|
OPTICS - types of lenses, uses and ray diagrams all
explained
and the correction of eye defects
IGCSE AQA GCSE Physics Edexcel GCSE Physics IGCSE OCR GCSE
Gateway Science Physics OCR GCSE 21st Century Science Physics
Doc Brown's school physics revision notes: GCSE
physics, IGCSE physics, O level physics, ~US grades 8, 9 and 10
school science courses or equivalent for ~14-16 year old students of
physics
This page will answer many questions e.g.
How do lenses collect light and form
images? What is a convex lens? What is a concave lens? What is the focal length of a lens? How can you measure the focal length of a
convex lens?
Sub-index for this page
(a)
Reminders of what happens when light
rays pass through different shaped prisms
(b)
The types and properties of lenses
and examples of how to construct ray
diagrams
(c)
Convex lens ray
diagram for a real image when object is at a distance of 2F from the lens
(d)
Convex lens ray
diagram for a real image when object is at a distance between F and 2F from
lens
(e)
Convex lens ray
diagram for virtual image when object is at a distance between F and the
lens
(f)
Convex lens ray diagram for when object is at a distance
beyond 2F
(g)
Ray diagram for a
concave lens showing the divergence of parallel rays
(h)
Ray diagram showing
the formation of a virtual image by a concave lens
(i)
A comparison between convex and concave lens images
(j)
Eye defects - explaining short sightedness and long sightedness -
their correction using lenses
See also
The
eye (gcse biology notes)
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(a) Reminders of what happens when light
rays pass through different shaped transparent
objects
-
-
1. No refraction when a light
ray strikes a different medium at 90o to the surface ie 'down'
the normal.
-
The same applies to 3 and 4 for the
central ray in the diagram.
-
Most light is transmitted, but a little light can be
reflected, especially if the incident angle is >90o (<
normal angle).
-
2.
Double refraction through a
rectangular glass block at the air/glass interfaces, note that when the ray
emerges back into air its path is parallel to the original incident ray.
-
3. Refraction of two rays at the
two surfaces
of a diverging
concave lens (this page), the central ray passes straight on.
-
4. Refraction of two rays at two
of the surfaces of
a triangular glass or plastic prism.
-
5. Refraction of two rays at the two surfaces of
converging concave
lens (this page).
-
Note that 4 is effectively what
happens at the top end of the convex lens
5 - two refractions, one at
each of the air/glass boundaries.
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and sub-index
(b) The types and properties of
lenses
-
Be able to explain how to measure the focal length of a
converging lens using a distant object (see Ray diagram 2 below).
-
You should revise any
investigations on the behaviour of
converging lenses, including real and virtual images.
-
Lenses are usually made of glass,
and
form images by refracting the rays of light that pass through them.
-
Ray diagram 1 (below): Conventions
in light ray diagrams for the two types of lenses - convex or concave.
-
1c representations of convex and concave lenses
-
The ray line that goes through the centre
of the lens at 90o to its surface is called the axis.
-
Note the simple representations of a
convex and concave lens <-------> and >-------<
-
F is the abbreviation for focal
length.
-
Depending on the type of lens and the
position of the object the images can be
-
upright (right way up) or
inverted (upside down),
-
smaller than the object, same
size as object or bigger than the object (magnified),
-
the image can be real - formed
when the rays directly come together after lens refraction from a convex
lens (never from a concave lens),
-
or the image can be virtual - when
the light rays from the object appear to come from a different place than
where they originate - here you are dealing with virtual rays.
-
Concave lenses always produce a virtual
image and a convex lens can under particular circumstances (see later).
-
A convex lens usually produce a real image, but can give a
virtual image under specific circumstances.
-
The above 'reference' points, and in
particular, understanding the differences between real and virtual images,
can only be really appreciated by studying the examples of ray diagrams below.
-
Ray diagram 2 (below): Ray diagram
to show how to measure the focal length of a convex lens.
-
2.
converging convex lens
-
Here, refraction in a convex lens
causes the rays to be converged beyond the lens.
-
The parallel set of rays are effectively
from an object an infinite distance from the convex lens.
