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WAVES RAY MODEL OF LIGHT REFLECTION and REFRACTION DISPERSION |
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A
great deal of evidence suggests that light is a wave and under a wide range
of circumstances, light travels in a straight line. For example, sunlight
casts sharp shadows. Another example is refraction where light passes from one
transparent medium into another (figure 1).
Such observations, has led to the ray model of light. A ray is an idealization that represents an
extremely narrow beam of light. According
to the ray model, we see an object because light reaches our eyes from each
point on the object. Although the light leaves a point on the object in all
directions, only a small bundle enters your eye. The ray model of light has
been very successful in explaining many aspects of the behaviour of light
such as reflection, refraction, dispersion, and the formation of images by
mirrors and lenses.
Fig.
1. We can use a ray model to explain
the straight line propagation of light. How do we see? A small
bundle of light rays come from each single point on an object and enters your
eye. A pencil in water looks bent even
when it isnt. When a ray of light of
is obliquely incident upon a medium of different refractive index, the ray is
bent. The relationship between the angle of incidence and angle of refraction
is described by Snells Law
(1A) (1B) (1C) Refraction
is responsible for several common optical illusions. When
you look into a lake and see a fish where is the fish located?
Fig.
2. Where is the fish located? |
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Thinking Exercise When you watch a person standing in
waist-deep water, it appears that their legs are shorter. Explain this
observation using a scientific annotated ray diagram.
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Figure 3 shows a ray of light that
emerges from a rectangular slab of glass such that the direction of the beam
of light is unchanged.
Fig.
3. Light passing through a glass
slab. Why does a diamond
sparkle? The refractive index of glass is 1.5
whereas for diamond it is
2.42. The critical angle for glass is 41o and the
critical angle for diamond is 24.4o which is smaller than for any
other common substances. (Check the calculations for the critical angles for
diamond and glass). When light enters a cut diamond, the large
refractive index compare with air results in the strong dispersion of the
light and this dispersed light is mostly incident on the sloping backsides of
the gem at angles greater than 24.4o, hence most of the light is
totally internally reflected. Further dispersion occurs as the light exists
through the many facets of its face. Hence, we see flashes of a wide range of
colours, but with only one eye are they noticeable at any one time these
narrow flashes are what makes diamond sparkle.
Why do we see the
Sun after it has set? Because of refraction, when the Sun is
near the horizon, it appears higher in the sky than it actually is. So, if
you watch a sunset, we see the Sun for several minutes after it has sunk
below the horizon and thus, slightly more daylight each day. The Earths
atmosphere is more dense towards the ground and
light travels faster in the thinner atmosphere further from the ground, so
the light from the sun does not travel in a straight line, but travels in
longer and higher path in penetrating the atmosphere. Since the density of the atmosphere changes
gradually, the light also bends gradually to propagate in a curved path. When
the Sun (Moon) is near the horizon, the rays from the lower edge are bent
more than the rays from the top edge this produces a reduction in the
vertical diameter causing the Sun (Moon) to appear flatten like a pumpkin.
MIRAGES A mirage is an optical phenomenon that
creates the illusion of water or an inverted reflection and results from the refraction
of light through a non-uniform medium.
You may see a mirage when driving along a
hot road the distant road appears to be wet, yet it is dry. Why? The air near the surface of the road is
hot and much cooler above. Light travels faster through the thin hotter air
then it does through the denser and more cooler air. So, instead of the light
travelling in a straight line, it travels in a curved line the wetness on
the road we observe is a reflection of the sky. The bending of light is
simply refraction and is a consequence of light having different speeds in
different media.
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VISIBLE
SPECTRUM and DISPERSION Visible light is part electromagnetic
spectrum to which our eyes are sensitive and falls within the range of
wavelengths from ~ 400 nm to ~ 750 nm. The colour of light is related to
its wavelength (or frequency).
Fig. 4. Electromagnetic spectrum.
There is no white light. When different
colours (fixed wavelengths) are mixed together in certain combinations, our
eye perceives the light to be white. A glass prism separates white light into a
rainbow of colours. This occurs because the index of refraction of a material
depends upon the wavelength of the light the shorter the wavelength, the
higher the refractive index.
Fig. 5.
Index of refraction as a function of wavelength for some transparent
solids. N.B. the shorter the wavelength, the higher the refractive index. White light is a mixture of all the visible
wavelengths, so when the white light enters the glass prism, different
wavelengths (colours) will be bent through different angles (refraction).
Because violet light is bent the most and red light the least, the white
light is separated into its component colours and this phenomenon is called dispersion.
Fig. 6.
White light dispersed by a glass prism into the visible spectrum. Rainbows are a spectacular example of dispersion
caused by reflection and refraction from droplets of water. You observe a
rainbow by looking at falling water drops with the Sun at your back. The red
light is bent the least and is observed higher in the sky, whereas violet
light is bent the most and is observed lower in the sky.
Fig. 7.
Rainbows are formed by reflection and refraction of sunlight from
falling water droplets.
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If you have any feedback, comments, suggestions or corrections please email: Ian
Cooper matlabvisualphysics@gmail.com |