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Optical and medical physics
first stage
Optics
Optics
“Geometrical optics”
ex: applications of
Lenses and Mirrors
“Wave optics”
ex: Interference
Diffraction
Polarization
“Quantum optics”
ex: Photoelectric
effect
Light: is electromagnetic wave, the electric field is vertical to the magnetic
field (wave theory), or is a stream of photons which are a particles have no
rest mass.
electro-magnetic wave (light)
The sensitivity of the human eye is a
function of wave length. It has peak
sensitivity at a wave length of about
5500 Å corresponding to yellowgreen.
A chart of the electro-magnetic spectrum
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Lecturer: MSc. mervat kadhem
Optical and medical physics
first stage
Reflection and Refraction
a- Laws of reflection:
1- The reflected and the incident rays, and the normal to
the mirror at the point of incidence all lie at the same
plane.
2- The angle of incidence(i) = the angle of reflection(r).
Where AO is a ray of incident light and OB is the
refracted ray.
plane mirror
b- Laws of refraction:
1- The incident and the refracted rays, and the normal at the point of
incidence, all lie in the same plane.
is a constant, where ө1 is
2- For tow given media
the angle of incidence and ө2 is the angle of
refraction.
Where AO is a ray of incident light, OC
reflected and OB is the refracted ray.
refraction at
plane surface
Refractive index (n)
Light is refracted because it has deferent velocity in deferent media,
the refractive index (n) can be defined as follows:
n=
=
Where (c) is the velocity of light in vacuum (3×108 m/s), and (v) is the
velocity of light in medium. In practice the velocity of light in air can be
replaced by the velocity of light in vacuum in this definition.
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Lecturer: MSc. mervat kadhem
Optical and medical physics
first stage
Snell’s law
Consider a ray of light AO incident in air on a
plane glass, then refracted from the glass into a water
medium, and finally emerging along a direction CD
into air as shown in figure, then:
na sin ia= ng sin ig = nw sin iw
n sin i = constant
or n1sinө1=n2sinө2
na= 1 for air
refraction at
parallel plane surfaces
Example: suppose a ray is incident on water-glass boundary at an
angle of 60˚, if the refractive index is 1.33 for the water and 1.5 for glass
find the angle of refraction?
Applying: nwsinөw=ngsinөg
or n1sinө1=n2sinө2
n=1.33
1.33sin60=1.5sinө2
n=1.5
sinө2=
ө2= sin-1(0.7678)
.: ө2= 50.1˚
Total internal reflection, critical angle
Light is partially reflected and partially transmitted at an inter face
between two materials with deferent indexes of refraction. Under certain
circumstances, all of the light can be reflected back from the interface, with
none of it being transmitted, even though the second material is transparent.
Critical angle өc : is the angle of incidence, for which the refracted
ray emerges tangent to the surface, ө2=90˚.
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Optical and medical physics
first stage
Beyond the critical angle, the ray cannot pass into the upper material
and is completely refracted at the boundary surface. This is called total
internal reflection.
Light propagation within the glass (n=1.5) will totally reflected if it
strikes the glass-air surface at an angle of about 41˚ or more.
Sinөc =
Optical fiber
An optical fiber is a transparent conduit as thin as human hair, made
of glass or clear plastic, designed to guide light waves along its length. An
optical fiber works on the total internal reflection.
When light enters one end of the fiber, it undergoes total internal
refractions from sidewalls and travels down along the length of the fiber as a
zigzag path.
The optical fiber has three regions:
1- Core
2- Cladding
3- Sheath
The refractive index of the cladding always lower than that of the
core, the purpose of the cladding is to make the light to be confined to the
core. Light striking the core-to-cladding interface at an angle greater than
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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critical angle will be reflected back into the core. Since the angles of the
incidence and reflection are equal, the light will continue to rebound and
propagate through the fiber. The sheath protects the cladding and the core
from abrasions, contamination and the harmful influence of moisture. In
addition, it increases the mechanical strength of the fiber.
Reflection: Image formation by plane mirror
Image forms behind the mirror
Spherical mirrors
Convex and concave mirror
Difinitions:
P: pole
C: center of curvature
PC: principle axis,
AB: aperture
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Optical and medical physics
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Fig.i: concave mirror has a real focal point (real focus).
Fig.ii: convex mirror has a virtual point (virtual focus).
Focal length (f) and radius of curvature
r: radius of curvature
f: focal length
Consider a ray of light AX parallel to the
principal axis, CX is the normal
Since ө1=ө2 reflectance
and
ө1=ө3 alternative angles
then Triangle FXC is isosceles and: FX=CF
since X a point very close to P, we assume that:
FX=FP
Then FP=CF=½CP
Since FP=f, CP=r
Then [f= ]
is the same for convex and concave mirror.
Formation of images by spherical mirror
A. Images in concave mirrors
Image is inverted and real, and sometimes is erect and virtual.
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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Object locations in concave mirror:
1. When the object is very long distance away (infinity), the image is small,
real and is formed inverted at the focus.
2. When the object is approaches to the center, C, the image remains real
and inverted, and in front of the object.
3. When the object is between C and F, the image is real, inverted, and
larger than the object.
4. As the object Approaches the focus, the image recedes farther from the
mirror.
5. When the object is at the focus, the image is at infinity.
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Optical and medical physics
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6. When the object is nearer to the mirror than the focus, the image becomes
erect and virtual and the image is magnified and can be used as a shaving
mirror.