-
As already pointed out, after refraction, a convex lens brings a
set of rays parallel to the principal axis to converge to the principal focus point (F on ray diagram 2
above).
-
The distance from the centre of the lens to the principal
focus F is called the focal length (f) of that lens and it applies to both
sides of the lens - see later convex lens forming a virtual image.
-
With a set of parallel rays the image is formed at distance
F on the right of the lens and any ray passing through the centre of
the lens is considered to be undeviated - not refracted.
-
These comments on what happens to the rays are really
important when constructing and drawing ray diagrams.
-
Along the line of the principal axis,
the thicker the convex lens (the more curved), the shorter the focal length
f and the greater the magnifying power of the lens.
-
The thicker the lens (the more curved),
the greater the distortion in trying to produce a well focussed image.
-
The focussing power of materials varies.
-
However, with a more refracting material you
can make the lens thinner to improve the quality of the image and keep the
same magnifying power (same focal length).
-
Unless you have an optical set-up to produce a parallel beam
of light from an object, you will have to resort to a much simpler method to
get an approximate value of the focal length of a convex lens e.g.
-
To measure the focal length of a
convex lens
-
You set up a lens to focus on a distant object - perhaps out
of the laboratory window.
-
Focus the image on a screen and measure the distance from
the centre of the lens to the centre of the image.
-
You can repeat the experiments with lenses of different
thickness - any difference?
-
You should find the thicker the lens,
the shorter the focal length.
A simple experiment using a
magnifying glass to focus the Sun's rays onto a paper screen
The rays from the very distant Sun are
effectively parallel and can be brought to a focus to such an extent that
the converging visible light rays (and some infrared) producing such a
concentration of light energy that the paper heats up sufficiently to cause
charring and even ignite the paper - note the burn marks.
TOP OF PAGE
and sub-index
(c)
Convex lens ray diagram for when object
is at a distance of 2F from the lens
Ray diagram 3a (below): Ray diagram
showing the formation of an image from an object O at a distance of 2F
from the convex lens (twice
the focal length) beyond the convex lens.
-
3a
converging convex lens
-
To construct the ray diagram 3a, draw a
vertical line tipped with an arrow for the object O, at the
appropriate distance from the lens, in this case a distance exactly 2F from
the lens.
-
Imagine the object is standing on the principal axis of the lens.
-
Apart from the axis line, this is
essentially a 2 ray diagram for an object 'standing' on the axis line.
-
(i) Draw a ray from the arrow tip of the
object parallel to
the principal axis into the lens.
-
Since this ray is parallel to the axis,
beyond the lens, the
ray must continue down through the principal focus F (in this case beyond a
2F distance to the right of the lens).
-
Check this line in ray diagram 2
above.
-
(ii) You then draw a line, again from the top
of the object, diagonally down through the centre of the lens, and continue the line
until it is beyond intersecting with the first ray (i) you drew.
-
Again, check
this line in ray diagram 3a above, which must pass through the centre of the
lens without deviation.
-
A ray passing through the centre of a
lens is considered NOT to be deviated - NOT refracted.
-
Please remember this applies to
ANY lens, and, for convex lenses only, a ray parallel to the principal
axis, after refraction, passes through the principal focus point F, when
studying the rest of the diagrams on this page.
-
The intersection point gives you
the position of the bottom of the image and the inverted arrow gives
you the size of image I.
-
3b converging convex lens
-
Above is quick sketch 3b of how to do the ray diagram 3a
on graph paper.
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and sub-index
(d)
Convex lens ray diagram for when object
is a distance between F and 2F from lens
-
Ray diagram 4 (below): The
formation of a real image by a convex lens when the object O is a
distance from the convex lens between F
and 2F.
-
(ii) You then draw a line, again from the top
of the object, down through the centre of the lens, and continue the line
until it is beyond intersecting with the first ray you drew.
-
The intersection point gives you
the position of the bottom of the image and the inverted arrow gives
you the size of image I. From this you can see that ....
-
The image is real, inverted and larger
than the object and on the opposite side from
the object.
-
The image is further than a distance
beyond 2F from the lens on the image side of the lens.
-
So here the convex lens is acting as a
magnifying glass.
