Lesson 8
• Light and Optics
• The Nature of Light
• Properties of Light:
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Reflection
Refraction
Interference
Diffraction
Polarization
• Dispersion and Prisms
• Total Internal Reflection
• Huygens’s Principle
The Nature of Light
• Light exhibits the characteristics of a wave in some situations
and the characteristics of a particle in other situations.
• The quantization model assumes that the energy of a light wave is
present in particles called photons; hence, the energy is said to
be quantized.
• According to Einstein’s theory, the energy of a photon is
proportional to the frequency of the electromagnetic wave:
The Nature of Light
Reflection of Light
• When light ray traveling in a medium encounters a
boundary leading into a second medium, part or the entire
incident ray is reflected back into the first medium.
• The reflected rays are parallel to each other. Reflection of
light from a smooth surface is called specular reflection.
• If the surface is rough the reflected rays are not parallel but
set into various directions.
• Reflection from rough surface is known as diffuse
reflection.
• A surface behaves as a smooth surface as long as the
surface variations are much smaller than the
wavelength of the incident light.
Reflection of Light
Schematic representation of (a) specular Reflection, where the reflected rays are all
parallel to each other, and (b) diffuse reflection, where the reflected rays travel in random
directions. (c) and (d) Photographs of specular and diffuse reflection using laser light.
Reflection of Light
According to the law of reflection,
i. The angle of reflection equals the angle of incidence
ii.
The incident ray, the reflected ray, and the normal all lie in the same plane.
Image in a Concave Mirror
Refraction of Light
• When a ray of light traveling through a transparent
medium encounters a boundary leading into another
transparent medium, part of the energy is reflected
and part enters the second medium. The ray that
enters the second medium is bent at the boundary
and is said to be refracted.
• The incident ray, the reflected ray, and the refracted
ray all lie in the same plane. The angle of refraction,
depends on the properties of the two media and on
the angle of incidence through the relationship
The equation is called Snell’s law
Refraction of Light
(a) A ray obliquely incident on an air–glass interface. The refracted ray is bent toward the
normal because v2 < v1. All rays and the normal lie in the same plane.
(b) Light incident on the Lucite block bends both when it enters the block and when it
leaves the block
Refraction of Light
(a) When the light beam moves from air into glass, the light slows down on entering the
glass and its path is bent toward the normal.
(b) (b) When the beam moves from glass into air, the light speeds up on entering the air
and its path is bent away from the normal
Refraction of Light
Index of Refraction
The speed of light in any material is less than the speed in vacuum except near
very strong absorption bands.
n
speed of light in vacuum
speed of light in a medium
c
v
From this definition, index of refraction is dimensionless number usually greater
than unity, because v < c.
Refraction of Light
As light travels from one medium to another, its
frequency does not change but its wavelength does
Therefore, because the relationship
must be valid in both media and because
Therefore,
Refraction of Light
Example : An Index of Refraction Measurement
Refraction of Light
Example: Angle of Refraction for Glass
A light ray of wavelength 589 nm traveling through air is incident on a smooth,
flat slab of crown glass at an angle of 30.0° to the normal. Find the angle of
refraction.
Solution
Refraction of Light
Example: Laser Light in a Compact Disc
A laser in a compact disc player generates light that has a wavelength of 780 nm in
air.
(i) Find the speed of this light once it enters the plastic of a compact disc (n = 1.55).
(ii) What is the wavelength of this light in the plastic?
(i)
(ii)
Refraction of Light
Example: Light Passing Through a Slab
A light beam passes from medium 1 to medium 2, with the latter medium being a thick
slab of material whose index of refraction is n2 (see Fig. below). Show that the emerging
beam is parallel to the incident beam.
Refraction of Light
Thin Lenses
Lenses are commonly used to form images by
refraction in optical instruments, such as cameras,
telescopes, and microscopes. We can use what
we just learned about images formed by refracting
surfaces to help us locate the image formed by a
lens. We recognize that light passing through a
lens experiences refraction at two surfaces. The
development we shall follow is based on the
notion that the image formed by one refracting
surface serves as the object for the second surface.
Interference of Light Waves
Interference of Light Waves
(a) If light waves did not spread out after passing through the slits, no interference would
occur.
(b) The light waves from the two slits overlap as they spread out, filling what we expect to
be shadowed regions with light and producing interference fringes on a screen placed to
the right of the slits.
Interference of Light Waves
Young’s double-slit experiment.
