Course: Physics
The Telescope (Refraction and
Lenses)
Notes for Learners
Level: National 5
April 2013
This advice and guidance has been produced for teachers and other staff who
provide learning, teaching and support as learners work towards qualifications.
These materials have been designed to assist teachers and others with the
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promote development of the necessary knowledge, understanding and skills.
Staff are encouraged to draw on these materials, and existing materials, to
develop their own programmes of learning which are appropriate to the needs
of learners within their own context.
Staff should also refer to the course and unit specifications and support notes
which have been issued by the Scottish Qualifications Authority.
http://www.sqa.org.uk
Acknowledgements
© Crown copyright 2013. You may re-use this information (excluding logos) free of charge in
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Contents
Introduction
4
Refraction of light
5
Lenses
9
The magnifying glass
17
The refracting telescope
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INTRODUCTION
Introduction
Humankind has long been fascinated with space. The telescope is a key tool
used by astronomers for exploring space. It allows us to look at objects that
are many millions of miles away and therefore study the universe and learn
about its origins. By studying the development of solar systems, we have
learned how our own solar system developed.
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REFRACTION OF LIGHT
Refraction of light
Refraction is the physics that explain how glass lenses work and why
rainbows are produced when sunlight shines through raindrops. When light
travels from one medium to another, such as from air to glass, its direction
and speed change. This change of speed and direction as light moves from
one medium to another is referred to as refraction.
Refraction at an air–glass boundary
The principle of refraction can be shown by an experiment using a glass block
and a ray box, as shown below. The photograph shows how the angle of
incidence, i, and the angle of refraction, r, compare to each other.
normal
i
r
Image: Zátonyi Sándor/Wikimedia Commons:
http://en.wikipedia.org/wiki/File:F%C3%A9nyt%C3%B6r%C3%A9s.jpg
A line is drawn (dashed) at 90 to the surface that the light ray hits. This line is
called the normal. The angles of incidence and refraction are always
measured between the ray and the normal.
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REFRACTION OF LIGHT
Experiment: Refraction of light
This experiment will find the refractive
index of perspex by comparing the angle
of incidence to the angle of refraction.
By examining the relationship
between these angles, Snell’s law will be
derived.
You will need:




a ray box
a semicircular perspex block
a protractor
a ruler.
Image: Cristan/Wikimedia Commons:
http://en.wikipedia.org/wiki/File:Snells_law.
svg
Instructions
1. Place the semicircular block on a sheet of paper and draw round it.
2. Use a protractor to draw a normal line at 90° to the flat surface of the
semicircle.
3. Using a protractor, measure the angle of incidence (θ1) at 20° and draw
the incident ray with a pencil.
4. Using the ray box, shine a ray of monochromatic light along the incident
ray into the perspex block. Mark the position of the refracted ray.
5. Use a ruler to draw the refracted ray.
6. Use a protractor to measure the angle of refraction, θ2.
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REFRACTION OF LIGHT
Refraction in practice
We can see refraction in practice if we
put a pencil into a beaker of water. The
pencil will look like it is bent at the
surface of the water. The light rays
bend at the surface of the water by
refraction. Although the light rays are
coming from position X at the bottom of
the pencil, the eye thinks the light rays
are travelling from position Y. This is
because the eye always thinks that
light is travelling in straight lines, so
sees a virtual image of the pencil.
Theresa Knott/Wikimedia Commons:
http://en.wikipedia.org/wiki/File:Pencil_in_a_bowl
_of_water.svg
Applying refraction
Consider a fisherman on a river bank trying to spear a fish.
Observed
fish
Actual
fish
The eye can be tricked by refraction. Light rays from the actual fish bend at
the surface of the water due to the change in refractive index between water
and air. However, the eye thinks the light ray has travelled in a straight line
and therefore sees an image of the fish higher up.
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REFRACTION OF LIGHT
Consider the example of a treasure chest shown below.
Apparent depth
Actual depth
Image
Chest
Explain why the man in the boat thinks the treasure chest is at a shallower
depth than it actually is.