-
4b convex lens
-
Above is quick sketch of how to do the ray diagram 4a
on graph paper.
-
If done very carefully to scale,
from diagram 4b, you can then
calculate the height of the inverted image I and the distance from
the lens to the image I.
-
From the graph, and measuring in
'squares' you can work out the ...
-
magnification = size of
image / size of object = 8 / 5 =
1.6
-
Below is a more elaborate graph paper ray
diagram 4c for a convex lens where the object is placed at a distance
between F and 2F from the lens, BUT, above the central axis of the lens -
four rays are marked (i) to (iv), each intersecting pairs of lines ('rays')
gives you the top and the bottom of the image.
-
 4c
-
(i) Draw a line from the top of the
object to the lens and, after the lens, down through the focal point F to
well beyond a distance of 2F.
-
(ii) Draw a diagonal line from the top of
the object down through the centre of the lens and beyond the intersection
with ray (i).
-
(iii) Draw a line from the bottom of the
object parallel to the principal axis and, after the lens, diagonally down
through F.
-
(iv) Draw a line from the bottom of the
object diagonally down through the centre of the lens and beyond the
intersection with ray (iii).
-
From the graph, and measuring in
'squares' you can work out the ...
-
magnification = size of
image / size of object = 9 / 5 =
1.8
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and sub-index
(e) Convex lens ray
diagram for when the object is at a distance between F and the lens
-
Ray diagram 5 (below): The
formation of a virtual image by a convex lens when the object O is between F
and the convex lens - here the convex lens is acting as a magnifying
glass.
-
5a
converging convex lens
-
To construct the diagram 5a, as with the
others, (i) from the top of the object you take the ray parallel to the
principal axis down through the principal focus point F. That is what
parallel rays with the object is standing on the axis.
-
(ii) The second ray from the top of the object
you take down through the centre of the lens without deviation.
-
However, in this case these rays do not
intersect to give you the position of the image - they diverge, but all is
not lost to get to an image!
-
Therefore you have to extrapolate back
with the dotted line virtual rays until they intersect.
-
Virtual rays are where the rays from the
object appear to come from, they do NOT exist in reality.
-
BUT, you can't construct the ray diagram
to get to the characteristics of the image without using them!
-
This then gives you the position and size
of the virtual image - this time on the same side of the lens as the object.
-
The image I is virtual, upright - right way up (erect, NOT
inverted), bigger than the object (a 'magnifying glass' effect)
-
Unlike all the other situations for a
convex lens, the (not
real) virtual image
is on the same side of the lens as the object and beyond the object.
-
In this case the image is between
the distances F and 2F to the left of the lens.
-
Along the line of the principal axis,
the thicker (more curved) the convex lens, the shorter the focal length
F and the greater the magnifying power of the lens.
-
The thickness of the lens affects its
magnifying power - the thicker the lens, the more powerful the magnifying
glass.
-
5b converging convex lens
-
Above is quick sketch of how to do the ray diagram 5
on graph paper. If done very carefully to scale, you can then
calculate the height of the image I and the distance from
the lens to the image I.
-
This is the ray diagram for a convex lens
acting as a magnifying glass.
-
You should know the magnification
formula:
-
magnification = size
(height) of image ÷
size (height) of object
-
e.g. from diagram 5b, if the image was 20 mm high and the
object was 4 mm high
-
magnification = 20 ÷
10
= 2 (no units,
but remember the two sizes must be in the same length units!)
-
2nd example of calculation
-
Suppose the magnifying power of a lens
is 3.0.
-
If an object is 2.0 cm high, calculate
the size of the image.
-
Rearranging the magnification formula:
-
size of image = magnification x size of
object
-
size of image = 3.0 x 2.0 =
6.0 cm
-
From the diagram you can also see
the focal length of the lens is 2 cm.
-
This is a very simple example, but
the method works for any given set of data.
-
All you need to be given is the (i)
focal length of the lens, (ii) the size of the object and (iii) the
distance from the lens to the object. From the graph diagram you can
work out everything else e.g. the size of the image and the magnifying
power of the lens.