7. A special case occurs when the object is at the center of curvature, C, the
image is real, inverted and the same size of the object and locate at C
also.
B. Images in convex mirrors
1. Image is erect, virtual and diminished in size no matter where object is
situated.
2. Convex mirror has a wide field of view, and is used as a driving mirror.
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Lecturer: MSc. mervat kadhem
Optical and medical physics
first stage
New Cartesian sign
Left(-)
Right (+)
Not: the focal length(f) and the radius(r) are both: negative(-) in concave
mirror or lens, and positive(+) in convex mirror or lens.
Standard formula for both convex and concave mirror
This equation is very important in applications of mirrors
Formula for magnification
The lateral magnification (m) produced by mirror is defined by:
m=
=
the angle OPH=the angle IPR
then tan OPH=tan IPR
i.e
=
=
IR: height of image
OH: height of object
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Optical and medical physics
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IP: image distance = v
OP: object distance = u
Then m=
Since [
Then
1+ m=
.:
m= -1
Some applications of mirror formula
1- An object is placed 10 cm in front of a concave mirror of focal length 15
cm, find the image position and the magnification?
Since the mirror is concave, f= -15 cm, the object is on the left of the
mirror, and hence u= -10 cm. substituting in
Then
(
)
(
)
Then v=30 cm
Since v is positive in sign, the image is (30 cm) on the right of the mirror
(virtual).
The magnification m=
So that the image is three times as height as the object.
2- The image of an object in a convex mirror is 4 cm from the mirror. If the
mirror has a radius of curvature of 24 cm, find the object position and the
magnification?
The image in a convex mirror is always virtual, then v= +4cm
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Lecturer: MSc. mervat kadhem
Optical and medical physics
first stage
The focal length of the mirror f=
, since the mirror is convex,
then f= +12 cm, substituting in
(
)
(
)
u= -6
since u is negative in sign the object is 6cm on the left of the mirror.
The magnification:
3- An erect image, three times the size of the object, is obtained with a
concave mirror of radius of curvature 36 cm, what is the position of the
object?
Suppose the object distance from the mirror = x cm
Image distance = 3x cm
Magnification
Now an erect image is obtained with a concave mirror only when the image
is virtual then image distance v= +3x
Object distance u= -x
Focal length
f=
Substituting in
(
)
(
)
(
)
x=12
the object is 12 cm from the mirror.
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Lecturer: MSc. mervat kadhem
Optical and medical physics
first stage
Refraction at spherical surfaces
Images can be formed by reflection as well as by refraction. We study
here the refraction at spherical surfaces, that is, at a spherical interface
between two transparent materials having different indices of refraction.
1. When the object distance is large, the rays passing through the
refracting surface come together and form a real image.
2. If the object is moved closer to the surface to position F1 the emergent
light is parallel and the image forms at infinity.
3. If the object is brought even closer, the emergent rays do not come
together, they appear to come from a point I, and the image is virtual.
Lenses
Lens: is a piece of glass bounded by one or two spherical surfaces, when a
lens is thicker in the middle than at the edges it called a (convex lens)
(converging lens), and when it is thinner in the middle than that the edges it
called a (concave lens) (diverging lens).
Not: A convex lens is called a converging lens because a parallel beam of
light, after refraction, converge to a point F.
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Lecturer: MSc. mervat kadhem
Optical and medical physics
first stage
Convex lens (converging lens)
while a concave lens called a diverging lens because rays that coming
parallel to the principal axis after refraction, diverge out and seem to come
from appoint F.
Concave lens (diverging lens)
Thin lens
Lenses are classified into thin and thick lenses. (A lens is said to be
thin if the thickness of lens can be neglected when compared to the lengths
of the radii of curvature of its two refracting surfaces, and to the distances
of the objects and images from it).
Types of lenses
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Optical and medical physics
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Lens notations
The principal axis: is the line joining the centers of curvature of two
surfaces and pass through the middle of the lens.
The focal length (f) and the radius of curvature (r) are: positive
(+)(real) in convex lens, and negative (-)(virtual) in concave lens.
General lens equation:
(for both convex and concave lens)
Focal length values
The focal length of a lens depends on the refractive index of its
material. The refractive index equal 1.5 for glass, and 1.3 for water.
(
)(
)
Where r1, r2 are the radii of curvature of the lens surfaces.
Examples:
1. Find the focal length of a biconvex lens, whose radii of curvature, r1, r2,
are each 10 cm?
Solution:
The centers of curvatures of the surfaces are on opposite
sides of the lens, and r1= +10 and r2= - 10, substitute in:
(
)(
)
Since the lens made of glass so that n=1.5 (always)
(
)(
(
)
(
) = 0.5×
bi-convex lens
0.1
)
.: f= +10 cm.
2. Find the focal length of a biconcave lens, whose radii of curvature, r1, r2,
are each 10 cm?
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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Sol:
Since its surfaces are both concave, r1= -10 and r2= +10,
Substitute in:
.:
(
)(
(
)
)= 0.5×
(
)
.: f= -10 cm.
3. Find the focal length of a plano-convex lens whose radii of curvature are
each of 8 cm?
Sol:
r1= +8 and r2= ∞ for plane side
.:
(
)(
(
)
)
.: f= +16 cm.
4. Find the focal length of converging meniscus (positive meniscus), whose
radii of curvature, r1, r2 are 16 cm, 12 cm respectively?
