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CHAPTER 22 How can human vision be enhanced?
Contents
Sight
Exploring light using the ray model
Objects and images
Looking in the mirror
FS
The behaviour of light when changing media
Bending of light
O
Snell’s law
PR
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The speed of light in glass
Total internal reflection and critical angle
Cameras
The thin lens formula
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Human and animal vision
Accommodation mechanisms
PA
Correcting eye defects
Restoring sight
TE
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Extending vision
Telescopes
Microscopes
EC
Chapter review
Summary
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Questions
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Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
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CHAPTER 22 How can human vision be enhanced?
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Sight is one of the senses we heavily rely on for collecting data and making observations. How can vision be
extended to gather even more information?
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
REMEMBER
Before beginning this chapter, you should be able to:
■
describe light as the part of the electromagnetic spectrum detected by the human eye.
KEY IDEAS
After completing this chapter, you should be able to:
describe the use of ray tracing as a technique to investigate the behaviour of light in optical devices
■
explain that reflected rays obey the law of reflection
■
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explain that, when passing from one medium to another, light refracts in accordance with Snell’s Law, n1 sin θ1
= n2 sin θ2
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describe how optical devices such as eyes, cameras, telescopes and microscopes form images by
manipulating light
describe how the size of an image compares with the size of an object in magnification
■
apply ray tracing to explain common problems with sight.
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Sight
EC
Physics is about making sense of the physical universe. To do this we collect data and look for connections and
patterns. Senses are the means by which animals, including humans, collect information about the world. From
birth our sense of sight is one of the most significant methods we use to collecting data. Sight detects just a small
part of the spectrum of electromagnetic radiation, but with it we can do so much.
Exploring light using the ray model
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In this chapter we will use of the ray model for light. The ray model makes use of the fact that light travels in
straight lines in uniform media. Rays are arrows drawn from a light source. The direction of light moving out from
its source is called the direction of propagation.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
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Rays are straight lines indicating light propagating from a light source. The further they are apart, the dimmer the
light.
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Objects that emit light are called luminous objects. They include the Sun, the stars, light globes and computer
screens (when switched on), lit candles, and glow worms. Light propagates away from luminous objects.
Luminous objects shine even when there is no other light source. Luminous objects that produce light as a result
of being hot are described as incandescent.
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All other objects are described as non-luminous. They need a luminous object to shine light on them for us to be
able to see them. Non-luminous objects include trees, tables and the Moon.
Digital docs
Investigation 22.1:
Luminous or not?
Classify objects as luminous or
non-luminous.
doc-0000
Investigation 22.2:
Luminosity and temperature
Investigate change in colour
and brightness with
temperature.
doc-0000
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
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The Sun is luminous; clouds, rocks, trees and water are all non-luminous.
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It turns out that all objects are luminous to some extent, but ones that we call non-luminous are radiating light that
is invisible to the unaided eye. We know that very hot objects tend to glow, for example a hot coal in a fire. What
we see depends on the object’s temperature. When the coal cools down, it is still radiating, but the light it emits
has a longer wavelength than the human eye can see. We call this radiation infrared, microwave or radio wave
radiation, depending on how cool the object is.
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Devices such as night-vision goggles are able to detect some of these wavelengths that our unaided eyes cannot,
and turn them into wavelengths on a screen that are visible to the human eye. Night-vision devices are used by
soldiers and journalists, and are also useful in firefighting to find the hotspots behind the smoke.
Chapter 22 How can human vision be enhanced?
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An image seen through a night-vision device
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Objects and images
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We can see luminous objects because the light from them directly enters our eyes. We can draw rays from the
luminous object to the retinas of our eyes, through the iris. Notice that in the following diagram, rays of light leave
the flame in all directions. Only some are drawn. Our eyes only see the rays that enter the eyes. All of the other
rays play no part in our perception of the flame.
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Some terminology will help us here and for the rest of this topic. In this example, the flame is called the object. It
is the source of the rays. Optical devices such as our eyes collect the rays that enter them to form an image of
the object. Without these images, we would not be able to see.
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Eyes do not always successfully form clear images. Many people cannot form clear images of letters on the page
in front of them. Reading glasses are able to help some people form clear images of the letters they read.
Chapter 22 How can human vision be enhanced?
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Light radiating from a flame with some entering an eye
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Looking in the mirror
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Most of what we see depends significantly on the phenomenon of reflection. We can see the light emitted by
luminous objects, but we can see everything else around us because light reflects from non-luminous objects into
our eyes.
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In the last section we mentioned that rays of light radiate in all directions from a luminous object such as a flame.
What happens to those other rays that do not enter the eye? Some of them might hit a book that is lying on the
table beside the flame. When they hit the book, two things can happen: the ray can be absorbed or the ray can be
reflected.
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Different materials absorb different amounts of light. Compare the sunlight striking snow and soil. The snow
absorbs very little light but the soil absorbs a lot. This means that most of the light hitting the snow is reflected, but
only a little of the light hitting the soil is reflected. The snow and soil have irregular surfaces, so the reflected light
leaves them in many different directions. Any ray that reflects so that it enters your eye will help form an image of
the snow or the dirt. Many more rays come from the snow, so it is very bright, whereas the soil has absorbed a lot
of the light, so it appears dark.
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The book next to the flame is visible to us because some of the light that hits it reflects into our eyes, which use
that light to form an image of the book. This is how we see all non-luminous objects. This type of reflection, in
which the directions of the reflected rays appear random, is called diffuse reflection. The directions of rays in
diffuse reflection are not really random; they are simply a result of the rays striking an irregular surface. Regular
reflection, also referred to as specular reflection, is reflection from a smooth surface.
Light rays from a luminous object hitting a book and reflecting into an eye
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
The more polished a surface is, the less we see the surface itself and the more we see the reflection of other
objects in the surface.
The Law of Reflection
Reflection occurs in a particular way that has been described by the law of reflection since the times of Ancient
Greece.
The angle of incidence equals the angle of reflection. The incident ray, the normal and the reflected ray all lie
in the same plane.
FS
The ray of light approaching the surface is called the incident ray. The angle this ray makes with the normal to
the surface is called the angle of incidence (i). The ray of light reflecting from the surface is called the reflected
ray. The angle this ray makes with the normal to the surface is called the angle of reflection (r).
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The normal is an imaginary line sticking out at right angles to the surface. The reference to the normal may seem
like an unnecessary complication. Why not just say that the angles that the rays make with the surface are equal?
But the surface is not necessarily flat, so the angle with the surface can be different depending on the direction of
the ray. Also, there are lots of possible reflected rays where i = r, but only one of these is in the same plane as the
normal (if we do not count the light simply returning along the same path as the incident ray). It is this one path
that the ray of light will follow.
Chapter 22 How can human vision be enhanced?
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Diagram showing incident and reflected rays for a plane surface
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The ray model can explain diffuse reflection. On a microscopic scale, the surfaces of most objects are not flat or
smooth. Rays hitting the surface only a tiny distance apart will therefore be reflected at different angles. Although
the law of reflection is satisfied on the microscopic scale, the overall effect of light hitting that surface is for it to be
scattered in all directions. This scattering of the light in random directions is called diffusion, hence the term
diffuse reflection.
This is diffuse reflection. Each of the incoming parallel rays meets the irregular surface at a different angle of
incidence. The reflected rays will therefore go off in different directions, enabling observers in all directions to
receive light from the surface; in other words, to see the surface.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
If we polish a surface so that it becomes smoother, then more of the light will be reflected in the same direction.
There comes a point where the reflection is so uniform that we stop seeing the surface and instead see images of
the space we are in reflected in the surface. This is a mirror. In this case, most of the light rays hitting the surface
of the mirror from a given angle, i, reflect with the same value of r. This is called specular reflection.
Forming images in a mirror
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We can use rays to determine where the image in a mirror is located and what its nature is. We need to start with
the object. When you look in the mirror, what you see is an image of your head. Assuming that the mirror you are
looking at is a plane (flat) mirror, you can see that the image is about the same size as you would expect your
head to be when viewed at that distance, and it is the right way up. We describe this image as having a
magnification of 1 (it is the same size as the object) and it is upright. You might also notice that the image
appears to be behind the mirror at the same distance behind it as you are in front of it. You know that there is not
really an image behind the mirror. That space is probably in another room or outside. The image of your face in
the mirror is an optical illusion caused by the reflection of light in the mirror. This image is called a virtual image.
The image of your face in the mirror is an optical illusion caused by the reflection of light in the mirror. It is called a
virtual image.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
The ray model helps us to understand how this image forms. In the diagram below you can see the object (your
head) and the mirror from a view to one side. Your head is non-luminous, but because you are in a lit room, light
striking your head is diffused in all directions. Consider light striking the top of your head. Some of this light
reflects in the direction of the mirror. We can choose to investigate the behaviour of any of the rays that hit the
mirror, but let’s start with the ray that passes horizontally to the mirror (ray 1). It will reflect with i = r so that the
reflected ray retraces the path of the incident ray. Since this ray returns to the top of your head, it never actually
enters your eye, so it does not contribute to the image formed by your eye.
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Now consider what happens to a ray of light that passes from the top of your head to the mirror and reflects back
to your eye. Again, we know its path because i = r. This ray helps to form the image that your eye sees.