-
Below is a more elaborate graph paper ray
diagram 5c for a convex lens where the object is placed at a distance
less than F from the lens, BUT, above the central axis of the lens - four
rays are marked (i) to (iv), each intersecting pairs of lines ('rays') gives
you the top and the bottom of the image.
-
5c magnifying lens
-
(i) Draw a line from the top of the
object to the lens and, after the lens, down through the focal point F to
well beyond a distance of F - then extrapolate back with dotted lines
-
(ii) Draw a diagonal line from the top of
the object down through the centre of the lens and beyond the intersection
with ray (i).
-
In both cases, extrapolate back with
dotted lines
-
The intersection of dotted lines from (i) and (ii)
gives you the position of the top of the upright virtual image.
-
(iii) Draw a line from the bottom of the
object parallel to the principal axis and, after the lens, diagonally down
through F.
-
(iv) Draw a line from the bottom of the
object diagonally down through the centre of the lens and beyond the
intersection with ray (iii).
-
In both cases, extrapolate back with
dotted lines.
-
The intersection of dotted lines from (iii) and (iv)
gives you the position of the bottom of the upright image.
-
The intersection of rays (iii) and (iv)
gives you the position of the top of the upright virtual image.
-
From the graph, and measuring in
'squares' you can work out the ...
-
magnification = size of
image / size of object = 16 / 5 =
3.2
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and sub-index
(f)
Convex lens ray diagram for when object is at a distance
beyond 2F
-
Ray diagram 6a When the object O
is beyond a distance of 2F from the convex lens
-
6a
converging lens
-
If the object is a long way from the lens the image is
formed between F and 2F and is standing on the axis.
-
(i) Draw a ray from the arrow tip parallel to
the principal axis into the lens.
-
Since this is parallel to the axis,
beyond the lens, the
ray must continue down through the principal focus (in this case beyond an F distance to the right of the lens). Check this line in ray diagram
6a
above.
-
(ii) You then draw a line, again from the top
of the object, down through the centre of the lens, and continue the line
until it is beyond intersecting with the first ray you drew.
-
The intersection point gives you
the position of the bottom of the image and the inverted arrow gives
you the size of image I. From this you can see that ....
-
The image I is real, inverted (upside
down!) and smaller than the object O.
-
If the
object O is at infinity, the focussed image is at
a distance F beyond the lens.
-
This means the further the object O
is from the lens, the nearer the image I is to distance F.
-
This is also the image formed in a
telescope from a very distant object like a star which is so far away that the
incoming rays are effectively parallel.
-
The image can then be magnified by
another lens or lenses in conjunction with an eyepiece or camera.
-
6b convex lens
-
Above is quick sketch 6b of how to do the ray diagram 6a
on graph paper. If done very carefully to scale, you can then
calculate the height of the image I and the distance from
the lens to the image I.
-
Below is a more elaborate graph paper ray
diagram 6c for a convex lens where the object is placed at a distance
beyond 2F from the lens, BUT, above the central axis of the lens - four rays
are marked (i) to (iv), each intersecting pairs of lines ('rays') gives you
the top and the bottom of the image.
-
6c
-
(i) Draw a line from the top of the
object to the lens and, after the lens, down through the focal point F.
-
(ii) Draw a diagonal line from the top of
the object down through the centre of the lens and beyond the intersection
with ray (i).
-
(iii) Draw a line from the bottom of the
object parallel to the principal axis and, after the lens, diagonally down
through F.
-
(iv) Draw a line from the bottom of the
object diagonally down through the centre of the lens and beyond the
intersection with ray
-
If the object is a F, the image is at
infinity, which is not very useful? (not needed for GCSE/GCSE physics?).
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and sub-index
(g)
Ray diagram for a concave lens showing
the divergence of parallel rays
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and sub-index
(h)
Ray diagram showing the formation of a
virtual image by a concave lens
-
Ray diagram 7b The formation of an
image
O by
a concave lens.
-
7b
diverging concave lens
-
(i) The ray from the top of the object is
taken down through the centre of the lens undeviated.
-
Apart from the axis line, this is
essentially a 2 ray diagram for an object 'standing' on the axis line.
-
The object is standing on the principal
axis of the concave lens.