Sol:
r1= -16, and r2= -12
(
.:
)(
(
)(
)
(
)
(
)
(
)
)
.: f= +96 cm
Some applications of lens equation:
1. An object is placed 12 cm from a convex lens of focal length 18 cm, find
the position of the image?
Sol:
Since the lens is convex, f= +18 cm, the object is left of the lens, and hence
u= -12 cm, substituting in
.:
(
)
(
)
.:
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Optical and medical physics
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.: v= -36
Since v is negative in sign the image is left of the lens (virtual), and it
is 36 cm.
2. A beam of light, converging to a point 10 cm, behind a convex lens, is
incident on the lens, find the position of the point image if the lens has a
focal length of 40 cm?
Sol:
If the incident beam converges to the point O, then O is a virtual
object
Thus u= +10 cm, f= +40 cm (convex lens), substituting in:
.:
(
)
(
)
.:
.:
Since v is positive in sign the image (I) is 8 cm on the right of the lens.
3. An object is placed 6 ins. In front of a concave lens of focal length 12 ins.
Find the image position?
Sol:
Since the lens is concave, f = -12 ins. The object is real u= -6 ins.
Substituting in
.:
(
)
(
)
.:
.:
Since v is negative in sign the image is virtual and 4 ins. left of the lens.
4. A converging beam of light is incident on a concave lens of a focal length
15 cm, if the beam converges to a point 3 cm behind the lens, find the
position of the point image?
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Lecturer: MSc. mervat kadhem
Optical and medical physics
first stage
Sol:
If the beam converge to the point O, then O is virtual object thus u= +3 cm,
since the lens is concave f= - 15 cm, substituting
in
.:
(
)
(
)
.:
Since v is positive in sign the point image I is real
and 3
right of lens.
Image in lenses
a. Images in Convex lens
The image formed by a convex lens is always real and inverted
until the object moved nearer to the lens than its focal length; the image
becomes erect and virtual.
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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Not: least possible distance between object and screen must be equal to (4f)
in order to get a real image in convex lens.
b. Images in concave lens
The image formed by a concave lens is always virtual and erect.
Magnification (m)
Magnification:
Lateral magnification:
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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Power
The power of a lens is the measure of its ability to produce convergence of a
parallel beam of light. which is given by the inverse of its focal length.
power =
A convex lens of a large focal length produces a small converging
effect and a convex lens of small focal length produces a large converging
effect. Therefore the power of a convex lens is taken as a positive. On the
other hand, a concave lens produces divergence. Therefore, its power is
taken as a negative.
The power of a pair of lenses placed in contact is given by:
p = p1+p2
Aberration
It is the influences which cause different rays to converge to different
points. Aberration is divided into: monochromatic aberration and chromatic
aberration.
1. Monochromatic aberration: it is the defects due to wide-angle incidence
which occur even with monochromatic light.
2. Chromatic aberration: it is the aberration that occur due to dispersion of
light, it is occur with light that contains at least two wave lengths.
Monochromatic aberrations are again divided into five types:
1. Spherical aberration
2. Coma
3. Astigmatism
4. Curvature of field
5. Distortion
Spherical aberration: when the rays passing through different zones of a
lens surface, come to different foci.
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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“The eye”
Elements of the eye
Human eye is an essential part of all optical instruments, it is nearly
spherical in shape and about 2.5 cm in diameter, and it contains:
1. Sclera: it is a tough outer skin, which protects the eye and gives the
necessary stiffness.
2. Cornea: is a transparent spherical bulge at the front of the eye which
made of tough material.
3. Iris: is a diaphragm with a circular hole in the middle called the pupil,
the iris is responsible of color the person’s eye.
4. Pupil: is a black circular hole in the middle of the iris which contracts
when the light that received by the eye is high and painful to the eye.
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Optical and medical physics
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5. Crystalline lens: which is a biconvex lens made of gelatinous
transparent substance, (1.437 refractive index), hard at the center and
softer at the outer portions which attach to the ciliary muscle.
6. Ciliary muscles: it is at the edges of the lens which enable the eye
clearly objects at different distances by pulling and pushing lens.
7. Aqueous humor: it is a weak salt solution behind the lens.
8. Vitreous humor: is a gelatinous substance which fills the eye between
the lens and the retina. Both vitreous and aqueous humor have a
refractive index of about 1.336.
9. Retina: is a sensitive screen at the back of the eye-ball, the retina has
a shape of hemisphere and contains light receptors called rods or
conse. The human eye has a total of 125 million rods and 6.5 million
cones; they sense the image and transmit via the optic nerve.
10. Optic nerve: it carries the sensation produced by the image to the
brain.
11. Blind spot (papilla): is the portion of retina where optic nerve enters
the eye, in this portion there are no rods or cones, therefore it’s called
blind spot.
12. Macula: is the region with the highest density of color receptors. An
image formed on the fovea, the central section of the macula, is
characterized by best vision. Thus, macula and fovea are the most
important segments of the retina
Refraction at the cornea and the lens produces a real and inverted
image of the object on the retina. The optic nerve sends a signal to the brain,
which makes correction necessary for us to see objects in their natural
positions.
Accommodation
Is the ability of the eye to see clearly objects at different distances
with the help of ciliary muscles, the lens-to-retina distance does not change
but the focal length is adjusted by varying the radii of curvature of the
crystalline lens. This ability is limited with near and far points.