PA
Locating the image in a plane mirror
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Consider another ray that travels from the top of your head to the mirror and reflects back to touch your chin.
Again, this ray does not enter your eye.
EC
What we can see is that all three rays can be traced back to a single point behind the mirror. This point, labelled I,
is exactly where we see the image of the top of our head in the mirror. There is nothing special about the three
rays chosen. Draw any other ray and trace back its reflected ray, and we see that it too appears to come from this
point.
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Only one ray that we drew enters the eye. How can the eye form an image of the top of the head from a single
ray? A ray represents an infinitesimally small beam of light. Many rays of light enter the pupil of the eye, all from
slightly different angles, so the eye can interpret them as diverging from a point behind the mirror.
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When drawing diagrams such as this, it is much easier to use rays of light that are well spread out, even if they do
not enter the eye. It does not make any difference to the result.
Light diverging from a virtual image to your eye
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
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We have now located the position of the image of the top of your head using the technique of ray tracing. We can
do the same for the chin. See the diagram below. What we find is that the image is the same size as the object, it
is upright and appears to be at the same distance behind the mirror as the object is in front of the mirror. It is also
a virtual image, because the light only appears to come from the image. In reality, the light from your head does
not pass through the image at all.
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Locating the image of your chin
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Next we will investigate the formation of other types of images. Real images are actually formed by the light rays.
These are essential in the eye and in cameras, both of which have sensors that respond to the light of the image.
We can only see virtual images because our eyes make real images of the light appearing to come from virtual
images.
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An interesting fact about plane mirrors is that the image is laterally inverted. This means that the left-hand side
of the object is the left-hand side of the image, but the image is facing the object. So if you wear a watch on your
left hand (the object), the image will have the watch on its right hand. This is simply explained by drawing a ray
diagram as seen from above the situation.
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Hi
Ho
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Images are not always the same size as their objects. The effect of an optical device on the size of the image is
indicated by the magnification:
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where Hi is the height of the image and Ho is the height of the object. As the image in a plane mirror is the same
height as the object, the magnification is 1. In a device such as the bottom of a spoon, where the height of the
image is smaller than the height of the object, then the magnification is between 0 and 1. This is known as a
diminished image. When the magnification is greater than 1, the image is said to be enlarged. If you look at the
reflection of your eye in the concave (curved inwards) side of a polished spoon, with your eye very close to the
spoon, you may see an enlarged image of your eye.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
eModelling
Model of a concave mirror
doc-0055
Digital doc
Investigation 22.3:
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Concave mirrors — an
observation exercise
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Observe yourself in a concave
mirror.
Weblink
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Concave mirror
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PHYSICS IN FOCUS
Curved mirrors
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Sometimes mirrors are used for purposes that require them to be curved. For example, a car headlight has a
curved mirror behind its bulb. This mirror collects the rays that would otherwise illuminate objects behind the light
and reflects them forward. A plane mirror behind the light would cause the light to reflect in a forward direction but
diverge. The curved mirror results in all of the rays reflecting in the forward direction without diverging, to create
an intense beam of light. Mirrors curved like this are called concave mirrors. The edge of a concave mirror is
closer to the object than the centre. Such mirrors are also used in many forms of telescope.
(a) Rays from a light source in front of a plane mirror are reflected in all directions. (b) The curved circular mirror
brings the reflected rays inwards. (c) When the curved mirror is in the shape of a parabola, the reflected rays
become parallel to each other and the light source is said to be at the focus of the curved mirror.
Chapter 22 How can human vision be enhanced?
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In a car headlight, the filament of the globe is placed at the focus of the curved reflective surface. This produces a
narrow beam of light.
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Convex mirrors are like the bottom side of a spoon: the middle is closer to the object than the edge. These
mirrors can be used to help see around corners in driveways and small streets by producing a wider field of view.
The magnification of convex mirrors is always less than one, and the image is virtual.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
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Convex mirrors are often used to help improve vision around corners.
The behaviour of light when changing media
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So far we have considered opaque objects such as books, heads and mirrors. Light does not pass through these
objects. Materials that light passes through are called transparent and translucent materials.
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Materials that are transparent include clear glass. The light passes through undeviated so that you can see the
objects on the other side clearly.
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Translucent materials are used when you want some light but you do not want to be able to see through clearly,
for example glass in a bathroom window. The glass is etched so that the surface is not smooth, or it has some
other material embedded in it that diffuses the light.
Light that strikes the surface of transparent glass is partially reflected from the material and is partially transmitted
through the material. When light moves from one medium to another (in this case from air into glass), the speed
of the light tends to change. If the light strikes the surface at an angle other than 90 degrees, this usually results in
bending of the light. This bending is called refraction. (The occasions when it does not bend are when the two
materials are such that they convey light at the same speed.)
You may have noticed some of the effects of bending of light. Hunters spearing for fish in the shallows must aim
the spear below where the fish appears to be in the water. At the beach or in a pool, people standing in the
shallows appear to have shorter legs. Our perception is distorted by light travelling from one medium into another.
This may be more apparent when we set up a straight rod in a beaker of liquids that do not mix, as seen in the
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
diagram. Each time the medium changes, the light changes direction, distorting our vision. This change in the
direction of the light is refraction.
Digital doc
Investigation 22.4:
Seeing is believing
doc-0000
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Observe the bending of light.
An example of refraction
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
Bending of light
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The ray model can help explain these observations. If we try to spear a fish and the fish swims safely beneath
where the spear passes, that is because a virtual image of the fish has formed above where the fish actually was.
The rays of light from the fish that enter our eyes are bent when they leave the water. To our eyes, the rays seem
to be coming from another direction. Given that light can travel both ways along a light path, the fish will see spear
throwers stand taller above it than they in reality are.
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The rays from the fish bend when they enter the air. To the eye, the rays appear to come from a point closer to
the surface.
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The ray model not only gives us a way of describing our observations of the bending of light; it also helps us to
take measurements. The angle that a ray of light makes with the normal (either the angle of incidence or the
angle of refraction) can be measured and investigated.
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Snell’s law
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In 1621, the Dutch physicist Willebrand Snell investigated the refraction of light and found that the ratio of the
sines of the angles of incidence and angle of refraction was constant for all angles of incidence. The diagram
below shows how an incident ray is affected when it meets the boundary between air and water. The normal is
the line at right angles to the boundary, and all angles are measured from the normal. Some of the light from the
incident ray is reflected back into air. The rest is transmitted into the water. The following ratio is a constant for all
angles for light travelling from air to water:
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sin i
 constant
sin r
Chapter 22 How can human vision be enhanced?
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sin  i
is constant for all angles for light travelling from air to water.
sin  r
TABLE 22.1 Values for absolute refractive index
Value
1.0000
1.00028
1.33
1.49
1.46
1.52
1.65
1.63
2.42
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Material
Vacuum
Air at 20°C and normal atmospheric pressure
Water
Perspex
Quartz
Crown glass
Flint glass
Carbon disulfide
Diamond
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The ratio
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Snell repeated his experiments with different substances and found that the
ratio was still constant, but it had a different value for different substances. This
suggested that different substances bend light by different amounts.
(Remember that some light is always reflected.)
eLesson
Refraction of light and
Snell’s Law
The bending of light always involves light travelling from one substance to
another. It is not possible to find the effect of a particular substance on the
deflection of light without adopting one substance as a reference standard.
Once you have a standard, every substance can be compared with it. A natural
standard is a vacuum, the absence of any substance. The absolute refractive
Refraction of light and
Snell’s Law
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In fact, there is a different ratio for each pair of substances (for example air and
glass, or air and water). A different ratio is obtained for light travelling from air
into glass than for light travelling from air into water. The value of the ratio is
called the relative refractive index, because it depends on the properties of
two different substances.
Chapter 22 How can human vision be enhanced?
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Interactivity
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© John Wiley & Sons Australia, Ltd
index of a vacuum is given the value of 1. From this, the absolute refractive index of all other substances can be
determined. Some examples are given in table 22.1. (The word ‘absolute’ is commonly omitted, and the term
‘refractive index’ usually refers to the absolute refractive index.)
The refractive index is given the symbol n because it is a pure number without any units. This enables a more
useful restatement of Snell’s Law:
nair sin air  nwater sin  water
More generally this would be expressed as follows:
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n1 sin 1  n2 sin  2
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A graphical depiction of Snell’s Law for any two substances. Note that the light ray has no arrow, because the
relationship is true for the ray travelling in either direction.
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As with all formulas, it is important to enter the data carefully into Snell’s Law. The refractive index inserted for n1
must be the refractive index of the medium in which the light makes an angle of θ1 with the normal. Similarly, the
refractive index inserted for n2 must be the refractive index of the medium in which the light makes an angle of θ2
with the normal.
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SAMPLE PROBLEM 22.1
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Solution:
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A ray of light strikes a glass block of refractive index 1.45 at an angle of incidence of 30°. What is the angle of
refraction?
nair  1.0; air  30 ; nglass  1.45;  glass  ?
1.0  sin 30  1.45  sin  glass
sin  glass 
sin 30
1.45
(divide both side by 1.45,the refractive index of glass)
 0.3448
(calculate value of expression)
  glass  20.17
  glass  20
(substitute values into Snell’s Law)


