REFRACTION OF LIGHT
This is the change in speed of light as it travels though different transparent media.
The bending of light is results or effects of the change in speed of light
Effects of refraction:
• The bending of light at angle of incidence greater than zero.
• Rule looks bent when placed in glass of water.
• A deep swimming pool or dam appears shallow.
RAY DIAGRAM FOR REFRACTION
This shows the path of light ray through a parallel sided glass block.
TERMS RELATED TO REFRACTION
Incident ray: the light ray travelling towards the boundary of a medium.
Refracted ray: light ray that travels away from the boundary of the media.
Emergent ray: light ray that leaves the other parallel side of glass block.
NB: Emergent ray is always parallel to the incident ray.
Normal is an imaginary line perpendicular to the boundary between the two media
Angle of incidence (i): angle between the incident ray and the normal.
Angle of refraction (r): angle between the normal and the refracted ray.
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FACTS ABOUT REFRACTION
When light travels from a less optically dense medium to a more optically dense medium it
bends towards the normal.
When light travels from a more optically medium to a less optically dense medium it bends away
from the normal
When light travels along the normal it does not bent.
WHY? Angle of incidence is zero therefore angle of refraction is also zero.
REFRACTIVE INDEX
The standard symbol for refractive index is n.
Refractive index is a unit less quantity.
REFRACTIVE INDEX IN TERMS OF SPEED OF LIGHT
The rate of change in speed of light as it travels through different media i.e.
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The ratio of speed of light in air to speed of light in medium.
Mathematically is represented as follows:
speed of light in air
refractive index=
speed of light in medium
In symbols is represented as follows:
c
n=
v
EAMPLES
1 Light travels from air at the speed of 3 х108 m/s into glass at the speed of 2 х108 m/s
Calculate the refractive index of glass.
8
3 × 10 m/ s
n= 8
2 ×10 m/ s
n=1.5
2 Light travels from air into glass of refractive index 1.5. The speed of light in air is 3 х10 8 m/s.
Calculate the speed of light in glass.
c
n=
v
c
v=
n
8
3 × 10 m/s
v=
1.5
8
v=2 ×10 m/s
REFRACTIVE INDEX IN TERMS OF ANGLES
The rate of bending of light as it travels through different media at angle of incidence greater than zero
i.e.
The ratio of sine of angle of incidence in air to sine of angle of refraction in medium.
Mathematically is represented as follows:
sine of angle of incidence
refractive index=
sine of angle of refraction
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In symbols is represented as follows:
sin i
n=
sin r
EAMPLES
1 Light travels from air into glass at an angle of incidence 30° and produces an angle of refraction
of 19°.
Calculate the refractive index of glass.
sin i
n=
sin r
sin 30 °
n=
sin19 °
n=1.54
2 Light from air enters a diamond block and produces an angle of refraction of 10°. The refractive
index of water is 2.42.
Calculate the angle of incidence.
sin i
n=
sin r
−1
i=sin (n ×sin r )
−1
i=sin (2.42× sin 10 °)
i=24.8 °
3 Light from air enters water at an angle of incidence 50°. The refractive index of water is 1.33.
Calculate the angle of refraction in water.
sin i
n=
sin r
−1 sin i
r =sin ( )
n
−1 sin 50 °
r =sin ( )
1.33
r =35.2°
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EXPERIMENTAL DETERMINATION OF REFRACTIVE INDEX OF GLASS
RAY BOX METHOD
Shines a light ray at angle to the glass block
Mark and draw the normal and path of the emergent ray
Draw the path of refracted ray between the point of incidence and the point of emergence
Measure the angle of incidence, i and angle of refraction r.
Calculate the refractive index, n using the equation
sin i
n=
sin r
Repeat the above steps for other angles and calculate average refractive index
OPTICAL PINS METHOD
Apparatus: glass block, 4 optical pins, protractor, plain paper, soft board
Set up:
Procedure:
Place a plain paper on soft board.
Place glass block on paper and draw its outline.
Remove the glass block and draw a normal.
Draw incident ray at angle of incidence of 60°from normal
Place two optical pins P1 and P2 along the incident ray
Place glass block within its outline and view images of optical pins P1 and P2 through opposite
side of the glass block
Place two other optical pins P3 and P4 such that they are aligned with images of pins P1 and P2
Remove the glass block and draw a line joining P3 and P4 until touches the side of block.
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Draw refracted ray between point of incidence and point of emergence
Measure the angle of refraction, r
Calculate refractive index, n using equation
sin i
n=
sin r
Repeat the above steps for other angles and calculate average refractive index
REAL DEPTH AND APPARENT DEPTH
One of the effect of refraction is why a coin in water appears shallower.
Real depth is distance between the object and boundary.
Apparent depth is distance between the image and boundary.
REFRACTIVE INDEX IN TERMS OF REAL AND APPARENT DEPTHS
The ratio of real depth to apparent depth.
Mathematically is represented as follows:
real depth
refractive index=
apparent depth
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EXAMPLES
1. A swimming pool cleaner notices a stone lying on the bottom of the pool, as shown Fig.1.1.
Fig.1.1
(a) On the diagram above continues the two rays A and B as they leave the water and locate
image of stone and label it I. [2]
(b) The stone lies at bottom of pool 8.0 m deep. To the cleaner above, the stone appears to be
6.0 m below the surface.
