investigate what happens when light moves from an optically dense
medium (glass) to an optically less dense medium (air). The phenomenon found is used in
modern telephone communication to transmit information over long distances.
OBJECTIVES
At the end of this unit you should be able to:
•
explain what is meant by total internal reflection.
•
explain what is meant by critical angle θc.
•
describe the principles of a method for measuring the critical angle.
•
derive the relationship sin θc = 1/n where θc is the critical angle for a medium of
absolute refractive index n.
•
carry out calculations involving the relationship sin θc = 1/n .
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Radiation and Matter
Total Internal Reflection
ACTIVITY 6
Critical angle of a perspex block
Aim
Measurement of the critical angle θc of a perspex block.
Apparatus
Ray box and single slit, 12 V power supply, semicircular perspex block, sheet of white paper,
protractor.
Instructions
• Place the block on the white paper and trace around its outline. Draw in the normal at the
midpoint B.
•
Draw a line representing the angle θp = 10°, the line AB in the diagram above.
•
Direct the raybox ray along AB and mark in the point C where the ray emerges.
•
Draw a line representing the refracted ray, the line BC in the diagram above.
•
Measure the angle θa, the refracted angle in air.
•
Use an appropriate format to record your results.
•
Repeat for other values of incident angle θp.
•
Determine the critical angle θc for this perspex block.
Strathaven Academy
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Radiation and Matter
Total Internal Reflection
Critical angle and total internal reflection
When light travels from a medium of high refractive index to one of lower refractive index
(e.g. glass into air), it bends away from the normal. If the angle within the medium θm is
increased, a point is reached where the angle in θa becomes 90º.
The angle in the medium which causes this is called the critical angle, θc.
If the angle in the medium is greater than the critical angle, then no light is refracted and
Total Internal Reflection takes place within the medium.
Fibre-optics
A thin glass fibre uses the principle of total internal reflection. The rays of light always strike
the internal surface of the glass at an angle greater than the critical angle.
A commercial optical fibre has a fibre core of high refractive index surrounded by a thin,
outer cladding of glass with lower refractive index than the core. This ensures that total
internal reflection takes place.
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Radiation and Matter
Total Internal Reflection
Relationship between critical angle and refractive index
At the critical angle, θm = θc and θa = 90°
sin θ a
sin 90 
1
=
=
sin θ m
sin θ c
sin θ c
n=
1
sin θ c
Total internal reflection is more likely to take place in a material with a small critical angle;
therefore, it is desirable to use a medium of high refractive index when designing optical
fibres.
Examples
1.
Calculate the critical angle for water of refractive index = 1.33.
sinθ c =
2.
1
1
=
= 0.752
n 1.33
θc = 49°
A ray of light strikes the inside of a glass block as shown. Will the ray emerge from
the glass?
sinθ c =
1
1
=
n
1.5
θc = 41.8°
The angle inside the glass is 60º, which is greater than 41.8º.
Hence total internal reflection occurs.
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Radiation and Matter
Total Internal Reflection
Uses of internal reflection
1.
The critical angle of glass is 42° so a ray of light striking a face in a 45° prism will
undergo total internal reflection (see diagrams below). Prisms of this type are used in
binoculars and periscopes. Car reflectors and road signs also use this principle to shine
brightly when headlights strike them.
45°
45°
45°
45°
2. Diamonds and other precious stones have high refractive indices and therefore low
critical angles. The light is totally internally reflected inside the stone, with the stone
cut in certain ways to maximise the effect. The reflected light is only emitted in certain
directions giving bright beams of coloured light (different colours are refracted
differently, remember). This is what causes the stone to sparkle.
3. Fibreoptic cables (in communication and medicine) use total internal reflection to
transmit information along a glass fibre - see your SG notes for more information.
Refraction & Total Internal Reflection in nature
1. Apparent depth - water looks shallower than it is
EYE
LIGHT IS REFRACTED
AWAY FROM THE NORMAL.
APPARENT
DEPTH
REAL
DEPTH
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Radiation and Matter
Total Internal Reflection
2. A stick appears bent where it enters water
EYE
AIR
WATER
3. Mirage
Hot air near the ground is less
dense than the cooler air above.
T.I.R. Takes place at the boundary
between the two.
TIR TAKES
PLACE HERE
DENSE AIR
LESS DENSE AIR
The person sees the tree directly, and what looks like a reflection of the tree
due to the T.I.R. The human brain interprets this as meaning that there must
be water causing the reflection - it is a powerful optical illusion. The air is
swirling around; this causes the reflection to ripple, and this reinforces the
illusion of water.
There must be rain in front of you and
sunlight behind you to produce a rainbow.
The sunlight is split into colours by the
refractions as shown.
4. Rainbow
SUNLIGHT
T.I.R.
RAINDROP
VIOLET
EYE
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Note that you will only see one colour from
each raindrop. This diagram might confuse
you - red is always on the outside of the
rainbow. If this person sees violet from
this drop, the red of the rainbow would
come from higher up raindrops.
Raibows are caused by the angle that the
light enters your eye. This is why you can’t
ever get to the end of a rainbow, and why
they are curved - all red rays are entering
your eye at the same angle and so on.
Moonlight can also cause this effect - it is
known as a moonbow and is quite rare to
see. Search for moonbows using Google
Images!
RED
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Radiation and Matter
Total Internal Reflection
Total Internal Reflection
25. Calculate the critical angle for each material using the refractive index given in the table
below.
Material
n
Glass
1.54
Ice
1.31
Perspex
1.50
26. A beam of infrared radiation is refracted by a type of glass as shown.
a) Calculate the refractive index of the glass for infrared.
b) Calculate the critical angle of the glass for infrared.
27. A ray of light enters a glass prism of absolute refractive index 1.52, as shown:
a)
b)
c)
d)
e)
Why does the ray not bend on entering the glass prism?
What is the value of angle X?
Why does the ray undergo total internal reflection at O?
Redraw the complete diagram showing the angles at O with their values.
Explain what would happen if the experiment was repeated with a prism of material
with refractive index of 1.30.
28. The absolute refractive indices of water and diamond are 1.33 and 2.42 respectively.
a) Calculate the critical angles for light travelling from each substance to air.
b) Comment on the effect of the small critical angle of diamond on the beauty of a well
cut stone.
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Radiation and Matter
Total Internal Reflection
Total Internal Reflection Extension Question
The four blocks shown are Perspex, and have a refractive index of 1.5. Use this information to
determine the path of the ray of light until it leaves the block. Your answer should have a
sketch of the ray(s) and all working and reasoning shown!
45°
25°
60°
60°
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Radiation and Matter