OPTICS  types of lenses, uses and ray diagrams all
explained and the correction of eye defects
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 ~1416 year old
students of physics
This page will answer many questions e.g.
How can 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? What is total internal reflection?
Subindex for this page
(a)
Reminders of what happens when light
rays pass through transparent rectangular or triangular 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
(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 lenses
(j)
Eye defects  short sightedness and long sightedness 
their correction using lenses
(a) Reminders of what happens when light
rays pass through transparent rectangular or triangular prisms:


1. No refraction when a light
ray strikes a different medium at 90^{o} to the surface ie 'down'
the normal.

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).

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 subindex
(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, usually made of glass,
form images by refracting the rays of light that pass through them.

The characteristics of the image
formed depends on the shape of the lens.

There are two main types of lens with quite different shapes
and have opposite effects when rays of light strike them. They are:

convex lenses that converge
light rays to form an image (convex lens image below),

the faces of a convex lens curve outwards
so it bulges towards it centre,

1a
A simple ray diagram for a converging convex lens.

For a convex lens, parallel rays are
brought to focus at
F, the
principal focus
(on the other side of the lens from the object).

The distance from the centre of the
convex lens to F is called the focal length.

The thinner the convex lens, the longer
its focal the length  smaller angles of refraction.

The thicker the convex lens, the shorter
the focal the length  greater angles of refraction.

In terms of diagrams, the AXIS of
a lens is a horizontal line that passes through the centre of the lens,
perpendicular to the lens.

Note the refraction effects at both
air/glass boundaries of the convex lens to produce the converging
effect  look carefully at the fine purple lines of the normals.

The image produced is
real,
meaning it can be projected onto a screen or any other surface.

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 90^{o} 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. 2F simply means twice the focal length 2 x F.

Focal length f is defined as the
distance from the principal focus point to the centre of the lens  explained in
Ray diagram 2 below.

Depending on the type of lens and the
position of the object the images can be

upright (right way up) or
inverted (upside down),

they can be 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.

The above 'reference' points, and in
particular, understanding the differences between real and virtual images,
can only be really appreciated by studying the examples 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.

Unless you have an optical setup 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) cause the paper to
burn.
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and subindex
(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. The object is standing on the principal axis of the lens.

(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.

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. 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 3c for a convex lens where the object is placed at a distance
of
2F from the lens, BUT, O placed 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.

3c

(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 (iii).


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and subindex
(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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(e) Convex lens ray
diagram for when 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 do. 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) and
on the same side of the lens as the object..

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!

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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(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 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, 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 from 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.

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 physics?).
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(g)
Ray diagram for a concave lens showing
the divergence of parallel rays
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and subindex
(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 subindex
(i) A comparison between convex
and concave lenses
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and subindex
(j)
Eye defects and their correction using convex and concave lenses
The eye contains a convex lens 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
transmit the electrical signals to the brain giving you vision. 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 shortsightedness
(the medical term for short sightedness is myopia)
There are two principal
reasons why a person can suffer from shortsightedness (both
indicated on the diagrams).
Short sighted people can't
focus correctly on distant objects.
There are many 'biological'
causes to make a person shortsighted, 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 longsighted, 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 shortsightedness
(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
shortsightedness
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 shortsightedness 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 longsightedness 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.
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and subindex
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.
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WAVES  electromagnetic radiation, sound, opticslenses, light and astronomy revision notes index
General
introduction to the types and properties of waves, ripple tank expts, how to do
wave calculations
Illuminated & selfluminous objects, reflection visible light,
ray box experiments, ray diagrams, mirror uses
Refraction and diffraction, the visible light
spectrum, prism investigations, ray diagrams explained
gcse physics
Electromagnetic spectrum,
sources, types, properties, uses (including medical) and dangers gcse physics
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 gcse
chemistry
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 gcse physics revision notes
Sound waves, properties explained, speed measure,
uses of sound, ultrasound, infrasound, earthquake waves
The Structure of the Earth, crust, mantle, core and earthquake waves (seismic wave
analysis)
gcse notes
Astronomy  solar system, stars, galaxies and
use of telescopes and satellites gcse physics revision notes
The life cycle of stars  mainly worked out from emitted
electromagnetic radiation gcse physics revision notes
Cosmology  the
Big Bang Theory of the Universe, the redshift & microwave background radiation gcse
physics
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