(use inverse sine to find the angle whose sine is 0.3448)
(round off to two significant figures)
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
REVISION QUESTION 22.1
A ray of light enters a plastic block at an angle of incidence of 40°. The angle of refraction is 30°. What is
the refractive index of the plastic?
AS A MATTER OF FACT
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Light can be bent by a strong gravitational field, such as that near the Sun. The gravitational field can act like a
convex lens. Light from a distant star that is behind and blocked by the Sun bends around the Sun so that
astronomers on Earth see an image of the star to the side of the Sun.
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The speed of light in glass
speed of light in a vacuum
speed of light in water
SAMPLE PROBLEM 22.2
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where the speed of light in a vacuum = 3.0 × 108 ms–1.
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absolute refractive index of water 
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During the seventeenth century, one model of light proposed that light travelled faster in glass. Another model of
light proposed that light travelled slower in glass. Scientists at the time did not have the technology to measure
the speed of light through materials such as water or glass. It was only in the nineteenth century that AugustinJean Fresnel and Jean Bernard Léon Foucault were able to measure the speed of light in water as being less
than the speed in air. This helped to improve understanding of the nature of light. This gave the refractive index a
physical meaning:
EC
The refractive index of glass is 1.5. How fast does light travel in glass?
Solution:
3.0  108
(speed of light in glass)
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1.5 
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3.0  108
(rearrange formula to get the unknown by itself )
1.5
 2.0  108 m s-1 .
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 speed of light in glass 
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REVISION QUESTION 22.2
How fast does light travel in diamond?
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
Digital doc
Investigation 22.5:
Using apparent depth to
determine the refractive
index
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Determine refractive index
using apparent depth.
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PHYSICS IN FOCUS
Apparent depth
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As described earlier in this chapter, spear throwers need to aim below a fish if they are to have a chance of
spearing the fish. A similar phenomenon occurs when a spear thrower is directly above a fish. The fish appears to
be closer to the surface than it actually is. This observation is known as apparent depth. Swimming pools provide
another example of apparent depth: they look shallower than they actually are. The refraction of light combined
with our two-eyed vision makes the pool appear shallower.
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real depth
 refractive index
apparent depth
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The relationship is illustrated in the figure below and can be expressed as follows:
The phenomenon of apparent depth
Chapter 22 How can human vision be enhanced?
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Total internal reflection and critical angle
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Light can play some strange tricks. Many of these involve refraction away from the normal and the effect on light
of a large increase in the angle of incidence.
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There are no mirrors in a fish tank but strange reflections can be seen. It appears that light is being reflected off
the side of the fish tank and the water surface.
EC
It has already been mentioned that some light is reflected off a transparent surface, while the rest is transmitted
into the next medium. This applies whether the refracted ray is bent towards or away from the normal. However, a
special situation applies when the refracted ray is bent away from the normal.
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This is illustrated in the figure below. As the angle of incidence increases, the angle of refraction also increases.
Eventually the refracted ray becomes parallel to the surface and the angle of refraction reaches a maximum value
of 90° (see figure (b)). The corresponding angle of incidence is called the critical angle. If the angle of incidence
is increased beyond the critical angle, all the light is reflected back into the water, with the angles being the same.
This phenomenon is called total internal reflection (see figure (c)).
Three stages of refraction leading to total internal reflection
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The critical angle can be calculated using Snell’s Law (see the following sample problem).
SAMPLE PROBLEM 22.3
What is the critical angle for water given that the refractive index of water is 1.3?
Solution:
nair  1.0; air  90 ; nwater  1.3;  water  ?
  water
 water
(substitute data into Snell’s Law)
sin 90
1.3
 0.7692
 50.28