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LENSES
Lenses
One of the major applications of refraction in everyday life is in lenses, which
can be used in glasses to cure sight defects or in telescopes to see deep into
space. Lenses can have different sizes and shapes to do different jobs. They
work by refracting the light that passes through them either towards or away
from a focus point.
There are two main shapes of lenses: convex and concave.
Convex lenses are sometimes called converging lenses because they make
light rays converge on a focal point (they bend light rays in towards one
common point). The distance between the lens and the focal point is known as
the focal length of the lens.
Concave lenses (which 'cave in') are sometimes called diverging lenses
because they make light rays diverge away from each other.
Convex and concave lenses are illustrated in the diagram below.
Light rays
Concave lens
Convex lens
Focal point
Light rays
Focal length
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LENSES
Experiment: How lenses work
This experiment investigates how light bends through the process of refraction
when it travels through differently shaped blocks. The findings are then
applied to convex and concave lenses to explain how their shape affects light
rays that pass through them.
You will need:
 a ray box
 perspex shapes (prism and rectangle)
 a ruler.
Instructions
Using the perspex blocks, investigate how light travels through them when it is
incident on the blocks at different angles.
Position the perspex blocks such that they form the shape of a basic convex
or concave lens and shine three rays of light at them.
Use the results of the experiment to write a short report on how lenses work.
Image: Wikimedia Commons reproduced under GNU Free Documentation License and Creative Commons
Attribution-Sharealike 3.0 Licence: http://en.wikipedia.org/wiki/File:Refraction.jpg
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LENSES
Lens power
The size (thickness) of a lens affects the amount by which it changes the
direction of the light. A thick lens will change the direction of the light more
than a thinner lens. In the case of a convex lens, if the lens is thick then it will
have a short focal length. A thin lens will have a long focal length.
The amount of bending of light that is done by a lens depends on the power of
the lens. The more powerful the lens the greater the refraction of the light. In
the case of a convex lens, the greater the power the shorter the focal length,
as shown in the diagram below.
Light rays
Focal point
Focal length
Focal length
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LENSES
Ray diagrams
Ray diagrams can be used to find out where a lens will produce an image of
an object. An accurate ray diagram will be drawn with a ruler, and a ruler used
to accurately make the positions of the focal point and the object.
Drawing a ray diagram
Ray diagrams are best drawn using graph paper, but if none is available they
can still be drawn very accurately using a ruler to measure the distances (and,
of course, using a ruler to draw the straight lines!).
To draw a ray diagram:
1.
Draw a horizontal line in the middle of the
diagram (the principal axis). Choose an
appropriate scale for the ray diagram.
Here the scale is 1:10 (1 cm on the
diagram = 10 cm in real life).
The object will be drawn onto this line. The
focal length of the lens is marked on this
line.
2.
Draw the lens on the diagram. Usually the
lens is placed in the middle of the diagram.
A convex lens is represented by a doubleheaded arrow as shown.
Mark on the position of the focal point. Do
this on both sides of the lens. You will
need to measure the distance with a
ruler from the lens to the focal point and
mark it accurately on the diagram. In this
example, the focal length of the lens is:
f = 40 cm
On the diagram this equates to a distance of 4 cm away from the lens on
each side.
Please note: In the ray diagrams above and on the following 4 pages, the
letter F shows the position of the focal point. In diagrams later on in these
notes, the symbol ‘f’ is also used to show the focal point.
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LENSES
3.
Draw a sketch of the object on the lefthand side of your diagram, as shown. It
is essential that the position of the
object is accurate so measure it with a
ruler. In this example, the object is 80
cm away from the lens, which equates
to 8 cm on the diagram.
Ensure the height of your sketch is
accurate according to the scale you
have chosen. The object is this example
has a height of 40 cm, which equates to 4 cm on the diagram.
4.
Draw the first ray: a horizontal line
between the top of the object and the
lens as shown. This ray then bends
(refracts) at the lens and travels
diagonally down through the focal point
as shown.
Draw the second ray: a straight line
which goes from the top of the object
through the centre of the lens as shown.
Remember to draw arrows on the rays to show the direction that the light
is travelling in.
5.
The image of the object is formed at the
point where the two rays cross, as
shown on the diagram.
Notice that the image that is formed is
upside down.
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LENSES
Types of image
There are two types of images
that can be formed by the lens.