Interference in light waves from two sources was
first demonstrated by Thomas Young in 1801. The
schematic diagram from the experiment is as
shown in the diagram to the left. Light is incident
on a screen in which there is a narrow slit not
shown in the diagram. The waves emerging from
this slit arrive at a second screen, which contains
two narrow parallel slits S1 and S2. These two slits
serve as a pair of coherent light sources because
waves emerging from them originate from the
same wavefront and therefore maintain constant
phase relationship. The light from the two slits
produces on screen a visible pattern of bright and
dark parallel bands called fridges.
Schematic diagram of Young’s double-slit experiment. Slits S1 and S2 behave as coherent sources of light
waves that produce an interference pattern on the viewing screen (drawing not to scale).
Interference of Light Waves
(a) Geometric construction for describing Young’s double-slit experiment (not to scale).
(b) When we assume that r 1 is parallel to r2, the path difference between the two rays is
r2 - r1 = d sinθ. For this approximation to be valid, it is essential that L >>d.
Interference of Light Waves
Interference of Light Waves
Example: Separating Double-Slit Fringes of Two Wavelengths
Huygens’s Principle
Huygens’s construction for
(a) a plane wave propagating to the right and
(b) a spherical wave propagating to the right
Huygens principle is a construction for
using knowledge of an earlier wavefront to
determine the position of a new wavefront
at some instant. In Huygen’s construction,
all points on a given wavefront are taken
as point sources for the production of
spherical
secondary
waves
called
wavelets, which propagate outward with
speeds characteristic of waves in that
medium. After sometime has elapsed, the
new position of the wavefront is the
surface tangent to the wavelets.
Diffraction
• Diffraction refers to the general behavior of waves spreading out as
they pass through a slit. The diffraction pattern seen on a screen
when a single slit is illuminated is really another interference pattern.
The interference is between parts of the incident light illuminating
different regions of the slit.
• When plane light waves pass through a small aperture in an opaque
barrier, the aperture acts as if it were a point source of light, with waves
entering the shadow region behind the barrier. This phenomenon,
known as diffraction, can be described only with a wave model for
light. We now investigate the features of the diffraction pattern that
occurs when the light from the aperture is allowed to fall upon a
screen.
• Electromagnetic waves are transverse. That is, the electric and
magnetic field vectors associated with electromagnetic waves are
perpendicular to the direction of wave propagation.
• Diffraction indicates that light, once it has passed through a narrow slit,
spreads beyond the narrow path defined by the slit into regions that
would be in shadow if light traveled in straight lines. Other waves, such as
sound waves and water waves, also have this property of spreading
when passing through apertures or by sharp edges.
Diffraction
Diffraction Patterns from Narrow Slits
Let us consider a common situation, that
of light passing through a narrow opening
modeled as a slit, and projected onto a screen.
To simplify our analysis, we assume that the
observing screen is far from the slit, so
that the rays reaching the screen are
approximately parallel. This can also be
achieved experimentally by using a converging
lens to focus the parallel rays on a nearby
screen. In this model, the pattern on the
screen is called a Fraunhofer diffraction
pattern.
(a) Fraunhofer diffraction pattern of a single slit. The pattern consists of a central bright fringe
flanked by much weaker maxima alternating with dark fringes. (Drawing not to scale.)
(b) Photograph of a single-slit Fraunhofer diffraction pattern.
Diffraction
• A diffraction pattern consisting of light and dark areas
is observed, somewhat similar to the interference
patterns.
• For example, when a narrow slit is placed
between a distant light source (or a laser beam)
and a screen, the light produces a diffraction
pattern.
• The pattern consists of a broad, intense central
band (called the central maximum), flanked by a
series of narrower, less intense additional bands
(called side maxima or secondary maxima) and a
series of intervening dark bands (or minima).
Diffraction
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To analyze the diffraction pattern, it is convenient to
divide the slit into two halves, as shown in the Figure.
Keeping in mind that all the waves are in phase as they
leave the slit, consider rays 1 and 3.
As these two rays travel toward a viewing screen far to
the right of the figure, ray 1 travels farther than ray 3 by
an amount equal to the path difference (a/2)sinθ,
where a is the width of the slit. Similarly, the path
difference between rays 2 and 4 is also (a/2) sin θ , as is
that between rays 3 and 5.
If this path difference is exactly half a wavelength
(corresponding to a phase difference of 180°), then
the two waves cancel each other and destructive
interference results.