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Optical and medical physics
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far point at infinity = ciliary muscles relaxed = lens flattened = eye is
un accommodated or at rest, fig.(i)
near point least 25 cm = ciliary muscles strained = lens bulge more =
eye is fully accommodated, fig.(ii)
Defect of vision (refractive errors)
1. Short sight (myopia):
Image formed in front of the retina because the eye-ball is too long.
Far point < infinity (∞)
Near point is normal
Spectacles or lenses: a concave lens is used to correct short sight (myopia)
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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2. Far sight (presbyopia):
Image formed behind
the retina.
Far point is normal,
But near point is
greater than the least
distance of normal
eye.
Spectacles: a convex lens is used to correct far sight (presbyopia).
Ex: let X be virtual image of
A, if XL= 50 cm, AL= 25
cm, what is the focal length
of required lens?
Sol:
(
)
(
)
.:
.: f= 50 cm
3. Long sight (hypermetropia) or (hyperopia):
Eye-ball is too short,
and the image is formed
behind the retina.
Far point is virtual, and
near point is farther than the
normal eye.
Spectacles:
a. A convex lens is used to
correct far point
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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b. A convex lens is required to correct near point because the eye un able
to focus an object at (P= 25 cm).
4. Astigmatism:
Refers to a defect in which the surface of the cornea is not
spherical, but more sharply curved in one plane than another. It correct
by using cylindrical lens.
Blindness
Blindness: is a partially loss of vision. It may be caused by number of
disorders such as cataract, glaucoma, and detached of retina. It may also
result from damage to the optic nerve.
Color blindness: is the inability to perceive certain colors, or more rarely, all
colors. Red-green color blindness the most common type, is characterized by
difficulty to distinguish reds and greens due to the absence of either red or
green cones. Color blindness is inherited, and occurs more often in men than
the women.
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Optical and medical physics
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Size of the image in the retina
The size of the retinal image depends upon the visual angle, which is
the angle subtended by the object at the eye, therefore it known as angular
size.
Consider the objects A1 and A2 placed in front of the eye. They are of
different sizes, but they subtended equal angles at the eye and their images
formed on the retina are of the same size.
If k is the distance between retina and the lens:
k
Thus, the size of the image on the retina is proportional to the angle ө.
We bring objects close to our eyes to see them in more detail. This action
makes subtended angle and the retinal image as large as possible. However,
the object cannot be brought nearer to the eye beyond the least distance of
distinct vision (NDDV), which is 25 cm. if the object is brought nearer than
this distance the eye cannot accommodate and will have to strain itself.
We can see small objects which cannot be seen with naked eye by using
an instrument called magnifying instruments.
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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Visual Acuity
Introduction
Visual acuity defined as the clarity or clearness of the vision,the ability to
distinguish details and shapes of objects, the word “acuity” comes from the
latine “acuitas” which mean sharpness. Also it is considered a measure of
form sense, In terms of visual acuity is defined as the reciprocal of the
minimum resolvable visual angle measured in minutes of arc for a standard
test pattern. Therefore to understand visual acuity, the knowledge about
visual angle is essential.
Visual angle
Visual angle is the angle subtended at the nodal point of the eye by the
physical dimensions of an object in the visual field (fig. 2.1). visual angle is
a useful mode of specifying the spatial extend of objects or elements in the
visual field.
It has been observed that the two adjacent points can be seen clearly and
discretely only when these two points (say A and B in fig. 2.1) produce a
visual angle not less than one minute. The dimensions of the visual angle
depend upon the size of the object as well as its distance from the eye.
Therefore to be seen clearly either the object should be large enough or it
should be placed near the eye (at an appropriate distance).
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Optical and medical physics
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In terms of the length of the retinal image, it has been seen that the two
points (A and B) will be seen clearly when their image size (A' B') is more
than 4.5µ. this is so, because the diameter of individual cone stimulated by
the image points A' and B' is 1.5µ each and at least one cone in between (of
1.5µ diameter) must be unstimulated. The retinal image size for a given
visual angle may vary slightly with changes in viewing distance and
associated changes in accommodation of the lens, but this effect is relatively
small.
Factors affecting visual acuity
In general, the factors that influence the spatial resolution can be classified
into physical and physiological.
1- Physical factors: include those which influence the light
characteristics of the distribution and hence influence the nature of the
retinal image.
2- Physiological factors: are those which influence the processing of the
stimulus and are thus mainly observer related.
However, there is some overlap between physical and physiological
groups. For example, the lens is a physical factor but the related
accommodation process is physiological. Similarly, the size of pupil that
controls the amount of light entering the eye is a physical factor but the
reflexes controlling its size are physiological processes.
Therefore, these factors have been classified into stimulus-related and the
observer-related factors.
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Optical and medical physics
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Measurement of visual acuity in school
children (above 5 years) and adults
Snellen´s test types
1. It consist of a series of black capital
letters on a white board, arranged
in lines,
2. Each letter of the chart is so
designed that it fits in a square, the
sides are five times the breadth of
the lines, each line (1 min. arc)
3. Thus at the given distance, each
letter subtends an angle of 5 minute
at the nodal point of the eye (fig.
2.3).
4. The letter of the top line of
Snellen´s chart (fig. 2.4) should be
read clearly at a distance of 60 m.
Similarly, the letters in the
subsequent lines should be read
from a distance of 36, 24, 18, 12, 9,
6, 5 and 4 m.
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Optical and medical physics
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Landolt´s test types
It is similar to Snellen´s test types except that in it instead of
the letter the broken circles are used. Each broken ring
subtends an angle of 5 minute at the nodal point (fig. 2.5).
