Refraction
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[6]
Light travels in a straight line through a uniform medium, but when it moves
into another medium, its speed changes and it changes direction.
The bending of light passing into another medium is called refraction.
Light travelling into a more optically dense material will slow down and be
refracted towards the normal [ the normal is a line perpendicular to the
boundary between the two materials ]
Light travelling into a less optically dense material, will speed up and be
refracted away from the normal.
light waves slowing as they travel from
air into water, resulting in the change
in direction = refraction
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ray of light refracted as it passes into
and out of a glass slab
The wave model of light is better able to explain refraction as the change in
direction that is observed as light enters a different medium.
As a wavefront strikes a boundary between mediums at an angle, the end of
the wavefront entering the new medium will change speed, the rest of the
wavefront will still be travelling at the same speed. The result is a change in
direction of the wavefront as it enters the new medium.
The Law of Refraction
no = sin i /sin r
r = angle of refraction; i = angle of incidence;
no = relative refractive index
i
medium 1
r
medium 2
boundary
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There is a different relative refractive index [no] for each pair of materials.
The greater the value of no, the more the light is deviated.
Example: If a light ray travelling in air hits a glass block at an angle of incidence of
40o and passes into it with an angle of refraction of 25o, find:(a) the relative refractive index, no[airglass
(b) the angle of refraction if the beam has an angle of incidence of 70o.
(a) no = sin i /sin r = sin40/sin25  1.52
(b) no = sin i /sin r … sin r = sin i/no = sin 70/1.52096.. = 0.6178..
r  38.2o
Optical Density and the Speed of Light
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Light travels fastest in a vacuum, slower in a different media.
The more optically dense a material is, the slower light will travel through it.
Light travels slowly in diamond [1.24x108 ms-1] because it is optically dense.
Absolute Refractive Index
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The ratio of the speed of light in a medium compared to in a vacuum can be
used to find the absolute refractive index … [n = c/v]
Using the absolute refractive index, Snells Law becomes …
sin i/sin r = v1/v2 = n2/n1
medium
vacuum
air
v1
v2
n1
n2
=
=
=
=
speed of
speed of
absolute
absolute
absolute refractive
index [n]
1.000
1.00
light in medium 1
light in medium 2
refractive index of medium 1
refractive index of medium 2
speed of light in
medium [ms-1]
3.00 x108
3.00 x108
water
1.33
2.26 x108
quartz
glass
diamond
1.46
1.52
2.42
2.05 x108
1.97 x108
1.24 x108
Example 1: A ray of light passes from air to quartz [n = 1.46] with an angle of
incidence of 40o. Find:(a) the angle of refraction
(b) the speed of light in quartz
(a)
sin r = n1sin i/n2 = sin40(1.00)/1.46 = 0.440265… r  26.1o
(b)
v = c/n = 3.0x108/1.46  2.05x108 ms-1
Example 2: If a light ray travels through water [n=1.33] and strikes the glass sides
of an aquarium [n = 1.60] at an angle of incidence of 28o, find:(a) the speed of light in the water
(b) the speed of light in the glass
(c) the angle that the ray is refracted into the glass
water
glass
28o
(a) v = c/n = 3.0x108/1.33  2.26x108 ms-1
(b) v = c/n = 3.0x108/1.60  1.88x108 ms-1
(c) sin r = n1sin i/n2 = sin28(1.33)/1.60 = 0.39024 … r  23.0o
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The refractive index also depends on the colour of the light passing through the
medium … the refractive index of quartz is 1.57 for red light, for violet light the
refractive index is 1.54.
Yellow light [ = 589 nm] is normally used for determination of the absolute
refractive index.
Example: The refractive index of quartz is 1.57 for red light, but 1.54 for violet
light. Compare the speed of red light and violet light in quartz.
v = c/n = 3.0x108/1.57  1.91x108 ms-1 for red light
v = c/n = 3.0x108/1.54  1.95x108 ms-1 for violet light
Refraction in the Atmosphere
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Air is denser at Earth’s surface, so is not a uniform medium. As air gets denser,
its optical density increases and light is gradually refracted towards the normal.
As layers of air move around, the optical density of the air is continually
changing … this causes light from an object to follow different paths at different
times, causing stars to twinkle and distant objects to shimmer on a hot day.