If this is true for two such rays, then it is true for any two
rays that originate at points separated by half the slit
width because the phase difference between two
such points is 180°.
Diffraction
• Therefore, waves from the upper half of the slit interfere destructively
with waves from the lower half when
Diffraction
Intensity distribution for a Fraunhofer diffraction pattern from a single slit of width
a. The positions of two minima on each side of the central maximum are labeled.
(Drawing not to scale.)
Diffraction
Diffraction of X-Rays by Crystals
A two-dimensional description of the reflection of an x-ray beam from two parallel
crystalline planes separated by a distance d. The beam reflected from the lower plane
travels farther than the one reflected from the upper plane by a distance 2d sinθ.
This condition is known as Bragg’s law
Example: The Orders of a Diffraction Grating
Polarization of Light Waves
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An ordinary beam of light consists of a large number
of waves emitted by the atoms of the light source.
Each atom produces a wave having some
particular orientation of the electric field vector E,
corresponding to the direction of atomic vibration.
The direction of polarization of each individual
wave is defined to be the direction in which the
electric field is vibrating. The plane formed by E and
the direction of propagation is called the plane of
polarization of the wave.
Under certain conditions these transverse waves
with electric field vectors in all possible transverse
directions can be polarized in various ways. This
means that only certain directions of the electric
field vectors are present in the polarized wave.
(a) A representation of an unpolarized light beam viewed along the direction of
propagation (perpendicular to the page). The transverse electric field can vibrate in any
direction in the plane of the page with equal probability.
(b) A linearly polarized light beam with the electric field vibrating in the vertical direction.
Polarization of Light Waves
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The Figure represents an unpolarized light beam incident on a first polarizing sheet, called the polarizer.
Because the transmission axis is oriented vertically in the figure, the light transmitted through this
sheet is polarized vertically. A second polarizing sheet, called the analyzer, intercepts the beam. In
Figure, the analyzer transmission axis is set at an angleθ to the polarizer axis.
We call the electric field vector of the first transmitted beam E0. The component of E0 perpendicular to the
analyzer axis is completely absorbed. The component of E0 parallel to the analyzer axis, which is allowed
through by the analyzer, is E0cosθ. Because the intensity of the transmitted beam varies as the square
of its magnitude, we conclude that the intensity of the (polarized) beam transmitted through the
analyzer varies as
Polarization of Light Waves
(a) When unpolarized
light is incident on a
reflecting surface, the
reflected and refracted
beams are partially
polarized.
(b) The reflected beam
is completely polarized
when the angle of
incidence equals the
polarizing angle θp ,
which satisfies the
equation n=tanθp . At
this incident angle, the
reflected and refracted
rays are perpendicular
to each other.
Polarization of Light Waves
Using Snell’s law of refraction
This expression is called Brewster’s law, and the polarizing angleθp is sometimes
called Brewster’s angle, after its discoverer, David Brewster (1781–1868). Because n
varies with wavelength for a given substance, Brewster’s angle is also a function of
wavelength.
Dispersion
Dispersion is the separation of white light by a prism into bands of colors – red, orange,
yellow, green, blue and violet. The spectrum is due to the difference in the velocities
and wavelength of the spectral colors. Violet is bent most and is slowed down more
than the red light.
Dispersion
When light passes through a prism, the angle of deviation δ is different for the different
wavelengths. This property can be put to use in the form of a prism spectrometer:
Dispersion
Example: Measuring n Using a Prism
The minimum angle of deviation δmin for a prism occurs when the angle of incidence θ1 is such that
the refracted ray inside the prism makes the same angle with the normal to the two prism faces,
as shown in the Figure. Obtain an expression for the index of refraction of the prism material .
Using the geometry shown in the Figure,
we
Hence, knowing the apex angle φ of the prism and measuring δmin, we can calculate the
index of refraction of the prism material.
Total Internal Reflection
We can use Snell’s law
of refraction to find
the critical angle.
When
Then
(a) Rays travel from a medium of index of refraction n1 into a medium of index of refraction n2,
where n2 < n1. As the angle of incidence θ1 increases, the angle of refraction θ2 increases until
θ2 is 90° (ray 4). For even larger angles of incidence, total internal reflection occurs (ray 5).
(b) The angle of incidence producing an angle of refraction equal to 90° is the critical angle θc.
At this angle of incidence, all of the energy of the incident light is reflected