Procedure of testing
For testing distant visual acuity:
1. the patient is seated at a distance of 6 m (20 feet) from the Snellen´s
chart, so that the rays of light are practically parallel and the patient
exerts minimal accommodation.
2. The chart should be properly illuminated (not less than 20
footcandle).
3. The patient is asked to read the chart with each eye separately and the
visual acuity is recorded as the fraction, the numerator being the
distance of the patient from the letters and the denominator being the
smallest letters accurately read.
4. When the patient is able to read up to 6-m line, the visual acuity is
recorded as 6/6, which is normal. Similarly, depending upon the
smallest line that the patient can read from the distance of 6 m, his or
her vision is recorded as 6/9, 6/12, 6/18, 6/24, 6/36 and 6/60.
5. If one cannot see the top line from 6 m, he or she is asked to slowly
walk towards the chart till one can read the top line. Depending upon
the distance at which one can read the top line, the vision is recorded
as 5/60, 4/60, 3/60, 2/60 and 1/60.
6. If the patient is unable to read the top line even from 1 m, he or she is
asked to count fingers (CF) of the examiner. His or her vision is
recorded as
CF-3´, CF-2´, CF-1´ or CF close to face, depending
upon the distance at which the patient is able to count fingers.
7. When the patient fails to count fingers, the examiner moves his or her
hand close to the patient´s face. If one can appreciate the hand
movements (HM), visual acuity is recorded as (HM positive). When
the patient cannot distinguish the hand movements, the examiner
notes whether the patient can perceive light (PL) or not. If yes, vision
is recorded as (PL positive) and if not it is recorded as (PL negative).
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Lecturer: MSc. mervat kadhem
Optical and medical physics
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Colour vision
The visible wavelengths of the electromagnetic spectrum are between
400 nm to 780 nm. The colour of any object is determined by the
wavelengths emitted or reflected from the surface. White light is a mixture
of wavelengths of the visible spectrum. Colour is perceive by three
populations of cone photoreceptors in the retina which are sensitive to light
of short (blue), middle (green), or long (red) wavelength (fig. 1.2).
A congenital colour vision defect occurs if a cone pigment is absent or
if there is a shift in its spectral sensitivity. Hence, deuteranopia, protanopia
and tritanopia indicate absence of green, red and blue cone function, and
deuteranomaly, protanomaly and tritanomaly indicate a shift in the
corresponding cone sensitivity. The X-chromosome carries genes encoding
for red and green pigment whereas chromosome 7 carries the blue pigment
gene. Of men 8% and of women 0.5% have a defect of the red /green
system; the commonest is deuteranomaly which occurs in 5% of men and
0.3% of women. Tritan defects are rare.
Congenital colour defects characteristically affect particular parts of
the colour spectrum. Acquired colour defects occurred throughout the
spectrum but may be more pronounced in some regions. For example,
acquired optic nerve diseases tend to cause red-green defects. An exception
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Optical and medical physics
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occurs in glaucoma and in optic neuropathy which cause a blue-yellow
deficit.
Acquired retinal disease tends to cause blue-yellow defects (except in
cone dystrophy and Stargardt’s disease, which cause a red-green defect)
Clinical testing of colour vision
Clinical tests of colour vision are designed to be performed in
illumination equivalent to afternoon daylight in the northern hemisphere.
several testes used for this purpose they are: (Fransworth-Munsell (FM) hue
100 test, D-15 test, Ishihara test, and Lanthony New Colour Test)
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Optical instruments
The simple microscope or magnifier
Is a converging lens used to examine a small object in detail since the
eye cannot focus sharply on objects closer than the near point. The magnifier
forms a virtual image of the object and the eye looks at this virtual image.
Angular magnifier ( ):
Since
.:
.:
⁄
⁄
(f in centimeters)
ө: subtended angle of unaided
ө΄ : subtended angle with using of
simple magnifier
y: height of object
that is the angular magnification of a simple magnifier of focal length 10 cm
is (2.5X) (2.5 times).
The compound microscope
When an angular magnification higher than that attainable with a
simple magnifier is desired, it is necessary to use a compound microscope,
usually called merely a microscope.
The compound microscope consists of two lenses: objective lens and
ocular lens, they are highly corrected compound lenses, and they are shown
as simple lenses for simplicity.
(The object to be examined is placed just beyond the first focal point
(F) of the objective lens, which forms a real and enlarged image in the first
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Lecturer: MSc. mervat kadhem
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focal plane of the ocular. The ocular then forms a virtual image of that image
at infinity).
Overall magnification (M):
⁄
⁄
.: M= mγ
Where
m: lateral magnification
γ: angular magnification
Ocular
An ocular or eyepiece is a magnifier used for viewing an image
formed by a lens or lenses preceding it in an optical system.
The front lens of an ocular is
called the field lens, and the other is
the eye lens which is the nearest to
the eye.
Its two common types:
1. Huygens eyepiece:
It consists of two lenses having focal
lengths in the ratio 3:1 and the distance
between them is equal to the difference
between them. This eyepiece is free
from chromatic as well as spherical
aberrations.
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2. Ramsden eyepiece:
It consists of two plano-convex lenses
each of focal length f separated by a
distance equal to (2/3) f. the lenses are
kept with their curved surfaces facing
each other, thereby reducing spherical
aberration.