FS

(rearrange formula to get the unknown by itself )
(determine sine values and calculate expression)
(u se inverse sine to find angle)

 50 .
(round off to two significant figures)
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REVISION QUESTION 22.3
O
 sin  water
 1.3  sin  water
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1.0  sin 90
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A glass fibre has a refractive index of x and its cladding has a refractive index of y. What is the critical
angle in the fibre?
TE
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Total internal reflection is a relatively common atmospheric phenomenon (as in mirages) and it has
technological uses (for example, in optical fibres).
Cameras
EC
Pinhole cameras
R
The earliest cameras did not have lenses, just a pinhole for light to pass through onto a screen. Pinhole cameras
help us to understand how modern cameras work, and this knowledge also applies to the human eye.
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A pinhole camera is essentially a box (possibly an entire room) with a small hole made in one side for light to
enter. The light passing through the hole shines on a screen on the other side of the box. Photographic film can
be placed on the screen to preserve the images formed.
Chapter 22 How can human vision be enhanced?
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The diagram above shows a pinhole camera forming an image of a person. Rays from the top of the person shine
in all directions. Because the pinhole is so small, very few rays pass through, but those that do make a small spot
of light on the bottom of the screen. The rays from the feet of the person that make it through the pinhole shine on
the top of the screen. You can draw rays from every other part of the object through the pinhole to the screen and
you will see that an inverted image is formed on the screen. It is a real image because light rays form it, rather
than it just being an illusion. The image is there even if we are not looking at it.
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The size of this image depends on the distance of the pinhole from the object: the closer the object, the larger the
image. The size of the object does not change; the size of the image depends on the distance to the object. It also
depends on the size of the box: the longer the distance from the pinhole to the screen, the larger the image. This
ability to form a clear image of objects at various distances from the camera is called depth of field. The depth of
field is essentially infinite for a pinhole camera; however, in reality none of the images are particularly sharp.
Pinhole cameras are a great way for safely viewing the Sun, particularly during an eclipse, as the event can be
viewed on the screen using only the small amount of light that has passed through the pinhole being spread out to
form an image of low intensity. Before viewing the Sun, you must be very careful to check that your method is
safe. It is very easy to permanently damage your eyes by observing the Sun.
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Stand with your back to the Sun and look through the view hole. Once you have lined up the pinhole with the Sun,
you will be able to see an image of the Sun reflected from the paper screen at the back of the box. Using
shadows of the box can help you line it up. NEVER turn to line it up by sighting directly.
EC
TE
D
Pinhole cameras have played a very important role in the history of the understanding of light, with Aristotle,
Leonardo da Vinci and Johannes Kepler all using them to further their understanding of light and optics. The
earliest cameras were pinhole cameras. Sometimes an early camera could be a room called a camera obscura,
with the image formed on a table. The image could then be recorded by drawing on paper placed on the table.
Only in relatively recent times (since 1850) has a sensitive material been placed on the screen to preserve the
image, such as emulsions, film, photographic paper or the image sensors found in digital cameras (charge
coupled devices).
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One of the features of a pinhole camera is that the images formed have fuzzy edges; the images are never in
sharp focus. This is because the hole allows rays to enter from a small range of angles. Instead of a point on the
object forming a point of light on the image, it forms a small disk. All of these small disks form the image. Making
the hole larger has the advantage of forming a brighter image because more light is allowed through, but the
image is more blurred. A smaller hole allows less light in, forming a clearer but duller image. If the hole is too
small, another effect called diffraction distorts the image.
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Pinhole cameras have been very useful for exploring the behaviour of light, but they have serious limitations. In
particular, the images formed are never in sharp focus and the images are very dim compared with the object.
Also, the image gets dimmer towards the edges.
Adding a lens
To overcome these limitations another component needs to be added to the camera. This is a lens. A lens makes
use of the refractive properties that we learned about on page 000. What we need a lens to do is to take all of the
rays that are coming from one point on the object and direct them to one point on the image. This will produce a
sharp image. If we can do that using a larger opening (aperture), then we will also have more light to make a
brighter image.
To begin to understand a lens, we can start with a rectangular block of glass as in Figure 1a below. Parallel rays
from the left pass through the lens unaffected if they are normal to the lens (red lines). Parallel rays that are not
normal to the lens are slightly displaced due to refraction when passing through the lens, but emerge parallel.
This is essentially what happens with light passing through a pane of glass in a window. This would not help the
Chapter 22 How can human vision be enhanced?
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function of our camera apart from keeping dust and rain out. In fact, the glass would absorb a little of the light
entering the camera.
PA
Figure 1a
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If we grind the lens down so that it is now shaped like Figure 1b, refraction converges the three rays in each case.
This works for these three rays from the two angles, but if we grind the lens so that it is a continuous curve in the
arc of a circle (or better, a parabola), we find that the convergence occurs for all sets of parallel rays that hit the
lens, as shown in Figure 1c.
Figure 1b
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Figure 1c
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Now that we have some idea about how a lens works for parallel rays, we need to think of how that might be
useful in a camera. If the object is distant from the camera, the light that enters the lens diverging from one point
on the object will be nearly parallel. As an example, light from an object 5 m from the camera enters a lens with a
radius of 1 cm. The angle of the light passing through the edge of the lens only differs from a line parallel with light
through the centre of the lens by 0.1 degrees. A pinhole camera with a pinhole of radius 1 cm and depth of 25 cm
would produce a disk of light of radius 1.05 cm on the screen for every point of light on the object. This would be
very blurred, which highlights why it needs to be a pinhole camera. Placing a lens at the large pinhole that
focuses that light onto a point on the screen enables the clear image to be produced.
Figure 2
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© John Wiley & Sons Australia, Ltd
Simple cameras, like many small ‘point and click’ cameras and those in mobile phones, use a very small aperture
so that they do not need to change focus for each photo taken. They have a large depth of field but do not
function well in low-light environments or when the objects are moving quickly. More sophisticated cameras have
lenses that can move to focus on near and far objects. This means that the aperture can be larger while still
producing a focused image. A large aperture means more light is allowed into the camera, making it possible to
take good photos in lower light levels, or to reduce exposure times so that clear images can be taken of moving
objects.
We will now look at lenses more generally before exploring how we can apply them to different situations.
Forming images with lenses
FS
The refraction of light at a boundary between two transparent media can be put to use if the boundaries are
curved. There are two possibilities for curved boundaries — curving inwards or curving outwards. A convex lens
has its faces curving outwards. A lens that curves inwards is a concave lens.
Digital doc
Investigation 22.6:
The convex lens as a
magnifying glass
Use a convex lens as a
magnifying glass.
doc-0000
Weblink
Convex lens
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The simple ray tracings in the figures below illustrate what each lens does to the light rays. As rays enter the
glass, they are bent towards the normal. When they reach the air on the other side of the lens, they are bent away
from the normal. In the case of the convex lens, the emerging rays converge (come together) at a point called the
focus (F). For the concave lens, the rays diverge (move apart) so that they appear to come from a point, also
called the focus, on the other side of the lens. For these reasons, convex lenses are sometimes called
converging lenses, and concave lenses can be called diverging lenses.
Chapter 22 How can human vision be enhanced?
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Refraction of rays through (a) a convex and (b) a concave lens
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In fact, the focus is more than just a point. It is a plane — a focal plane through the focus point.
Rays converge at a point on the focal plane, which passes through the focus point (F).
In the figure above, for example, parallel light rays from a distant object coming in at an angle to the lens are still
brought to a focus, not at the same focus as for light coming in directly, but elsewhere in the focal plane. The
distance from the lens to the focal point is called the focal length. The value of the focal length is positive for
converging lenses and negative for diverging lenses.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
Convex lenses — locating images using ray tracing
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FS
The features of a convex lens are illustrated in the figure below. The convex lens has two symmetrical curved
surfaces, which means that it has two focus points.
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The convex lens has two focal points.
Digital doc
Investigation 22.7:
Describing images
produced by a convex
lens
Use the ray tracing method
to describe the images
formed by a convex lens.
doc-0000
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The ray model can now be used to locate an image (see the figure below).
The location of the image is determined according to the point where the three rays cross. All the rays that pass
through the lens pass through the image.
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© John Wiley & Sons Australia, Ltd
The ray diagram in the figure above demonstrates the following:
•
All three rays converge on the same point after passing through the lens. This is
where the image of the head of the object is located. Note that the image could
have been located with any two of the rays, but the other can be used to confirm
the location of the image.
Model of a convex lens
doc-0056
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The features of the image can now be described — its location, size, orientation
and nature. In the example in the diagram, we have an image on the opposite
side of the lens to the object, and the image is enlarged, inverted and real.
eModelling
FS
•
Ray 1 leaves the head of the object parallel to the principal axis, is refracted by the lens, and passes through
the focus on the other side of the lens. (Note: It does not matter that this ray does not pass through the lens in
the diagram. If it did, this is the path it would take.)
Ray 2 passes through the focus on the same side as the object, is refracted by the lens, and emerges
travelling parallel to the principal axis.
Ray 3 travels towards the centre of the lens. If the angle of the incoming ray is small and the lens is
considered thin, then the ray would appear to continue on in the same direction.
O
•
Convex lenses are used in a variety of applications. The image obtained depends on the placement of the object
in relation to the focus. A range of these applications is given in table 22.2 below.
TABLE 22.2 Simple applications of convex lenses
Uses
Objective lens of refracting
telescope
Human eye; camera
At twice the focal length from
lens
Between twice the focal length
from lens and the focus
Correction lens for terrestrial
telescope
Slide projector; objective lens of
microscope
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At the focus
Searchlight; eyepiece of refracting
telescope
Magnifying glass; eyepiece lens
of microscope; spectacles for
long-sightedness
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Between focus and lens
Description of image
Real, inverted, diminished and located
near the opposite focus
Real, inverted, diminished and located on
other side between one and two focal
lengths from lens
Real, inverted, same size and located
two focal lengths from lens
Real, inverted, magnified and located on
other side of lens beyond two focal
lengths|
No image. The emerging parallel rays do
not meet.
Virtual, upright, magnified and located on
same side of the lens and further away
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Location of object
Very large distance away from
lens
Beyond twice the focal length
from lens
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© John Wiley & Sons Australia, Ltd
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The object is inside the focus. This makes the rays diverge after passing through the lens. ‘Backtracking’ these
rays reveals that they appear to be coming from a point behind the object. The image is located at this point.
PHYSICS IN FOCUS
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Flat lenses?
EC
A lens works by changing the direction of the light ray at the front surface and then again at the back surface. The
glass in the middle is there to keep the two surfaces apart. Augustin-Jean Fresnel devised a way of making a lens
without the need for all the glass in the middle.
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The glass surface of the lens is a series of concentric rings. Each ring has the slope of the corresponding section
of the full lens, but its base is flat. The slopes of the rings get flatter towards the centre.
A side view of a convex Fresnel lens showing how it is constructed
This design substantially reduces the weight of the lens, so lenses of this type are used in lighthouses. Their
relative thinness means they are also used where space is at a premium, such as in overhead projectors, and as
a lens to be used with the ground-glass screens in camera viewfinders.
Flat lenses, or Fresnel lenses as they are called, are now attached to the rear windows of vans and station
wagons to assist the driver when reversing or parking.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
Digital doc
Investigation 22.8:
Flat lens profile
Use a magnifying glass to
examine a flat lens and draw
its profile.
FS
doc-0000
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SAMPLE PROBLEM 22.3
A convex lens has a focal length of 10 cm. A candle 10 cm tall is located 16 cm in front of the lens. Use ray
tracing to determine the location, size, orientation and type of image formed.
Solution:
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Draw the principal axis, the focal points, the object and three rays, one passing through the centre of the lens
without deviation, one parallel to the principal axis and one passing through the focus.
The image of the candle is 27 cm on the opposite side of the lens, 15 cm tall, inverted and real.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
SAMPLE PROBLEM 22.4
The candle is moved so that it is now 5 cm in front of the same lens. Use ray tracing to determine the location,
size, orientation and type of image formed.
Solution:
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Draw the principal axis, the focal points, the object and the three rays.
R
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The image of the candle is 10 cm on the same side of the lens, 20 cm tall, upright and virtual.
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SAMPLE PROBLEM 22.5
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The lens is switched with a diverging lens with a focal length of –10 cm. What image of the candle is formed when
it is placed 15 cm from the lens?
U
Solution:
Draw the principal axis, focal points, object and the three rays.
Chapter 22 How can human vision be enhanced?
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The image of the candle is 6 cm on the same side of the lens, 4 cm tall, upright and virtual.
EC
These diagrams are excellent for understanding what is happening with the light when using lenses. We have
drawn three rays each time because we can predict where those will go, but once you know the position of the
image you can draw in any ray you like. Simply draw the ray from the object to the lens, then draw where the ray
would go passing through the lens so that it arrived at the correct point on a real image or appeared to come from
the correct point on a virtual image.
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The thin lens formula
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Ho u  f