-
(ii) You then take the ray parallel to the
principal focus and diverge it in line with the principal focus F - that's
how parallel rays behave. You extrapolate ray (i) back down to F with a
dotted line.
-
Where the two lines intersect gives you
the top of the image and hence its size too.
-
A concave lens always produces a
virtual image, the right way up, smaller than the object and is situated
somewhere between the object and the lens and on same side as object).
-
7c concave lens
-
Above is quick sketch 7c of how to do the ray diagram 7b
on graph paper. If done very carefully to scale, you can then
calculate the height of the image I and the distance from
the lens to the image I.
-
Below is a more elaborate graph paper ray
diagram 7d for a concave lens where the object is placed at a
distance less than F from the lens, BUT, above the central axis of the lens
- four rays are marked (i) to (iv), each intersecting pairs of lines
('rays') gives you the top and the bottom of the image.
-
 7d
concave lens
-
(i) Draw a line from the
top of the object O to the lens and, after the lens, diverging - you
then extrapolate back to the principal focus F - this is how rays parallel
to the principal axis behave.
-
(ii) Draw a diagonal line
from the top of the object down through the centre of the lens.
-
(iii) Draw a line from
the bottom of the object parallel to the principal axis and, after the lens,
diagonally diverged and extrapolated with a dotted line back to F.
-
(iv) Draw a line from the
bottom of the object diagonally down through the centre of the lens.
-
Note the image is again smaller than the
object - it always is for a concave lens.
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and sub-index
(i) A comparison between convex
and concave lenses
TOP OF PAGE
and sub-index
(j)
Eye defects, causes and their correction using convex and concave lenses
The eye contains a convex lens structure that,
ideally, focuses the incoming light rays to produce a sharp image on the
retina at the back of the eyeball.
The light receptors in the retina then
produce and transmit the electrical signals to the brain giving you vision.
It is the energy of the light photons that cause a
change in light sensitive molecules that trigger the electrical signal
to the brain.
However, the
eye does not always sharp images, but it is possible to correct these
defects using glass lenses.
See also
The
eye - structure, function and vision defects GCSE biology
revision notes - This page deals with all the GCSE biology required on
the eye and more notes on other methods of dealing with eye defects.
Cause of vision defects
A malfunction of the eye in some way to
give blurred vision because the incoming light rays do not form a sharp
image on the retina.
1. Causes of short-sightedness
(the medical term for short sightedness is myopia)
There are two principal
reasons why a person can suffer from short-sightedness (both
indicated on the diagrams).
Short sighted people can't
focus correctly on distant objects.
There are many 'biological'
causes to make a person short-sighted, but here we are most
concerned with optics of the situation and how to use concave lenses
to correct the defect.
The eyeball can be too long so
the image is formed in front of the retina.
Distant objects will seem
blurred, though close objects may be in focus.
The same effect is caused if the
lens is the wrong shape i.e. it is too powerful - too thick - with too short a principal focus,
so your vision is blurred.
This can be corrected with a
diverging concave lens (see the diagrams and explanation below).
2. Causes of longsightedness
(the medical term for long sightedness hyperopia)
Long sighted people can't
focus correctly on near objects.
There are many 'biological'
causes to make a person long-sighted, but here we are most concerned
with optics of the situation and how to use convex lenses to correct
the defect.
There are two principal
reasons why a person can suffer from short-sightedness
(both indicated on the diagrams).
The eyeball may be too short so
the image is formed behind the retina.
Distant objects might be in focus
but any relatively close objects will appear blurred.
The same effect is caused if the
lens is the wrong shape - too weak - too thin - with too long a principal focus, so
your vision is blurred.
This can be corrected with a
converging convex lens (see the diagrams and explanation below).
Using lenses to correct for eye
defects
1. Correcting for
short-sightedness
Reminder: Short sighted people
can't focus correctly on distant objects.
The eyeball is too long or the
lens to thick (too strong) to produce a sharp image on the retina.
Prior to correction, the focussed image is
formed in front of the retina.
In order to move the image back
to give it a sharp focus on the retina you need to diverge the rays.
This is done with a diverging concave lens in front of the eye.