Ophthalmoscopy
Ophthalmoscopy is a clinical examination of the interior of the eye by
means of an ophthalmoscope. It is primarily done to assess the state of the
fundus and detect the opacities of ocular media. Three methods of
examination in vogue are:
 Distant direct ophthalmoscopy
 Direct ophthalmoscopy
 Indirect ophthalmoscopy
Distant direct ophthalmoscopy
It should be performed routinely before the direct ophthalmoscopy, as
it gives a lot of information. It can be performed with the help of a selfilluminated ophthalmoscope or a simple plane mirror with a hole in the
center.
Procedure
the light is thrown into the patient eye – with the patient sitting in semidark
room – from a distance of 20-25 cm, and the feature of the red glow in the
pupillary area are noted.
Applications of distant direct ophthalmoscopy
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1. To diagnose opacities in the refractive media
2. To differentiate between a mole and a hole of the iris
3. To recognize detached retina or a tumour arising from the fundus
Direct ophthalmoscopy
It is the most commonly practiced method for routine fundus
examination.
Optics of direct ophthalmoscopy
The modern direct ophthalmoscope
works on the basic optical principal of glass
plate ophthalmoscope introduced by von
Helmoholtz.
Optics
of
direct
ophthalmoscope is depicted in figure 12.50.
A convergent beam of light is
reflected into the patient’s pupil (fig. 12.50,
dotted lines). The emergent rays from any
point on the patient’s fundus reach the observer’s retina through the viewing
hole in the ophthalmoscope (fig. 12.50, continuous lines). The emergent rays
from the patient’s eye are parallel and brought to focus on the retina of the
emmetropic observer when accommodation is relaxed.
 In hypermetropic patient, the emergent
ray from the illuminated area of the
retina will be divergent and thus can be
brought to focus on the observer’s retina
if the letter accommodates, or by the
help of a convex lens (fig. 12.51).
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 In a myopic patient, the emergent rays will be convergent and thus
can be brought to focus on the observer’s retina by the help of
concave lens (fig. 12.52).
Therefore, if the patient or/and the observer is/are ametropic, a correcting
lens (equivalent to the sum of the patient’s and observsr’s refractive error)
must be interposed (from the system of plus and minus lenses, in-built in the
modern ophthalmoscope).
Indirect ophthalmoscopy
Indirect ophthalmoscopy, introduced by Nagel in 1864, is now a very
popular method for examination of the posterior segment.
Optics of indirect ophthalmoscopy
Optical principal: the principal of indirect ophthalmoscopy is to make the
eye highly myopic by placing a strong convex lens in front of patient’s eye
so that the emergent rays from an area of the fundus are brought to focus as
a real inverted image between the lens and the observer’s eye, which is then
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studied (fig. 12.55).
Optical
system
of
binocular
indirect
ophthalmoscope
Optics
of
modern
binocular
indirect
ophthalmoscopy is shown in figure 12.56. binocularity
is achieved by reducing the observer’s interpupillary
distance from about 60 mm to approximately 15 mm by
prisms/mirrors (fig.12.57). Even this artificial reduction
of interpupillary distance requires larger patient’s
pupils for binocular viewing than those for the
monocular viewing.
Field of illumination: as shown in figure 12.58, the field of illumination is
more in myopia and less in hypermetropia as compared to emmetropia.
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lensometer
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Modern optics: laser
Laser: is Light Amplification by the Stimulated Emission of Radiation.
Production of laser energy (lasing process)
1. Laser pumping:
All atoms are most stable in
their lowest energy state, known
as the ground state. Pumping is the
process by which the energy is
delivered to atoms in a laser active
medium. Active medium contains
atoms or molecules which will be undergo stimulated emission. The atoms
will absorb this energy and that will elevate its electrons from their ground
stat to a higher energy level. The later level allows excited atoms to
accumulate there.
2. Population inversion:
Population inversion is occurred when there are more atoms in the
excited state than in the lower state (energy level).
3. Spontaneous emission
Atoms in the excited state are unstable (after population inversion),
and their electrons tend to
spontaneously return to the
ground state by emitting light
energy. Spontaneous emission is
the emission of a photon by
atoms without any external
impetus. This emitted light is
incoherent and it travels in all
directions.
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4. Stimulated emission
If an atom at higher energy
level is stimulated by a photon
whose wavelength is the same to
that the atom would emit, the
resulting emission will be coherent
with the stimulating photon, and
the atom will drop to the lower
energy level. Most of energy
released by the active medium is
incoherent, but the small amount released by the stimulated emission can be
amplified.
5. light Amplification:
all the light waves generated in the medium are due to one initial
waves and all of the waves are in phase. Thus, the waves are coherent and
interfere constructively.
6. Resonance:
The active laser medium is housed in a tube which has a mirror at
each end known as (resonance) or (cavity). The distance between the mirrors
must equal a multiple of the wavelengths of the emitted light, so that
resonance can occur.
Working: when a photon incident on
an excited electron and stimulated
emission occurs, the light emitted
travels down the tube, and reflected
and reselected at both mirrors. The
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mirrors are precisely aligned, so that the light which traversed the tube is
still in phase with itself. Thus it reinforces itself, this is known as
“resonance”.
Mean while other stimulated emission are taken place so that the light
traversing the tube gets stronger and stronger (amplified) while remaining
exactly in phase (coherent) and the lasing process is under way.
If one of the mirrors is made partially transparent, some of the light
may be allowed to leave the tube.
