Chapter 2
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Author: Wayne
FIGURE 2.1
The law of reflection: The angle of reflection (qr) equals the angle of incidence (qi).
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FIGURE 2.2
The image of a point formed by a plane mirror can be determined by using the law of reflection. Draw
several rays that obey the law of reflection. The rays diverge when they enter the eye. The brain
imagines that the diverging rays originated from a single point behind the mirror. The place where the
rays appear to originate is known as the virtual image.
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FIGURE 2.3
A virtual image produced by the eye and the brain of a person looking at a reflection of an object in a
plane mirror.
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FIGURE 2.4
Diffuse reflection from a rough surface. The angle of reflection still equals the angle of incidence, but
there are many angles of reflection. You can tell if a reflective surface is rough or smooth by observing
if the reflection is diffuse or specular.
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FIGURE 2.5
When light strikes a partially silvered mirror, some of the light is reflected and some of the light is
transmitted. In this way, a partially silvered mirror functions as a beam splitter.
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FIGURE 2.6
A beam of light, propagating parallel to the principal axis of a concave mirror, is brought to a focus
after it reflects off the mirror. The focal point is equal to one-half the radius of curvature.
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FIGURE 2.7
A virtual erect image is formed by the eye and brain of a person looking at the reflection of an object
placed between the focus and a concave mirror. The virtual image of a point appears at the location
from which the rays of that point appear to have originated.
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FIGURE 2.8
A real inverted image is produced by a concave mirror when the object is placed in front of the focal
point. The further the object is from the focal point, the smaller the image, and the closer the image is
to the focal plane.
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FIGURE 2.9
When an object is placed at the radius of curvature of a concave mirror, a real inverted image that is
the same size as the object is produced at the radius of curvature by a concave mirror. When the
object is the filament of a lamp, a concave mirror returns the rays going in the wrong direction so that
the lamp will appear twice as bright.
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FIGURE 2.10
A virtual erect image is formed by a person looking at the reflection of an object placed anywhere in
front of a convex mirror. The virtual image of a point appears at the location from which the rays of that
point appear to have originated.
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FIGURE 2.11
Because of the law of reflection, where the angle of reflection equals the angle of incidence, a
spherical mirror does not focus parallel rays to a point, but instead produces a zone of confusion. This
spherical aberration results because the rays that strike the distal regions of the mirror are bent too
strongly to go through the focus. Spherical aberration can be prevented by gradually and continuously
decreasing the radius of curvature of the distal regions of a concave mirror. Decreasing the radius of
curvature gradually and continuously results in a parabolic mirror without any spherical aberration.
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FIGURE 2.12
An observer (A) is looking over the rim of a dish so he or she can just not see a coin placed at B when
the dish is full of air. As water is gradually added to the dish the rays coming from the coin are
refracted at the water–air interface so that they will enter the eye. Consequently, the coin will become
visible to the observer. Thinking that light travels in straight lines, the observer will think that the coin is
at C.
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FIGURE 2.13
Rays from stars are refracted as they enter the Earth’s atmosphere. Since we think that light travels in
straight lines, we see the image of the star higher in the sky than it actually is.
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FIGURE 2.14
When light travels from air to glass it is bent or refracted toward the normal. By contrast, when light
travels from glass to air, it is bent away from the normal. This behavior is codified by the SnellDescartes law that states that the sine of the angle of incidence times the refractive index of the
incident medium equals the sine of the angle of transmission times the refractive index of the
transmission medium.
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FIGURE 2.15
The refractive index of a medium is a function of the wavelength of light. This is the reason that a
prism can disperse or resolve white light into its various color components.
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FIGURE 2.16
When a light ray travels from a medium with a higher refractive index to a medium with a lower
refractive index, the angle of refraction can be greater than 90°, resulting in internal reflection. The
critical angle qc is the incident angle that gives an angle of refraction of 90°.
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FIGURE 2.17
Light traveling from air through a piece of glass with parallel sides and back through air is slightly
displaced compared with where the light would have been had it passed through only air. The degree
of displacement depends on the thickness of the glass and its refractive index. The light that leaves
the glass is parallel to the light that enters the glass because the refraction at the far side of the glass
reverses the refraction at the near side.
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FIGURE 2.18
When the two surfaces of the glass are not parallel, but form a prism, the refraction that takes place
on the far side does not reverse the effect of the refraction that takes place on the near side. The
second refraction amplifies the first refraction and the incident light is bent toward the base of the
prism.
