Download Introduction to light 2

Introduction to Light
IN THIS LECTURE
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Reflection and refraction
Index of refraction
Snell’s Law
Critical Angle
Dispersion and refractive index
Interference phenomena
Retardation
Reflection
Light reaching the boundary between two transparent materials may
either be reflected or refracted. For reflected light the angle of
incidence (i) and the angle of reflection (r) are identical
Mineral lustre depends in part
on the amount of light that is
reflected from the surface.
In general the amount of light
reflected at a surface
increases as the angle of
incidence increases
Refraction
Wave fronts one wavelength
apart and the wave normal are
shown for light rays passing
from material 1 (low index of
refraction, higher velocity) to
material 2 (high index of
refraction, low velocity). The
wave fronts and wave normal are
bent at the interface because
the wavelength l2 in low-velocity
material is shorter than the
wavelength l1 in the highvelocity material.
Index of Refraction
•
A measure of how effective a material is in bending light is called the
Index of Refraction (n), which is a function of velocity
V
n= v/
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Vm
where Vv is the velocity in a vacuum and Vm is the velocity in a material
Index of Refraction in Vacuum = 1 and for all other materials n > 1.0.
•
The velocity of light in most minerals is in the range 2 – 1.4 x
1017nm/sec. Therefore most minerals have n values in the range 1.4 to
2.0.
•
A high refractive index indicates a low velocity for light travelling
through that particular medium.
Snell’s Law
•
Snell's law can be used to calculate how much light is bent on travelling
from medium one to medium two.
sin q1
sin q2
=
n2
n1
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If the interface between the two materials represents the boundary
between air (n ~ 1) and water (n = 1.33) and if angle of incidence = 45°,
using Snell's Law the angle of refraction = 32°.
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The equation holds whether light travels from air to water, or water to
air.
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In general, the light is refracted towards the normal to the boundary
on entering the material with a higher refractive index and is refracted
away from the normal on entering the material with lower refractive
index.
Critical Angle
Light following wave normals a, b and c
within the white arc can be refracted
from the high-index to the low index
materials because their angle of
incidence is less than the critical angle
(CA). Wave normals such as d, which have
an angle of incidence greater than the
critical angle are totally reflected to d'
at the boundary. A portion of the light
following wave normals a, b and c is
reflected to a', b' and c' as shown with
dotted lines. The amount of reflection
increases from a to c and is 100% for
angles of incidence greater than the CA.
If the indices of refraction are
known then the critical angle can
be calculated as from ->
n1 (low)
n2 (high)
= sin
CA
Dispersion
White light is dispersed into its spectral colors when passed through
a prism because the index of refraction for violet light is larger than
for red light
Therefore the index of refraction is higher for short wavelengths
and lower for long wavelengths of light
This relationship
is known as the
normal dispersion
of the refractive
indices
Dispersion and Refractive Index
For the normal dispersion of the
refractive indices, the index of
refraction decreases with increasing
wavelength. To describe the
dispersion of a particular material it
is necessary to report the index of
refraction at several wavelengths.
By convention indices of refraction
nF, nD and nC are reported for light
whose wavelengths are 486, 589 and
656nm respectively. When a single
index of refraction is reported it is
normally nD because 589 light is in
the middle of the visible spectrum
and is easily reproduced by a sodium
lamp in a laboratory.
Interference Phenomena
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For isotropic minerals all light is absorbed by the upper polariser and
the mineral appears dark (we will look at how optical microscopes work
in more detail later)
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For anisotropic minerals, light entering the mineral is split into two rays
that vibrate at right angles to each other and have different indices of
refraction (ie different velocities)
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Because the two different rays have different velocities they travel at
different speeds through the mineral. The light ray with the lower
velocity is called the slow ray, the ray with the higher velocity is called
the fast ray.
Retardation
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RETARDATION (D) represents the distance the fast ray has travelled
once leaving the mineral before the slow ray also leaves the mineral.
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Retardation is measured in nanometres, 1nm = 10-7cm, or the number of
wavelengths by which a wave lags behind another light wave.
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Retardation remains constant once the two rays have left the mineral
because their velocities in air will be the same.
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Retardation can result in light rays
• Constructively interfering
• Destructively interfering
• Partially interfering
Constructive Interference
Waves A and B are in phase (D = 1l) so that the waves
constructively interfere and produce the resultant wave R
Destructive Interference
Waves A and B are out of phase (D = 1 + 1/2l). The amplitude
of waves A and B are equal but opposite such that they
cancel each other out (destructively interfere). The
resultant wave R therefore has zero amplitude.
Partial Interference
Waves A and B are partially in phase with the interference being
partially constructive and partially out of phase with the
interference being partially destructive. The resultant wave R is
the sum of waves A and B at any given point.