Steps of lasing action
Types of lasers
There are several ways in which we can classify lasers into different
types. We can classify lasers according to the material used as active
medium. They are divided into four categories:
1. solid state lasers: such as (ruby laser, Nd:YAG laser)
2. gas lasers: such as (helium-neon, krypton, carbon dioxide)
3. liquid lasers: (dye)
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4. semiconductor diode lasers
Most of lasers emit light in the red or IR regions. Lasers work in a
continuous mode or in pulsed mod.
Diode lasers are used in wide variety of applications, it use in optical
fiber communications, CD players, CD-ROM drives, optical reading, high
speed laser printing etc.
Laser properties
1.
2.
3.
4.
5.
highly directional
negligible divergence
high intensity
coherent: (in phase)
monochromatic: (of one wave length)
Laser in medicine
Lasers in Medical Surgery
Almost every medical surgery in which a removal of tissue is required or
a cut needs to be made can be done with a laser. In general, the results of
surgery using lasers are better than the results using a surgical knife.
The Advantages of Laser Surgery [16]:
1. Dry field of surgery, because laser energy seals small blood vessels.
2. Less postoperative pain, because of the sealing of nerve ends.
3. No contact with mechanical instruments, so sterilization is built in.
4. Possibility to perform microsurgery under a microscope. The laser beam
passes through the same microscope.
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5. Possibility to perform surgical procedures inside the body without
opening it, using optical fibers to transmit the laser beam.
6. It can be controlled by a computer, and operate with a very small area of
effect under a microscope.
The Surgical Lasers
The most typical lasers and their wavelengths:
No.
Laser Acronym
Wavelength (nm)
1
CO2
10600
2
Nd:YAG
1064
3
KTP (SHG)
532
Nd:YAG
4
Ho:YAG
2130
5
Er:YAG
2940
6
Argon
514
7
Copper Vapour
578
8
Ruby
694
9
GaAlAs
800-870
10
Dye
400-800
11
Excimer
193, 284, 308, 351
In order for a laser to be suitable for use as a surgical laser, it must be
powerful enough to heat up the tissue to temperature over 50 C o. A surgical
laser can either be used in continuous wave or pulsed mode. These lasers can
be broadly divided into three groups, according to their output:
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1- Vaporizing 1-5 w.
2- Light cutting 5-20 w.
3- Deep cutting 20 – 100 w.
Medical Surgery Fields
The areas of medical laser surgery are well established, and include:
1
Ophthalmology
‫طب العيون‬
2
Dentistry
‫طب األسنان‬
3
Dermatology
‫طب األمراض الجلدية‬
4
Urology
‫طب المجاري البولية‬
5
Angioplasty and Cardiology
6
Orthopedics
7
Gastroenterology
‫التقويم الوعائي وطب القلب‬
‫جراحة العظام‬
‫طب الجهاز الهضمي‬
Lasers in Ophthalmology
In ophthalmology, various types of lasers are being applied today for
either diagnostic or therapeutic purposes. In diagnostics, lasers are
advantageous if conventional incoherent light sources fail. One major
diagnostic tool is confocal laser microscopy which allows the detection of
early stages of retinal alterations. By this means, retinal detachment and also
glaucoma1 can be recognized in time to increase the probability of
successful treatment. In this section, however, our interest focuses on
therapeutic laser applications.
The first indications for laser treatment were given by detachments of
the retina. Meanwhile, this kind of surgery has turned into a well-established
tool and only represents a minor part of today’s ophthalmic laser procedures.
Others are, for instance, treatment of glaucoma and cataract. And, recently,
refractive corneal surgery has become a major field of research, too.
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The laser was invented in 1960, and in 1961 this laser (Ruby) was used
by eye doctors. It is natural that the eye was chosen to be the first organ for
performing medical experiments, since the eye is transparent to the
electromagnetic spectrum in the visible range. Another natural device that
helps was the lens in the eye, which focuses the electromagnetic radiation
onto the retina. Thus, increasing the power density by orders of magnitude.
The targets of all therapeutic laser treatments of the eye can be classified
into:
1. The front segments consist of the cornea, iris, and lens.
2. The rear segments are given by the vitreous body and retina.
A schematic illustration of a human eye is shown in Figure. In the
following paragraphs, we will discuss various treatments of these segments
according to the historic sequence, i.e. from the rear to the front.
Advantages
1. Low risk of infection.
2. Painless.
3. No-need to hospital stay.
4. More precise.
Techniques of Eye Treatment by Laser
Figure show Scheme of a human eye
Photothermal Treatments Techniques
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Many diseases and medical problems of the eye can be treated using
lasers in a thermal regime. Here are a few of the more common treatments:
• Detached Retina: where the retina comes away from the back of the eye,
can treated by ‘gluing’ it back on again by photocoagulating it by using
Argon ion laser.
Figure shows Retinal Detachment
Glaucoma: is caused by a build-up of pressure in the eye. Closed-angle
glaucoma can be treated by making a hole in the iris, thus releasing the
pressure. This procedure is called laser iridotomy, Argon ion lasers or
pulsed neodymium lasers are used.
Figure shows Iris before and after laser treatment
Figure shows the pressure build up in the eye
Cataract: A cataract is the clouding of the crystalline lens of the eye is like
looking through a dirty window. As a result of the natural aging process, the
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lens gradually becomes cloudy. This opacity results in distorted vision and
can finally lead to blinding. The common treatment of cataract is to
surgically remove the cloudy lens and put a plastic lens using argon ion
lasers or pulsed neodymium lasers.