Hi
f
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Can we determine where the image is without drawing the ray diagram? Look at Figure 3. The two triangles
shaded in green are similar triangles as all of their angles are the same size. This would be true wherever the
image is located. This means that the ratios of equivalent sides are equal, for example:
U
Also, the triangles shaded in blue are similar:
Ho u

Hi v
The left-hand sides of these equations are equal, so we can say:
u u f

v
f
Which is the same as:
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
u u
 1
v f
1 1 1
 
v f u
1 1 1
 
f u v
This formula is known as the thin lens formula. It gives a good approximation for thin lenses. When using it, you
need to be careful with signs:
FS
f is positive for converging lenses and negative for diverging lenses
u is positive
v is positive when the image is on the opposite side of the lens to the object and negative when on the same
side
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•
•
•
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We can compare the results of this formula with what we have determined by ray tracing in Sample problem 22.3.
SAMPLE PROBLEM 22.6
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Use the thin lens formula to find the position of the image when f = 10 cm and u = 16 cm.
Solution:
R
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1 3

v 80
80
v
 27cm behind the lens.
3
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1 1 1
 
f u v
1 1 1
 
v f u
1 1 1


v 10 16
1 8
5


v 80 80
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SAMPLE PROBLEM 22.7
Use the thin lens formula to find the position of the image when f = 10 cm and u = 5 cm.
Human and animal vision
Now that we understand refraction and lenses, we can investigate the optics of the human eye. The human eye is
an extraordinary device. It is able to respond to an enormous range of light brightness. The strongest light that the
eye can safely detect is 10 000 million times as bright as the weakest light it can detect. It is able to focus on
objects from many billions of kilometres away to objects a few centimetres away. It can also detect colour.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
The parts of the human eye are shown in the figure below. The purpose of the eyeball is to produce a sharp, real
image on a screen. The retina is this screen. Light passes through many refracting elements in the human eye on
its way to the retina (see table 22.3).
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The eye achieves a focus in two stages. The curved cornea at the front of the eye does two-thirds of the focusing
due to the large difference in refractive index between the cornea and the air. The lens does the fine focusing as
there is little difference in the refractive index of the lens and that of the liquid on either side of it. In the rest of the
eye, the differences in refractive index are marginal, but they are crucial when the eye wishes to produce clear
images of far and near objects.
Cross-section of a human eye
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Refractive index
1.33
1.37
1.33
1.38
1.41
1.33
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Part of the eye
Tears
Cornea
Aqueous humour
Lens cover
Lens centre
Vitreous humour
EC
TABLE 22.3 Refractive index of the parts of the eye
AS A MATTER OF FACT
The eye is an amazing instrument. It has an automatic aperture adjustment called the iris. The act of blinking
operates the cornea’s built-in scratch remover, lens cleaner and lubricator. In dim light, the eye operates as a
supersensitive, black and white television camera. It allows us to see objects with less than 0.1 per cent, or onethousandth, of the light we need for colour vision.
The optic nerve packages the visual information from the retina so that the brain receives about 30 discrete
‘frames’ per second in a similar way to television and cinema.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
The pinhole camera helps us to understand how the eye works. The pinhole is the pupil and the screen is the
retina. As with a pinhole camera, the real image that forms on the retina is inverted and diminished. Two key
differences between the capabilities of a pinhole camera and the eye are that the eye can produce sharper
images and is able to function effectively over a greater range of brightness levels.
A pinhole camera relies on an opening (the pinhole) to allow the light in. If the pinhole is large enough to produce
a reasonable image, the image will be fuzzy. The eye has an opening (the pupil) that is larger than would provide
a reasonable image in a pinhole camera, but it also provides a more focused image than a pinhole camera. This
clear image is possible because of the refractive surfaces of the eye, in particular the cornea and the lens. The
eye can also open even wider in low light levels by dilating the iris so that there is more light available to stimulate
the retina.
FS
Accommodation mechanisms
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Consider light from a light globe passing through a convex lens onto a screen to produce an image of the globe’s
filament. If the lens is moved to a new position, the screen needs to be moved to obtain a sharp image. The
human eye can produce a sharp image on its ‘screen’ (the retina) of objects at various distances. But the eye’s
screen stays put, so something else has to change to achieve a sharp image. The only thing that can change is
the focal length of the lens.
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Convex lenses form images of very distant objects at their focus. As objects get closer to the lens, the image is
formed behind the focus. For the human eye with its fixed ‘screen’, this means that the focal length must shorten
to keep a sharp image on the retina. This adjustment is called accommodation.
PA
How short can the focal length of the lens in an eye become? When you bring an object closer to your eye from
an arm’s length away, there is a point at which the object becomes fuzzy in appearance. This point is called your
near point. As you age, your near point becomes further away (see Table 22.4). That is why some older people
hold the newspaper further away to read it.
Near point (cm)
7
8.5
10
15
Age (years)
40
50
60
70
EC
Age (years)
10
15
20
30
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TABLE 22.4 Average near points by age
Near point (cm)
22
40
65
200
Weblink
Modelling the eye
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To enable the focal length of the eye to change, the lens has to change its
shape. To achieve a shorter focal length, the lens needs to become fatter. This
raises important questions. How does the lens change shape? What is the
natural rest position of the lens in the eye? Is the lens relaxed in the short focal
length position so that it needs to be ‘stretched’ to see distant objects? Or is it
relaxed in the long focal length position and has to be ‘squashed’ to see near
objects? Muscles can act only by contraction, so how are the muscles
arranged in the eye to squash the lens?
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In fact, the relaxed human eye has a long focal length located at the retina to
form images of very distant objects. Ligaments attached to the outside edge of
the lens are continually pulling outwards, but around the lens itself there is a
circular muscle. When this circular muscle contracts, it produces a smaller
circle, making a lens that is smaller in diameter but thicker.
Some animals have different mechanisms for accommodation in their eyes.
Most animals’ eyes, like human eyes, are relaxed in the long focal length
position. This is ideal if the animal is roused from sleep by the sound of a
distant predator, as the eye is ready to focus on it.
Digital doc
Investigation 22.9:
Measuring your near point
Measure your near point and
compare it with those of your
classmates.
doc-0000
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© John Wiley & Sons Australia, Ltd
Although many animals use an adjustable focal length lens like humans, some
use other strategies. One strategy is to move the lens backwards and forwards.
In most fishes and snakes, the lens moves within the eyeball in the same way
that a camera lens is moved to produce a sharp image on the digital image
sensor or film.
Weblink
Animal eyes
PHYSICS IN FOCUS
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The power of the lens
1
f
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Power 
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Optometrists and opticians describe the focusing ability of a lens in terms of its power. The power of a simple lens
is defined as:
The unit of the power of a lens is the dioptre (D). For example, a concave lens of a focal length of 25 cm has a
power given by:
1
1