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FIGURE 2.19
Two prisms, with their bases cemented together, bend the incident light propagating parallel to the
bases of the prisms toward the bases. The prisms do not have the correct shape to focus parallel light
to a point since the rays that strike the two corresponding prisms farther and farther from the principal
axis will converge at greater and greater distances from the double prism.
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FIGURE 2.20
A lentil-shaped surface has the correct geometry to focus parallel rays to a point.
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FIGURE 2.21
A lentil-shaped biconvex piece of glass focuses parallel rays when the refractive index of the lens nl is
greater than the refractive index of the medium nm. When the refractive index of the medium is
greater than the refractive index of the lens, the lens must be biconcave to focus parallel rays.
Whether a lens is converging or diverging is not a function of the lens alone but of the lens and its
environment.
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FIGURE 2.22
Image formation by a converging lens with focal length f. The object with height yo and the image with
height yi are distances so and si from the lens, respectively. xo = so – f and xi _ si – f.
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FIGURE 2.23
Three pairs of similar triangles made by the rays shown in Figure 2-22.
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FIGURE 2.24
The lenses found in a microscope are composed of more than one element.
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FIGURE 2.25
Two converging lenses that are separated by a distance greater than the sum of their focal lengths
form a real erect image.
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FIGURE 2.26
Image formation by two converging lenses separated by a distance smaller than either of their focal
lengths.
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FIGURE 2.27
Finding the image produced by the first lens of the pair shown in Figure 2-26, if the second lens were
not there and deducing the ray that would go through the center of the second lens if it were there.
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FIGURE 2.28
Why does the reflected light go from A to B by striking point C on the mirror instead of rushing to the
mirror and striking it at D or rushing from the mirror after it strikes it at F?
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FIGURE 2.29
B and B¢ are equidistant to the mirror. BC = B¢C and EB = EB¢.
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FIGURE 2.30
The shortest distance between two points is a straight line. Since AB¢ = is a straight line and AB¢ =
AB, the shortest distance between A and B is when < ACN = < BCN, or the angle of incidence equals
the angle of reflection.
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FIGURE 2.31
Using Fermat’s Principle as the basis of the Snell-Descartes law, a = x + (a–x).
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FIGURE 2.32
A ray propagating through a specimen composed of layers with various refractive indices and
thicknesses has an optical path length. The optical path length differs from the length itself. The optical
path length is obtained by finding the product of the refractive index and thickness of each layer and
then summing the products for all the layers.
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FIGURE 2.33
On a hot day, when we look down at the road ahead of us, we see the image of a tree or clouds on the
road because light obeys Fermat’s Principle and travels to our eyes in an arc. However, we think that
light travels through a medium with a continuously varying refractive index in straight lines.
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FIGURE 2.34
Spherical aberration occurs because the rays from any given object point that hit a lens with spherical
surfaces far from the principal axis are refracted too strongly. This results in a circle of confusion.
Spherical aberration can be reduced by grinding the lens so that it has aspherical surfaces.
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FIGURE 2.35
Chromatic aberration occurs because the refractive index of glass is color-dependent. This results in
the violet-blue rays being more strongly refracted by glass than the orange-red rays.
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FIGURE 2.36
Chromatic aberration can be reduced by combining a diverging lens made of flint glass with a
converging lens made of crown glass. Because the flint glass has a greater dispersion than the crown
glass, the chromatic aberration produced by the crown glass is reduced more than the magnification
produced by the crown glass is reduced.
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FIGURE 2.37
The image plane of a converging lens is not flat. Additional lens elements must be added to the
converging lens to decrease the focal length of the image close to the axis.
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FIGURE 2.38
The lonely fungi obey the laws of geometric optics. In air, light is focused on the far side of the
cylindrical sporangiophore, and the fungus bends toward the light source. In a high refractive index
medium, light is dispersed over the far side of the sporangiophore and is brightest on the side closest
to the light source. In this case, the fungus bends away from the light source.
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FIGURE 2.39
The cornea and lens of the human eye act as a converging lens that throws an image on the retina.
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FIGURE 2.40
The closer an object is to our eye, the larger is the visual angle made by the object and the eye, and
the larger the image is on the retina.
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FIGURE 2.41
When a small object is placed at the near point of the naked eye, we still cannot see it clearly,
because the visual angle is too small and the image falls on a single cone. A lens placed between the
object and the eye produces an enlarged image on the retina. The size of the image on the retina is
the same as that that would be produced by a magnified version of the object placed at the near point
of our eye.
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