Real image
A real image is an image that the
light rays actually pass through.
An example of this is shown
opposite.
The image is inverted by the lens.
The image is formed on the right of the lens.
We get a real image if the object is placed at a distance greater than the
focal length away from the lens.
Virtual image
A virtual image is an image that
the light rays do not pass
through. The image is not really
formed, it only appears to be
formed – it is an illusion. This
is shown opposite.
The image is the right way up.
The image is formed on the left
of the lens.
The image is magnified.
We get a virtual image if the object is placed at a distance less than the focal
length away from the lens.
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LENSES
Ray diagrams exercise
Copy and complete each ray diagram, using a ruler to accurately draw the
positions of the object, lens, focal length and image.
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LENSES
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THE MAGNIFYING GLASS
The magnifying glass
Look closely at a magnifying glass and you will
see that it is a convex lens. When you hold
this convex lens at a small distance away from
an object, it will magnify the object. In other
words, it makes the object appear to be
bigger so that it is easier to see.
Image: Heptagon/Wikimedia Commons:
http://commons.wikimedia.org/wiki/File:Magnif
ying_glass2.jpg
In this section, we are going to investigate the magnifying glass to discover
how the refraction of light through the magnifying glass lens makes objects
appear bigger. The ability to draw ray diagrams is essential to understanding
the microscope.
Experiment: Finding the focal length of the magnifying glass
The aim of this experiment is to find the focal length of the convex lens in a
magnifying glass.
You will need:
 a distant source of light, for example a laboratory window
 a screen, for example the classroom whiteboard
 a ruler.
Instructions
1. Hold the lens up in front of the screen, and move it backwards and
forwards until you see an image of the distant window on the screen.
Ensure the image is in focus. Note: the image will be upside down.
2.
Measure the distance between the lens and the screen using a ruler.
3.
The measured distance is equal to the focal length.
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THE MAGNIFYING GLASS
Explanation
In order to see an image in focus, light rays from the object must be brought to
a focus. Light rays from a distant object enter the lens parallel to each other.
As shown in the diagram, this means that these light rays are brought to a
focus at the focal point. In other words the light rays are brought to a focus at
a distance equal to the focal length away from the lens.
Dr Bob/Wikimedia Commons: http://en.wikipedia.org/wiki/File:Lens1.svg
Fir002/Wikimedia Commons: http://en.wikipedia.org/wiki/File:Large_convex_lens.jpg
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THE MAGNIFYING GLASS
Experiment: Magnifying an image
The aim of this experiment is to examine the ideal distance to hold a
magnifying glass away from an object to get the greatest magnification while
still having the image in focus.
You will need:
 a magnifying glass (the same one as used for the above experiment)
 a piece of paper with writing on it
 a ruler.
Instructions
1. Hold the magnifying glass at a position where the object being examined is
biggest. Measure the distance between the lens and the object.
2. Move the magnifying glass closer to the paper. Measure the new distance
with the ruler. Comment on the size of the magnified image compared to
above.
3. Now hold the magnifying glass at a distance that is further away from the
object than in part 1. Measure this distance. How does the image appear
now?
Analyse
1. Compared to the focal length of the lens, at what distance should you hold
a magnifying glass away from the object to see the object at its biggest but
still in focus?
2. What happens to the size of the magnified image when you hold the
magnifying glass closer to the object?
3. What happens to the image when you hold the magnifying glass at a
greater distance away than the focal length of the lens?
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THE MAGNIFYING GLASS
Explanation
Think back to the ray diagrams.
When a virtual image is
produced, the object being
imaged is at a distance less
than the focal length away
from the lens. As shown in the
diagram opposite,1 the light
rays do not actually pass
through the place where the image
forms. However, if you place your
eye on the right-hand side of the lens, your eye thinks the light rays are
coming from an object at the position of the virtual image. The magnifying
glass tricks your eye and you see the object bigger than it actually is.
Try it!
Construct ray diagrams to examine the size and position of the image formed
by an object that is placed at various distances from the lens. Only consider
distances that are shorter than the focal length. Can you explain your
results using your ray diagrams?
Questions
1.