 4.0 D
f
0.25
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Power 
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Note: The power of a lens that diverges light is negative, like its focal length.
EC
Correcting eye defects
TE
D
Fish require higher-power (thicker) lenses than land-based animals. This is because the difference between the
refractive index of water and the refractive index of the transparent materials of the eye is much smaller than that
between the refractive indexes of eye materials and air.
R
Sometimes our eyes do not work properly and corrective lenses need to be prescribed. Corrective lenses to
improve vision were first invented in Italy in the late 1200s, but until early in the twentieth century, they were
available only to the wealthy. The two main eye defects are hypermetropia and myopia.
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Myopia, or short-sightedness, means that the person’s vision of nearby objects is good but distant objects are
unclear. Parallel rays of light from distant objects are brought to a focus in front of rather than on the retina. The
eyeball is too large for the ‘relaxed focal length’ of the eye. This defect is not usually noticed until the eyeball
approaches its final size in adolescence. It can be overcome by placing a diverging lens in front of the eye to
spread the rays apart slightly before they enter the eye.
Chapter 22 How can human vision be enhanced?
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Myopic vision causes light rays to focus in front of the retina.
Corrective diverging lenses are used in spectacles and contact lenses.
Chapter 22 How can human vision be enhanced?
© John Wiley & Sons Australia, Ltd
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Contact lenses can be a solution to eye defects. They alter the curvature of the front of the eye.
EC
Sometimes myopia can be caused by excessive curvature of the cornea, the principal focusing agent in the eye.
Laser eye surgery uses low-temperature ultraviolet lasers to ‘shave off’ some tissue from the front of the cornea,
to flatten the curvature.
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Hypermetropia, or long-sightedness, is the reverse of myopia. The lens produces an image of near objects that
would appear behind instead of on the retina. Near objects are not clear, whereas distant objects are in focus.
The muscles around the lens cannot contract enough to shorten the focal length to bring the image onto the
retina. The eye needs help to achieve this, and an extra lens can help. Converging lenses are used in spectacles
and contact lenses to correct hypermetropia.
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As people age, the muscles around the lens slowly weaken, and the lens itself becomes thicker and less flexible.
The loss in flexibility means that the near point moves further away and a newspaper has to be held at arm’s
length to be read. The thickening of the lens, even when the muscles are relaxed, means that distant objects start
becoming fuzzy. This means that the eye is showing signs of myopia for distant objects and hypermetropia for
near objects, which require different corrective solutions. Hence the need for bifocal lenses, which have a convex
surface at the bottom to look down to read the newspaper and a concave surface at the top to look up to drive the
car.
An associated feature that often comes with aging is a reduced ability to read at low light levels. This is the result
of pupils dilating to make the most of the available light. As the light is entering the eye from a greater range of
angles, the eye has to do more work to focus the incoming light onto the retina. A reason that hypermetropia
becomes more common in older age groups is that the lens in the eye becomes less flexible. This more rigid lens
is then less able to perform the additional focusing required at low light levels.
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Hypermetropia causes light rays to focus behind the retina. This produces a ‘fuzzy’ image.
Converging lenses are used in spectacles and contact lenses to correct hypermetropia.
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Prescriptions from the optometrist
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Most of us at some time in our lives need to start regular visits to the optometrist to check for common eye
conditions and to get prescriptions for any corrective technology that we might need, particularly glasses.
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There are a number of eye problems that glasses can correct for, but here we will focus on myopia and
hypermetropia.
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Prescriptions for these conditions will include the power of the lens required to correct the vision. In the case of
myopia, the optics within the eye are causing the light to form an image of distant objects in front of the retina. A
diverging lens is required to correct this. The prescription for myopia is a negative number, as the power of the
lens is negative for a diverging lens. A prescription for myopia might look like:
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P  2.50 D
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This means that the power of the lens is –2.50 diopters.
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This is a prescription for someone who requires more correction than a person whose prescription is –2.00 D and
less than someone whose prescription is –3.00 D.
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The focal length of the lens is given by:
1
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
 0.40 m
P 2.50
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F ocal length 
Glasses to correct myopia are thicker on the edges than in the centre. Like the lens in the diagram below, lenses
in glasses are concave on one side and convex on the other. Glasses to correct myopia have a greater curvature
on the concave side (the side facing the eye) than the convex side.
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A prescription for hypermetropia will be positive, for example 1.50 D. This indicates a converging lens of:
1
1

