13.1: Lenses and the Formation of Images
pg. 551
We see the world through lenses….
a) vision aids – contacts and eye glasses
b) eyes
Basic Lens Shapes
There are 2 basic lens shapes…
a) Converging Lens: the light rays running parallel will
converge as they pass through the lens and refracts, will
intersect at a single point. A converging lens is thinnest at the
edge and thickest in the middle.
Figure 1: A converging lens rings refracted rays together through a single
point.
b) Diverging lens: the light rays running parallel will diverge as
they pass through the lens and refracts. A diverging lens is
the thickest at the edge and thinnest in the middle.
Figure 2: Light rays spread apart after refraction in a diverging lens.
Simplifying the Path of Light Rays through a Lens
Refraction occurs, as light passes from the air into the glass lens it
slows down, but as it leaves the glass and reenters the air it will
speed up again. Therefore the light will refract twice (entering and
leaving). It is easier just to show it as one refraction point at a
central location within the lens, shown as a central dashed line
running through the lens.
Fig. 3: By drawing one refracted ray at the central dashed line of a lens, you can greatly
simplify ray diagrams. pg. 552
The Terminology of Converging Lenses
Optical Centre (O)– a point at the exact centre of the lens
Principal Focus (F)– is the point on the principal axis of a lens
where light rays parallel to the principal axis converge after
refraction.
Principal Axis (PA)– is the line running perpendicular to the
central dash line of the lens, dividing the lens into 2 equal parts
(top and bottom). Light rays running parallel to the principal axis
will converge on a single point.
There are two principal Foci – depending on the direction of the
incident ray, the focus on the same side as the incident ray is
known as the secondary focus. (F′)
Fig. 4: Terminology for a converging lens. pg. 552
The Terminology of the Diverging Lenses
Light rays running parallel to the principal axis will diverge. If you
project these rays backwards, it appears that they are coming from
the principal focus (F), which is now on the same side as the
incident rays.
(The F and F′ are equally apart from the optical centre on both
types of lenses)
Fig. 5: Terminology for a diverging lens. pg. 553
Check Your Learning, questions 1 – 6, page 553
13.3: Images in Lenses
pg. 556
Emergent Ray is the light that leaves a lens after refraction.
How to Locate the Image in a converging Lens
Figure 2: Imaging rules for a converging lens
Images in a Converging Lens
Using the imaging rules for converging lens, you can determine the
images for five different object locations.
Table 1: The Imaging Properties of a Converging Lens
1. The object is located beyond 2F1
(Image: smaller, inverted, between F and 2F, and real)
2. The object is located on 2F1
(Image: same size, inverted, at 2F, and real)
3. The object is located between 2F1 and F1
(Image: Larger, inverted, beyond 2F, and real)
4. The object is located on F1
(Image: no clear image is formed, emergent rays are
parallel)
5. The object is located inside F1
(Image: larger, upright, behind the lens, and virtual)
Figure 3: A converging lens produces a real image for these three object locations.
Figure 4: No image is produced when an object is at F1.
Figure 5: A larger, virtual image is produced on the same side as the object when the
object is between F1 and the lens.
Table 1: the Imaging Properties of a Converging Lens
Object
Image
Location
Size
Attitude
Location
Type
beyond 2F'
smaller
inverted
between 2F and F
real
at 2F'
same size
inverted
at 2F
real
between 2F' & F'
Larger
inverted
beyond 2F
real
same side as the
virtual
at F'
inside F'
NO CLEAR IMAGE
Larger
upright
object (behind lens)
How to Locate the Image in a Diverging Lens
The imaging rules for a diverging lens are similar to the
converging lens. The only difference is the light rays do not
actually come from the principal focus (F); the only appear to.
Figure 6: Imaging rules for a diverging lens.
Images in a Diverging Lens
The image in a diverging lens is always has the same
characteristics, no matter where the object is placed in front of the
lens. The image will always be smaller, upright, virtual and on the
same side as the object.
Figure 7: A diverging lens always forms a smaller, upright, virtual image that is on the
same side of the lens as the object.
Check Your Learning, questions 1 – 8, pg. 561
13.4: The Lens Equations
pg. 562
Lens Terminology
do = distance from the object to the optical centre.
di = distance from the image to the optical centre.
f = focal length pf the lens; distance from the optical centre to the
principal focus (F).
ho = height of the object
hi = height of the image
** Note the focal length (f) is the same distance whether it goes
to F or F'.
Figure 1: An illustration of the variables do, di, ho, hi, and f.
The Thin Lens Equations
The image distance, di, is negative if the image is behind the mirror (virtual image)
Thin Lens Equation
1
1
1
 
f di do
Note that h and d are used to denote
HEIGHT and DISTANCE
The subscripts i and o are used to
Magnification Equation
m
hi  d i

ho
do
denote IMAGE and OBJECT
The image height, hi, is negative if the image is inverted relative to the object
Thin lens equation is the mathematical relationship among do, di,
and f.
a) Object distances (do) are always positive.
b) Image distances (di) are positive for real images (when the
image is on the opposite side of the lens as the object) and negative
for virtual.
c) The focal length (f) is positive for converging lenses and
negative for diverging lenses.
Sample Problem #1:
The Tin Lens Equations applies equally well to diverging lens.
Figure 4: Lens equation variables for a diverging lens.