4.8.2 Non-thermal Treatments Techniques
Thermal effects are not always desirable, particular when attempting to
ablate or cut tissue very precisely without damaging the surrounding tissue.
Photoablation, plasma-induced ablation and photodisruption are all used as
non-thermal means of ablating or cutting tissue.
• Corneal Reshaping: to treat myopia or hyperopia (near or longsightedness) is the commonest application of lasers to ophthalmology
that uses a non-thermal mechanism. Three procedures are described
below: radial keratectomy, photorefractive keratectomy (PRK) and
laser in situ keratomileusis (LASIK), all of which use photoablation as
a mechanism to remove corneal tissue.
The difference between LASIK and PRK is that the first has a flap but the
second doesn’t have.
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Diffraction
It is a phenomenon when there are some alternate bright and dark
bands. Thus light can travels round corners.
This phenomenon occurs if the width of an illuminated opening is
small compared with the wave length.
There are two types of diffractions: Franhofer diffraction and Fresnel
diffraction.
Franhofer diffraction
1. The source and the screen are at
infinite distance from diffraction
element
2. Plane wave
3. Lenses are required
Fresnel diffraction
1. Either the source or the screen or
both are not at infinite distance
from the diff. element.
2. Spherical wave
3. Lenses not required
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Franhofer diffraction by a single slit:
At minima
sin =
AL= a sin
where ALis path deference
and it equal a multiple of the
wave length = pλ,
n=1, 2, 3, 4,……
.: a sin =nλ ……………minima
At 1st minima (a=1)
sin =tan = =
because is very small, x:reprecent half width of the
pattern, if we want the
width (d×2)
a sin =nλ
.:
Example 1: parallel beam of light of wave length 6563Å is incident
normally on aslit 0.3850 mm wide. A lens with a focal length of 50 cm is
located just behind the slit bringing the diffraction pattern to focus on a
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white screen. Find the distance from the the principal maximum to (a) the
first minimum (b) the fifth minimum?
Sol:
λ= 6563 Å
x1=?
a= 0.385 mm
x5=?
f= 50 cm
a sinө = nλ……. Min
n=1, 2, 3,….
At first minimum (n=1)
x1=
x5=
H.w: in franhofer diffraction pattern due to a narrow slit a screen is placed 2
m away from the lens to obtain the pattern. If the slit width is 0.2 mm on
either sides of the central maxima, find the wavelength of light?
H.W: plane waves of blue light, λ= 4340Å, fall on a single slit, then pass
through a lens with a focal length of 85 cm. if the central band of the
diffraction pattern on the screen has a width of 2.45 mm. find the width of
the single slit?
Diffraction by a double slit
d=(a+b)
d: distance between two slits centers
b: distance between slits
a: slit width
maxima: (a+b) sinө=nλ
minima: a sinө=pλ
p=1, 2, 3,….
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Missing orders:
The patterns
Ex.2: calculate the missing orders for a double slit Franhofer diffraction
pattern, if the slit widths are 016 mm and they are 0.8mm a part?
Here a= 0.16 mm, b= 0.8 mm
Equation for interference maxima= (a+b) sinө=nλ
Equation for interference minima= a sinө=pλ
Missing orders:
.:
(
)
(
)
.: n=6p
Thus missing orders are: 6, 12, 18,……
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Diffraction grating
Resolving power of a grating or (plane transmission grating)
The resolving power of a grating is defined as the ratio of the
wavelength (λ) of any spectral line to the smallest difference in wavelength
(dλ). Between this line and neighboring line.
So resolving power of grating =
Where: m: is the order of spectrum
N: the total number of lines on the
grating surface.
Polarization of light
Polarization: is a travelling vibration.
Vibration of light is one direction, and its waves are transverse waves
because the vibration of light is perpendicular to the direction of the light
wave’s travels. While sound waves is longitudinal waves, because the
vibrations occur in the same direction as the wave travels.
Polarized light has many important applications in industry and
engineering. One of the most important applications is in liquid crystal
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displays (LCDs) which are widely used in wrist watches, calculators, TV
screens etc.
Plane polarization wave
When the vibration of light is one direction thus that is called planepolarized.
Polarization by reflection
In 1808 Malus discovered that polarized light is obtained when
ordinary light is reflected by a plane sheet of glass. Malus also showed that
the light reflected by water is plane-polarised.
The production of the polarized light by the glass is explained as
follows:
Each of the vibrations
of the incident (ordinary)
light can be resolved in to
two components one is
parallel to the glass surface
and
the
other
is
perpendicular to the surface.
The light of a component parallel to the glass surface is reflected, but
the perpendicular component is refracted into the glass. Thus the light
reflected by the glass (plane-polarised).
H.W what is the tourmaline
Polarization by double refraction
Bartholinus in (1669) placed a crystal of Iceland spar on some words
on a sheet of paper; he found that two images were seen through. Therefore
he gave the name of double refraction to this phenomenon.
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Iceland spar is a crystalline form of calcite (calcium carbonate), this a
solid whose opposite faces are parallelograms.
When a beam of un polarized light is incident on one face of the
crystal, its internal molecular structure produces two beams of polarized
light E,O as in fig. below, whose vibrations are perpendicular to each other.
References:
1.
2.
3.
4.
5.
Optics
A textbook of optics
Anatomy and physiology
Laser applications
Section3 optics, refraction, and contact lenses
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