Determine refractive index of water.
real depth
n=
apparent depth
8.0 m
n=
6.0 m
1.33
refractive index = ………………………[2]
CRITICAL ANGLE AND TOTAL INTERNAL REFLECTION
Critical angle: angle of incidence in more optical dense medium that produces angle of refraction equal
to 90° in less optical medium.
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Diagram A: angle of incidence is less than critical angle i.e. i < c hence refraction occurs with 0 < r < 90°
Diagram B: angle of incidence is equal critical angle i.e. i.e. i = c hence refraction with r = 90°.
Diagram C: angle of incidence is greater than critical angle i.e. i > c hence total internal reflection occurs.
REFRACTIVE INDEX IN TERMS OF CRITICAL ANGLE
Refractive index is also calculated as follows.
1
n=
sin c
The table below shows some values of critical angle of some materials:
Material Critical angle / ° Refractive index
Diamond 24 2.42
Glass 41 1.52
Perspex(plastic) 42 1.49
Water 49 1.33
NB: Refractive index is inversely proportional to critical angle i.e. the larger the critical angle the smaller
the refractive index and vice versa.
EXAMPLES
1. The critical angle of diamond is. Determine the refractive index of diamond.
1
n=
sin c
1
n=
sin 24 °
2.26
refractive index =……………………… [2]
2. The refractive index of water as 1.33. Calculate the critical angle of water.
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1
n=
sin c
1
sin c=
n
−1 1
c=sin ( ¿ )¿
n
−1 1
c=sin ( )
1.33
critical angle =……………………… [2]
TOTAL INTERNAL REFLECTION
This is the bouncing back of all light inside a more optical dense medium.
Conditions for total internal reflection to occur are:
• Light must be travelling from optical dense medium towards less optical dense medium.
• Angle of incidence must be greater than critical angle i.e. i < c
EXAMPLES
1. Fig.1.1 shows a light ray passing through a clear glass rod.
Fig.1.1
Explain why the light does not leave the glass rod though the side wall.
angle of incidence is greater than critical angle
……………………………………………………………………………………………………………………………………………………
therefore light ray undergoes total internal reflection
…………………………………………………………………………………………………………………….…………………………[2]
APPLICATIONS OF TOTAL INTERNAL REFLECTION
Total internal reflection is used in:
• Formation of mirages
• Optical fibres
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MIRAGES
A mirage is an optical illusion that results from total internal reflection of light in air.
They are often seen on a hot day as a patches of water on tarred road some distance ahead.
Light from sky
Observer sees water patches
cool air layer
water
warm air layer
hot airair
layer
=
image of the sky
road surface
FORMATION OF MIRAGES
• Light from the sky undergoes multiple refraction away from the normal as it travels from
denser cool air to less dense warm air.
• Light hits hot air layer above road surface at angle of incidence greater than critical angle.
• Hence total internal reflection occurs.
• The image of sky appears as patches of water on the road surface to the observer.
OPTICAL FIBRES
These are very thin and flexible fibre glass rods with an outer plastic coating.
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ACTION OF OPTICAL FIBRES
• Light enters the optical fibre at an angle of incidence greater than the critical angle.
• Therefore light will be totally internally reflected.
USES OF OPTICAL FIBRE
• Telecommunication: for transmission of telephone and video signals.
• Endoscope: used by doctors to obtain image of an internal organ in the body.
LENSES
These are transparent curved glass devices used to refract light.
The two types of lenses are:
• Convex lens
also known as converging lens
is thinner at edges and thicker at middle.
Converges parallel light rays passing through it.
The focal point is real.
• Concave lens
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also known as diverging lens
is thicker at edges and thinner at middle.
Diverges parallel light rays passing through it.
The focal point is virtual.
FEATURES OF A THIN CONVEX LENS
They are used to describe convex lens.
• Optical centre, c: midpoint of lens
• Principal axis: line through optical centre and perpendicular to lens
• Focal point, F: where parallel light rays meet. It is also called principal focus.
• Focal length, f: distance between optical centre and focal point.
RAY DIAGRAMS
Ray diagram shows path of light ray passing through lens.
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They are used to locate image formed by convex lens.
• Ray 1 parallel to the principal axis is refracted through the focal point (principal focus).
• Ray 2 passing through the focal point (principal focus) is refracted parallel to the principal axis.
• Ray 3 passing through the optical centre is undeviated (does not bend).
CHARACTERISTICS OF IMAGES FORMED BY THE OBJECT BEYOND 2F
The diagram below shows the object in front a convex lens and its image formed.
The image is:
• real
• inverted
• diminished
• between F and 2F.
It is used in:
• camera
• eyes
CHARACTERISTICS OF IMAGES FORMED BY THE OBJECT AT 2F
The diagram below shows the object in front a convex lens and its image formed.
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The image is:
• real
• inverted
• same size as the object
• at 2F.
It is used in:
• photocopiers
CHARACTERISTICS OF IMAGES FORMED BY THE OBJECT BETWEEN 2F AND F
The diagram below shows the object in front a convex lens and its image formed.
The image is:
• real
• inverted
• magnified
• beyond 2F.
It is used in:
• microscopes
• projectors
CHARACTERISTICS OF IMAGES FORMED BY THE OBJECT BETWEEN F AND THE LENS
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The diagram below shows the object in front a convex lens and its image formed.
The image is:
• virtual
• upright
• magnified
• behind the object.
It is used in:
• magnifying glass
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