 0.667 m
P 1.50
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F ocal length 
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These lenses will be a little thicker in the centre than on the edge. The convex side of the lens is more curved
than the concave side.
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Restoring sight
One of the great challenges of medical science is to provide sight to the blind. Sight is a tremendously important
sense, but people can lose it for a number of reasons. These include damage to the eyeball due to injury or birth
defects, cataracts, deterioration of the retina, damage to the optic nerve (glaucoma), and brain damage. As a
result, efforts to prevent blindness and restore sight to the blind require a range of approaches.
The bionic eye
FS
Currently in Australia there is significant research into developing prosthetic vision devices or ‘bionic eyes’. These
devices are intended to help people with blindness resulting from conditions that damage the retina, such as agerelated macular degeneration and retinitis pigmentosa. In these situations, photoreceptor cells in the retina have
died. These cells are responsible for converting the light that strikes them into electrical impulses that carry the
information via the optic nerve to the brain.
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Bionic eyes rely on the optic nerve and the visual cortex of the brain to still be functioning. Some retinal cells must
also be working. This system relies on a recipient who has had sight for a significant time so that the brain has
been able to develop its visual capacity. What the bionic eye replaces is the retinal cells that no longer transmit
the images to the optic nerve.
An array of electrodes is implanted into the eye.
One system under development involves a small camera mounted on a pair of glasses that are worn by the
recipient. This camera converts the light it receives into electrical signals. These signals are converted to radio
waves, which are detected by an array of stimulating electrodes implanted on the retina of the eye. The array
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stimulates nerve cells that would normally receive stimulation from the photoreceptor cells in the retina. These
cells transmit the signals to the optic nerve. The brain detects these signals as variations in light.
Other research teams are looking at implants to directly stimulate the brain. These versions of the bionic eye will
be aimed at helping those who have damage to the optic nerve as well as the eyes.
A man who lost his eye in a shooting accident has had his eye replaced with a camera. In the future this could
potentially send information to an implant that directly stimulates the brain.
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These technologies may be successful at restoring some sight to people, but it will not be the same as that of a
fully sighted individual. In 2014, three people began a trial by being the first people in the world to have the retinal
implant inserted in their eyes. They report being able to make out outlines of people and objects that they are
looking at. The technology is still in an early stage, but it offers hope in the future for many people suffering from
blindness.
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Cataracts
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exposure to ultraviolet light from the Sun
obesity
diabetes
smoking
prolonged use of some medications
significant alcohol consumption
family history
previous eye problems.
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Cataracts are another cause of blindness. A cataract occurs when the lens within the eye turns cloudy, losing its
transparency. This opaque lens prevents light from reaching the retina. Cataracts are the leading cause of
blindness in the world, particularly affecting people over the age of 40. Risk factors identified for cataracts include:
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Cataract blindness can be treated by surgically removing the lens and replacing it with a clear plastic lens. These
artificial lenses are called intraocular lenses and can help restore sight in cataract sufferers. Most patients who
undergo surgery to remove cataracts regain good vision.
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This man has a cataract in his right eye.
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Extending vision
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In a fully functioning human eye, the lens can change its focal length to adjust to seeing at different distances.
Most intraocular lenses, however, are set to focus for distance vision, so the patient has to wear glasses for
reading. More sophisticated lenses are being used that are bifocal or multifocal to enable the patient to focus on
near objects as well.
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Telescopes
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An optical telescope is a device that improves our ability to see over long distances. Telescopes originally only
allowed direct viewing with the eye in the visible wavelengths of light. Later, the inventions of photography and
then of electronic sensors meant that images could be recorded on film and electronically.
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Telescopes have enabled astronomers to greatly improve their understanding of the objects in the sky. For
example, it is only because of telescopes that we have been able to develop a detailed understanding of the
universe. Before Galileo began his work with telescopes in 1609, the world that we knew was essentially made up
of the Earth and some poorly understood lights in the sky. Telescopes have also been put to powerful use on
Earth to assist in navigation, surveying and photography.
Telescopes improve the image formed by the eye by:
•
•
•
magnifying the image
collecting more light than the eye
providing better resolution of the image so that more detail can be seen in an object than with the unaided eye.
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The most important role of the telescope is to collect light. This is done by a large lens in a refracting telescope,
such as those developed by Galileo (the Galilean telescopes) and Kepler in the early 1600s, or a concave mirror
in the case of the reflecting telescopes developed by Isaac Newton and others
since the mid 1600s. The larger the lens or mirror, the more light the telescope is
able to collect.
Light collection
Weblink
Optical telescopes collect more light than the eye, enabling dimmer objects to be
seen. The ability of a telescope to collect light is determined by the area of its
objective lens or primary mirror. As area depends on the square of the radius,
doubling the radius of the objective lens means its area is four times greater, and
the telescope can collect four times as much light. The square of the radius is a
useful way to compare the ability of telescopes to detect faint stars.
Modelling telescopes
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Investigation 22.10:
The Galilean telescope
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Model a simple Galilean
telescope.
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The ability of telescopes to collect light has led to the discovery of many new
objects. Asteroids were unknown before large telescopes became available, as
were Neptune, Uranus, Pluto and all of the other smaller bodies of the solar
system. These objects simply do not reflect enough light for the human eye to
detect from the Earth without the aid of a telescope.
Digital doc
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SAMPLE PROBLEM 22.8
doc-0000
Compare the light-collecting power of a 150 mm diameter objective lens to that of a 200 mm objective lens.
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Solution:
For the 150 mm lens, r2 = 5625 mm2.
For the 200 mm lens, r2 = 10 000 mm2.
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The light-collecting power is proportional to the radius squared.
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The 200 mm diameter lens has nearly double the light-collecting power of the 150 mm lens.
The objective lens or primary mirror focuses all of the light it has collected to a point at the focus.
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Magnification
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Magnification is a ratio that describes how many times larger an object appears when viewed through a
telescope. The Moon will appear to have twice the diameter if viewed through a telescope that has a
magnification of 2. Magnification results from a telescope’s ability to bend light rays. How large something
appears to us depends on the angle between a line from the top of the object and our eye and a line from the
bottom of the object and our eye.
This diagram shows the same object at two different positions. At position 2 it appears smaller than at position 1
because the angle that light from the top and bottom of the object makes a smaller angle at position 2 than
position 1.
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Images formed in telescopes are generally much smaller than the size of the object, yet we generally think of
telescopes as magnifying the image. This is because the object looks bigger with the telescope than without the
telescope.
An eyepiece or ocular lens is used to achieve this magnification. Ocular lenses with shorter focal lengths (higher
power) achieve greater magnification for a given telescope.
The magnification of a telescope is determined by the focal lengths of the lenses or mirrors used in the telescope
according to the relationship
M 
fo
fe
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where
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fo is the focal length of the objective lens or primary mirror
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fe is the focal length of the eyepiece.
Refracting telescopes
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The most common design of refracting telescope used today is based on a telescope invented by Johannes
Kepler in 1611. It features two converging lenses arranged so that the focus from each lens is located at the same
point. The large lens at the front of the telescope is called the objective lens (it is at the same end as the object).
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(a) The Keplerian telescope (b) Image formation in a Keplerian telescope
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From this ray diagram we can see how widely spread rays from the object are converged by the telescope so that
more intense light will enter the eye. We can also see that the angle at which the rays enter the telescope is
smaller than the angle at which the rays enter the eye. When we view an extended object, we will see the object
as being larger than without the telescope.
PA
Notice also that the eye is looking down to see an object that is above the principal axis. This means the image
will be inverted. When Keplerian telescopes are used to view objects on Earth, an additional lens is put in front
of the eyepiece so that the image is upright.
Reflecting telescopes
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Isaac Newton built the first reflecting telescope in 1668, although others had proposed different designs earlier.
Newton ground his own mirrors to the shape required. This first Newtonian telescope had a concave objective
mirror but used a secondary plane mirror to divert the light out of the side of the telescope.
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Newtonian telescopes are popular with amateur astronomers. Newtonian telescopes can also use a right-angled
prism instead of a plane mirror; the light passes into the prism but undergoes total internal reflection on the back
face.
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(a) The Newtonian telescope (b) The path of light through a Newtonian telescope
The Newtonian design loses a small proportion of the light because the secondary mirror gets in the way.
However, a complete image is still formed because light from all parts of the object reaches the primary mirror.
The capacity of the telescope to collect much more light than the unaided eye is apparent, and mirrors of greater