The diverged rays are then
brought to a focus further back by the eye lens onto the retina.
The diagrams (1) show the normal
correct function of the eye, the effect of short-sightedness and the
correction produced by the concave lens.
2. Correcting for longsightedness
Reminder: Long sighted people
can't focus correctly on near objects.
The eyeball is too short or the
lens to thin (too weak) to produce a sharp image on the retina.
Prior to correction, the image is
formed behind the retina.
In order to form a sharp image on
the retina, you to use a converging convex lens in front of the eye
to bring the rays to a focus further forward.
The combined converging power of
the glass lens plus the eye lens bring the rays to a focus on the
retina on the inner surface of the eyeball.
The diagrams (2) show the normal
correct function of the eye, the effect of long-sightedness and the
correction produced by the convex lens.
See also
The eye -
structure, function and vision defects GCSE biology revision notes
- This page deals with all the GCSE biology required on the eye and more
notes on other methods of dealing with eye defects.
TOP OF PAGE
and sub-index
Some learning objectives for this page
-
Know the structure and
function of the parts of the eye.
-
Know and understand that correction of vision using convex and concave lenses to produce an image on the retina:
-
long sight, caused by the eyeball being too short, or the eye lens being unable to focus,
-
short sight, caused by the eyeball being too long, or the eye lens being unable to focus.
-
Appreciate the concept of range of vision
- the eye can focus on objects between the near point and the far point.
-
Be able to compare the structure of the eye and the camera.
-
Know that the power of a lens is given by:
-
P = 1 / f
-
P is power in dioptres,
D
-
f is focal length in
metres, m
-
You should know that the power of a converging lens is positive and the power of a diverging lens is negative.
-
The focal length of a lens is determined by: ¦ the refractive index of the material from which the lens is made, and ¦ the curvature of the two surfaces of the lens.
Keywords and phrases: IGCSE/GCSE physics notes
on what happens when light rays pass through different shaped prisms, the types
and properties of convex lenses and concave lenses, examples describing how to
construct ray diagrams, convex lens ray diagram for a real image when object is
at a distance of 2F from the lens, drawing a convex lens ray diagram for a real
image when object is at a distance between F and 2F from lens, how to construct
a convex lens ray diagram for virtual image when the object is at a distance
between F and the lens, explaining the construction of a convex lens ray diagram
when the object is at a distance beyond 2F from the lens, how to draw a ray
diagram for a concave lens showing the divergence of parallel rays, how to draw
a ray diagram showing the formation of a virtual image by a concave lens,
comparison of the properties of a convex lens image compared to a concave lens
image, eye defects - explaining short sightedness and long sightedness -
explaining how to correct eye defects using convex lenses and concave lenses how
do light rays behave with convex lens compared to concave lens? how do you
determine focal length of a convex lens? How do you draw ray diagrams showing
the formation of an image with a convex lens or concave lens? How do describe
the properties of real and virtual images with ray diagram - upright or
inverted, reduced size or magnification? What causes long-sight and short-sight
eye problems? How can you correct of eye defects caused by long-sight or
short-sight using convex lenses and concave lenses?
TOP OF PAGE
and sub-index
WHERE
NEXT?
WAVES - electromagnetic radiation, sound, optics-lenses, light and astronomy revision notes index
General
introduction to the types and properties of waves, ripple tank expts, how to do
wave calculations
Illuminated & self-luminous objects, reflection visible light,
ray box experiments, ray diagrams, mirror uses
Refraction and diffraction, the visible light
spectrum, prism investigations, ray diagrams explained
Electromagnetic spectrum,
sources, types, properties, uses (including medical) and dangers
The absorption and emission of radiation by
materials - temperature & surface factors including global warming
See also
Global warming, climate change,
reducing our carbon footprint from fossil fuel burning
Optics - types of lenses (convex, concave, uses),
experiments and ray
diagrams, correction of eye defects
The visible spectrum of colour, light filters and
explaining the colour of objects
Sound waves, properties explained, speed measure,
uses of sound, ultrasound, infrasound, earthquake waves
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1a
A simple ray diagram for a converging convex lens.
1b A
simple ray diagram for a diverging concave lens
3c