A 2-cm high object is placed 10 cm from a lens that has a focal length of
5 cm.
(a)
(b)
(c)
2.
A magnifying glass with a focal length of 1 cm is used to examine some
small objects. Each object is placed 0·5 cm from the lens. By drawing
ray diagrams, to an appropriate scale, find the size of the image
produced by each of the following objects:
(a)
(b)
(c)
1
Use a ray diagram to find out what kind of image is formed (real or
virtual; magnified, diminished or same size; inverted or upright?).
The same object is moved to a distance of 4 cm from the lens.
Describe the image which is now formed. (You will need to draw a
new ray diagram.)
The object is again moved, this time to a distance of 1.5 cm from
the lens. Describe what happens to the image now.
a printed letter that is 4 mm high
a 2-mm grain of rice
a 5-mm pearl.
Dr Bob/Wikimedia Commons: http://en.wikipedia.org/wiki/File:Lens3b.svg
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THE MAGNIFYING GLASS
3.
A man creates an image of a fuse using a 10 cm lens. The fuse is 2 cm
high and is positioned at a distance of 6 cm from the lens.
(a)
(b)
Draw a ray diagram to find the height of the image produced.
How far is the image from the lens?
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THE REFRACTING TELESCOPE
The refracting telescope
So far we have considered the magnifying glass and investigated how it
magnifies the image of an object. This will be very important to understanding
how a refracting telescope works. The diagram below shows a ray diagram
for a refracting telescope. This is for an object close to the telescope.
The basic refracting telescope has two lenses:
 objective lens – this gathers light from the distant objects and focuses it
inside the telescope
 eyepiece lens – this acts like a magnifying glass to enlarge the image of
the distant objects.
The objective lens gathers light from the distant objects (stars, planets) and
focuses it to a point inside the telescope. The bigger the objective lens, the
greater the amount of light it gathers allowing you to look deeper into space.
The eyepiece lens acts as a magnifying glass to make the small image of the
distant objects bigger. The image must be formed at a distance away from the
eyepiece lens that is smaller than the focal length. This means that it is
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THE REFRACTING TELESCOPE
magnified. Different eyepiece lenses offer a different amount of magnification
and can be changed depending on the object you are looking at.
The diagram below shows a ray diagram for a simple refracting telescope.
fo
fe
fe
fo
Objective lens
Eyepiece lens
fo is the focal point of the objective lens
fe is the focal point of the eyepiece lens
Notice that:
 the image of the tree formed by the objective lens is real, inverted and
diminished
 the image formed by the objective lens is in front of the eyepiece lens
 the image is at a distance smaller than the focal length away from the
eyepiece lens
 the eyepiece lens forms a virtual image of the object
 the virtual image is magnified and is the same way up as the small
image
 this simple refracting telescope forms an image of the distant tree that is
upside down.
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THE REFRACTING TELESCOPE
Experiment: Design and build your own refracting telescope
You are going to use your knowledge of lenses and telescopes to design and
build your own refracting telescope.
You will need:
 cardboard tubes
 two convex lenses
 sticky tape.
Design
The important thing to remember when designingyour telescope is to have the
lenses the correct distance apart to ensure maximum magnification of a
small image (star). This will dictate the length of the cardboard tubes required.
Consider the following points:
 How far from a convex lens is the image of a distant object formed? (Hint:
think about the experiment where you measured the focal length of a lens.)
 How far away from an object should a magnifying glass lens be held to give
the greatest magnification while still keeping the image in focus? (Hint:
think about the magnifying glass experiments.)
Build
From your design considerations build a refracting telescope that can be
used to view a distant object.
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THE REFRACTING TELESCOPE
Extra: The microscope
A microscope works using a similar principle to a telescope – it makes very
small images much bigger. The diagram below shows how a microscope
forms an image of a small insect.
Real
Insect
Objective lens
fo
image
fe
fe
fo
Eyepiece lens
Virtual
image
fo is the focal point of the objective lens
fe is the focal point of the eyepiece lens
Use the diagram to describe how a microscope forms an image of a small
object. Comment on:
 the different positions of the object for a telescope and a microscope
 the sizes of the real image for a telescope and a microscope
 the 'length' of a microscope based on the lenses used.
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