than 10 metres diameter have been constructed to achieve enormous light-gathering power. These mirrors are
made of several sections to reduce the cost and difficulty of producing such a large mirror. Large telescopes tend
to be reflecting telescopes because the mirror can be supported from behind, whereas a large lens would tend to
change shape under its own weight.
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Microscopes
To magnify very small things using an optical microscope, a similar process is used to the refracting telescope. A
convex lens can be used as a simple magnifying glass, but to obtain greater magnification another lens is
needed.
Compound microscope
FS
In its simplest form, a compound microscope has two convex lenses, one fatter and with a shorter focal length
than the other. The fatter one is located near the object to be magnified and is called the objective lens. The other
lens is close to the eye and is called the eyepiece. This is the opposite of a telescope, where the higher-powered
lens is in the eyepiece.
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An object placed just outside the focus of the objective lens produces a real, inverted, magnified image. The
eyepiece lens is adjusted so that this image is formed inside the focus of the eyepiece lens. The real, inverted
image now becomes the object for the eyepiece lens. Because it is inside the focus of the eyepiece, it produces a
final magnified image, which is virtual and inverted compared with the original object.
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Ray diagram for a compound microscope
Unlike a telescope, the key to a microscope is magnification rather than light collection. Optical microscopes
require the object to be well lit in order to form a bright image.
Chapter review
Summary
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The ray model depicts light as straight lines in a uniform medium.
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Rays of light reflect from a plane surface so that the angle of incidence equals the angle of reflection.
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The incident ray, reflected ray and the normal to the surface all lie in the same plane.
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When passing from one medium to another, light refracts in accordance with Snell’s Law, n1 sin 1  n2 sin  2 .
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Pinhole cameras are powerful tools for understanding the behaviour of light and image formation.
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Convex lenses cause parallel rays of light to diverge. Concave lenses cause parallel rays to converge.
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The operation of the eye can be explained with an understanding of refraction and lenses.
Two of the major conditions that are corrected using glasses and contact lenses are short-sightedness
(myopia) and long-sightedness (hypermetropia).
The power of a lens is calculated using P 
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Small objects can be enlarged by using a compound microscope with the object placed inside the focal length
of the objective lens.
1
.
focal length
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Light from distant objects can be gathered by telescopes to form clearer and larger images. Telescopes use
either concave mirrors or convex lenses to collect light.
The lens of the human eye can focus on near and distant objects by changing the curvature of its lens. This
ability tends to decrease with age, causing hypermetropia.
The lens in the eye can go cloudy (cataracts), causing blindness. This can be treated by removing the lens
and replacing it with an plastic lens.
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Using technology to replace damaged retinas and optic nerves with a ‘bionic eye’ is an area of intensive
research and development.
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the position of image formed by thin lenses can be determined by accurate ray tracing and by using the thin
1 1 1
lens equation,   .
u v f
v
For pinhole cameras and simple cameras, the magnification is given by M  .
u
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Reflection
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Questions
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Convex lenses result in image formation that depends on where the object is placed. Concave lenses
produce upright, virtual, diminished images.
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1. Describe the light path from a light source to your eye in seeing an object.
2. Use the ray model and the sources of light to rephrase the statements (a) ‘I looked at a flower through the
window’ and (b) ‘I watched the TV’.
3. Explain how early astronomers knew the Moon must have a rough surface.
4. Copy the following figure and draw the incident and reflected rays from the two ends of the object to the eye.
Locate the image.
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5. Calculate the angles, a, b and c in the following figure.
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6. The two arrowed lines in the figures below represent reflected rays. The line AB represents the plane mirror.
Locate the image and the light source in each of the two figures.
Chapter 22 How can human vision be enhanced?
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7. A student argues that you cannot photograph a virtual image because light rays do not pass through the
space where the image is formed. How would you argue against this statement?
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8. Sketch the path of each of the rays entering each of the pair of joined mirrors in the following figure.
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9. You are walking towards a plane mirror at a speed of 1.0 m s–1. How fast is your image walking? How quickly
are you and your image approaching each other?
10. a. You are standing 2.0 m in front of a plane mirror and you wish to take a sharp photograph of yourself in
the mirror. At what distance do you set the camera lens?
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b. Your friend is standing beside you, 1.0 m away. At what distance do you set the camera lens for a sharp
photograph of your friend?
11. How can you see raindrops if water is transparent?
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Refraction
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12. What is the angle of refraction in water (n = 1.33) for an angle of incidence of 40°? If the angle of incidence is
increased by 10°, by how much does the angle of refraction increase?
13. A ray of light enters a plastic block at an angle of incidence of 55° with an angle of refraction of 33°. What is
the refractive index of the plastic?
EC
14. A ray of light passes through a rectangular glass block with a refractive index of 1.55. The angle of incidence
as the ray enters the block is 65°. Calculate the angle of refraction at the first face of the block, then calculate
the angle of refraction as the ray emerges on the other side of the block. Comment on your answers.
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15. Immiscible liquids are liquids that do not mix. Immiscible liquids will settle on top of each other, in the order of
their density, with the densest liquid at the bottom. Some immiscible liquids are also transparent.
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a. Calculate the angles of refraction as a ray passes down through immiscible layers as shown in the figure
below.
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b. If a plane mirror was placed at the bottom of the beaker, calculate the angles of refraction as the ray
reflects back to the surface. Comment on your answers.
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16. Light rays are shown passing through boxes in the figure at the base of the page. Identify the contents of
each box from the options (a)–(g) given below. Option (b) is a mirror. All others are solid glass. Note: There
are more options than boxes.
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17. a. To appear invisible you need to become transparent. What must your refractive index be if your movement
is not to be detected?
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b. The retina of your eye is a light-absorbing screen. What does that imply about your own vision if you are to
remain invisible? (Hint: If you are invisible all light passes through you.)
18. Calculate the angle of deviation at a glass–air interface for an angle of incidence of 65° and refractive index of
glass of 1.55.
19. Calculate the sideways deflection as a ray of light goes through a parallel-sided plastic block (n = 1.4) with
sides 5.0 cm apart, as in the figure below.
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20. Calculate the angle of deviation as the light ray goes through the triangular prism shown in the figure below.
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Convex lenses
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21. Use ray tracing to determine the full description of the following objects:
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a. a 4.0 cm high object, 20 cm in front of a convex lens with a focal length of 15 cm
b. a 3.0 mm high object, 10 cm in front of a convex lens with a focal length of 12 cm
c. a 5.0 cm high object, 200 cm in front of a convex lens with a focal length of 10 cm.
22. What does ‘accommodation mechanism’ mean? Give an example.
23. a. You are carrying out a convex lens investigation at a bench near the classroom window and you obtain a
sharp image of the window on your screen. A teacher walks past outside the window. What do you see on
the screen?
b. The trees outside the classroom are unclear on the screen. What can you do to bring the trees into focus?
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24. Use ray tracing to determine the magnification of an object placed under the following two-lens microscope.
The object is placed 5.2 mm from an objective lens of focal length 5.0 mm. The eyepiece lens has a focal
length of 40 mm. The poles of the lenses are 150 mm apart.
25. A convex lens with a focal length of 5.0 cm is used as a magnifying glass. Determine the size and location of
the image of text on this page if the centre of the lens was placed:
a. 4.0 cm above the page
b. 3.0 cm above the page.
26. A 35 mm slide is placed in a slide projector. A sharp image is produced on a screen 4.0 m away. The focal
length of the lens system is 5.0 cm.
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a. How far is the slide from the centre of the lens?
b. What is the size of the image?
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c. Looking from the back of the slide projector, the slide contains a letter ‘L’. What shape will appear on the
screen?
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d. The slide projector is moved closer to the screen. The image becomes unclear. Should the lens system be
moved closer to or further away from the slide?
27. A teacher is using a slide projector but the image on the screen is smaller than the screen. What needs to be
done to produce a clear image on the full screen?
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Correcting eye defects
28. A person suffers from myopia. Describe what this means to them.
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29. Sketch a diagram of a myopic eye, using rays to show what is happening to cause this problem.
31. Identify one cause of hypermetropia.
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30. Sketch the profile of a lens that might be used to correct myopia.
32. Sketch a profile of a hypermetropic eye, using rays to show what is happening to cause this problem.
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33. Cataracts are the leading cause of blindness. What treatment is required to restore the sight to those with
cataracts?
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34. Investigate three different research programs on bionic eyes. What is the difference between each of their
approaches, and what conditions do they aim to alleviate the symptoms of?
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