Sample Proablem #2:
The Magnification Equation
When you are comparing the size of the image with the size of the
object, you are determining the magnification of the lens.
Object (ho) and the image (hi) heights are positive when measured
upward from the principal axis and negative when measured
downward.
Magnification (M) is positive for an upright image and negative
for an inverted image.
The magnification (M) is a dimensionless quantity because the
units divide out.
Check Your Learning, questions 1 – 8, pg. 566
13.5: Lens Applications
pg. 567
The Camera
The converging lens in the camera produces an inverted, real
image, when the image is at a distance greater than F' (secondary
principal focus).
The light from large, distant objects is received by the camera and
forms a smaller, real image on its film on a traditional camera and
on the sensor of a digital camera.
The object must be located beyond the beyond 2F', if closer the
appropriate image will not b created. A camera is equipped a lens
to compensate for object location, to make sure the image falls on
the film, this is called focusing.
The Movie Projector
The movie projector is the opposite of a camera. It takes a small
object (on the film) and projects onto a screen a larger image. The
image is inverted and real. The projector film is loaded upside
down so the image appears to be upright on the screen.
The Magnifying Glass
A magnifying glass uses a converging lens. When the object is
located between F' and the lens, although the image is not located
in front of the lens, the human eye sees the image behind (same
side as the object) the lens, which is larger, virtual. The magnifying
lens is also a simple microscope.
The Compound Microscope
The compound microscope uses two converging lenses. The first
lens produces a real image, and the second lens produces a virtual
image. Both images are larger and inverted.
The Refracting Telescope
The refracting telescope is similar to the microscope. The object is
found beyond 2F', and the incident rays running through the
objective lens are running parallel to the principal axis. Two
images are created, both larger and inverted. The first image is real
and not seen, where the second one is virtual and seen.
Check Your Learning, questions 1 – 8, pg. 570
13.6: The Human Eye
pg. 572
The human eye is an optical instrument that allows us to see the
external world.
Parts of the Human Eye
The human eye is an amazing optical device.
The Iris in the eye has the function of controlling the amount of
light that is entering the eye. It is the colour portion of the eye
which opens and closes around the central hole, controlling light
entering the eye.
The Pupil is the hole in the Iris, in which light passes into the eye.
The eye also has a lens and a cornea. The Cornea is the transparent
bulge on top of the pupil that focuses light. The light is refracted at
this point.
The lens causes the light to converge, as it passes to the back of the
eye.
The Retina, found at the back of the eye. It is responsible to sense
light rays. The Retina converts light rays into electrical chemical
signals that run along the optic nerve to the brain.
The optic nerve creates a blind spot at the back of the eye. This is
because thee are no light sensitive nerves in this area.
This is not noticeable, the opposite eye compensates for this.
Figure 1: The anatomy of the eye
We think we see with our eyes, but this is not true. The eye is a
light gathering instrument. The Brain is responsible for interpreting
the message. The Cornea and Lens acts as a converging lens and
produce a smaller, real, inverted image on the retina. Nerve
impulse sends the massage to the brain. The brain takes the image
and flips it upright.
Eye Accommodation
Muscles within the eye are responsible for focusing and creating a
clear image. Ciliary Muscles help focus on distant and nearby
objects, by changing the shape of the eye lens. The change in shape
changes the focal length of the lens, and focusing on the retina.
This is called accommodation.
Figure 3: A healthy eye can focus light from both distant objects (a) and nearby objects
(b) on the retina. Notice that the lens is slightly fatter when focused on nearby objects.,
pg 574
Focusing Problems
When the process of accommodation does not work as well as it
should, people will have problems focusing on images at every
distances.
a) Hyperopia (Far-sightedness)
Hyperopia – the inability of the eye to focus light from near
objects.
A person with Hyperopia is able to focus and see clearly objects
that are far away. It is the objects that are near that are out of focus.
The eye cannot refract light well enough on the retina. It is caused
when the distance between the lens and the retina is too small or
because the cornea-lens combination is too weak. The light is
focused behind the retina, instead of on it.
Figure 4: (a) A normal, healthy eye focuses light from a nearby object onto the retina. (b)
A far-sighted eye focuses light from a nearby object behind the retina. pg. 574
This can be corrected using a basic converging lens, also known as
positive meniscus.
b) Presbyopia
Presbyopia – a form of far-sightedness caused by the loss of
accommodation as a person ages.
As people get older they lose elasticity in their eye lens. This can
be corrected by glasses with converging lenses.
c) Myopia (Near-sightedness)
Myopia – the inability of the eye to focus light from distant
objects.
This means the eye can focus on light rays from the nearby objects
on the retina. Distant objects are not in focus because the distance
between the lens and the retina is too large or the cornea-lens
combination converges light too strongly. The image appears in
front of the retina.
Figure 6: (a) A normal, healthy eye focuses light from a distant object onto the retina. (b)
A near-sighted eye focuses light from a distant object in front of the retina. pg. 575
This can be corrected using a basic diverging lens, also called a
negative meniscus .
Check Your Learning, Questions 1 – 6, page 577
13.7: Laser Eye Surgery
pg. 578
Laser eye surgery is an alternative to wearing eye glasses and
contact lenses.
Laser eye surgery involves using a laser to reshape the cornea of
the eye to improve vision.