With
Lenses
Created by Derek J. Wells. Under the expressed written consent of Derek J. Wells in
accordance with the rules and by-laws of Derek J. Wells. All events depicted here are
fictional. Any similarity to real life situations are merely coincidental.
What Do Lenses Do ??
When light passes through a Lens, it is refracted (bent). This bending of light
produces an image of the object that is different from it original appearance.
Objects viewed through lenses produce images that vary based on where the
object is located and on the type of lens that is used.
There are two types of lenses.
A converging lens.
And
This is also called a
convex lens because
the surface of the
lens has a convex
shape.
A diverging lens
This is also called a
concave lens
because the surface
of the lens has a
concave shape.
This lens looks like a
“cave” if you were
walking into it.
The converging lens causes horizontal light rays to converge (come together) when it hits.
The diverging lens causes horizontal light to diverge (move apart) when it hits.
Terminology
2f
f
Principle Axis = The horizontal
line drawn through the center
f
f = Convex lens Focal point
= the point through which all
horizontal rays hitting the lens
pass through when they
refract (bend)
2f
2f
f
f
f = Concave lens Focal point
= the point at which all
horizontal rays hitting the
lens appear to come from
when they refract (bend)
IMPORTANT
These focal points are negative (-)
In the diverging lens
Point 2f is twice the focal point and is used as a reference point in a lens problem
2f
Terminology
Continued ...
Also
Distance object
is placed from
the lens center
ho = object height
hi = image height
d0
An object
placed
near a lens
2f
f
f
2f
di
Front Side of Lens
(the virtual side)
When images are formed on the front side
of the lens they are virtual images. When
you look through a lens and the object
looks different than usual you see a virtual
image (such as a magnifying glass)
Distance image
is formed from
the lens center
The image of
the object that
is produced by
the lens
Back Side of Lens
(the real side)
When images are formed on the back
side of the lens they are real images.
Real images can be projected onto a
screen.
Lens Equations
Lens Equations - You can find out where and what an image should look like by
using the lens equations
To find the distance of
the image from the lens
1
1 1


f d0 di
To find the Magnification and
Orientation of the Image
M
d i
do
M
hi
ho
Important - when using a diverging lens the focal point (f) must be made negative (-)
Determining the Image
di = (+)
di = (-)
M = (+)
M = (-)
|M|=1
|M|<1
|M|>1
real image
virtual image
upright
inverted (upside down)
same size
smaller
larger
note | M | = (absolute value of M)
Convex lenses can form any types
of these images
- real or virtual
- smaller, same size, or larger
- inverted or upside down
Concave lenses can only form
one type of image ALWAYS
- smaller, upright, virtual
Example: A concave lens with (f = 4 cm, d0 = 8 cm)
1
1 1


f d0 di
Note that the f is (-) since it’s
a concave lens
1 1 1
 
 4 8 di
 0.25  0.125
 0.375 
M
M
1
di
1
di
di   2.67 cm
d i
do
 (2.67 cm)
8
M  0.33
di = (-)
so its virtual
M = (+)
so its (upright)
|M|<1
so its smaller
Ray Diagrams (for convex lenses)
We use ray diagrams to draw a picture of what the image would look like
3 Light rays are drawn all originating from the tip of the OBJECT. The point
where these rays intersect gives the location where the tip of the IMAGE will be
Lets try an example with f = 5 cm, do = 12 cm
The first light ray we draw
goes through the center of
the lens
2f
f
f
This light ray passes
through unaffected and
keeps going the same way
2f
Ray Diagrams (for convex lenses)
The second light ray we draw goes
horizontally towards the lens and
stops in the center of it (the light
actually bends the whole time its in
the lens, but as a convention we make
it bend when it hits the center.
2f
f
f
This light bends and passes
through the focal point on
the other side of the lens
2f
Ray Diagrams (for convex (CONVERGING) lenses)
The last light ray we draw
goes through the focal point
on the front side at stops at
the center of the lens
2f
f
f
This light ray bends and
emerges horizontal on the
back side
2f
A convex lens (converging) with (f = 2 cm, d0=5 cm)
Putting it all together.
Draw all three rays and the point where
they intersect represents the point where
the tip of the image will be formed
Describe the image:
Real
Smaller
Inverted
image
2f
f
f
2f
Check the math
1
1 1


f d0 di
1 1 1
 
2 5 di
1
0.5  0.2 
di
1
0.3 
di
M
di  3.33 cm
M
d i
do
 3.33
5
  0.67
di = (+)
so its real
M = (-)
so its inverted
|M|<1
so its smaller
Special Examples (For Convex Lenses)
1- When the object is located exactly on (f) the rays will not intersect anywhere and
there will be no image
2- When the object is placed in front of (f) the rules are a little bit different
Lets try - A convex lens with
(f = 2 cm, d0=1 cm)
The first two rays
are the same as
before
The intersection of the
extensions through the lens
show you where the tip of
the image will be formed
Image
2f
Notice the rays do not intersect on this
side. So we have to extend these
refracted rays back to the front of the
lens to see where they appear to come from
f
The third ray cannot be drawn
through (f) since we are in front
of it so it is drawn as if it
originated at (f), and this ray
refracts horizontal after hitting
the center.
f
2f
Describe the image:
Virtual
Larger
Upright
Ray Diagrams (for concave (DIVERGING) lenses)
The nice thing about Concave lenses is that the ray diagrams are ALWAYS,
ALWAYS the same. They are slightly different then the convex lenses however
and you should be careful to notice the differences. In this type of lens, you
always have to extend the refracted rays back behind to find the image
Lets try an example with f = 5 cm, do = 12 cm
The first light ray we draw
goes through the center of
the lens
2f
f
f
This light ray passes
through unaffected and
keeps going the same way
2f
Ray Diagrams (for concave lenses)
The second light ray we
draw goes horizontally
towards the lens and stops
in the center of it
2f
f
This light bends as if it
came from the focal point on
the front of the lens
f
2f
Ray Diagrams (for concave lenses)
The last light ray we draw
goes TOWARDS the focal
point on the other side and
stops at the center of the
lens
2f
f
f
This light ray bends and
emerges horizontal on the
back side
2f
Putting it all together.
Draw all three rays and extend the refracted
rays back behind the lens. The point where
the extensions meet is the image point
2f
f
Image
A concave lens (diverging) with (f = 2 cm, d0=5 cm)
Rays don’t intersect over
here so they are extended
back to the front of the
lens
f
2f
Describe the image:
Virtual
Smaller
Remember when doing the
math (f = (-)).. The math for
this lens will always show
Upright
di = (-)
so its virtual
M = (+)
so its upright
|M|<1
so its smaller
Chromatic Aberration
White light is made up of all the difference colors of light (frequencies). When
light passes through glass, it slows. This slowing causes the light to bend which is
why we get refraction. Each of the different frequencies in light bend a little
differently and come out at different angles. This phenomenon is known as
Dispersion and is how a Prism produces the rainbow colors when light enters it.
Since each of these frequencies bend a little differently they fall at the focal
point in slightly different spots and can cause a distorted image (example will be
shown below). This is corrected with the use of color filters or multiple lenses.
Red light bends less
than blue light
Incoming
white light
2f
f
f
2f
They are slightly off
from the focal point
Red light bends less
than blue light
Glasses and Contacts
An eyeball is a lens. Light bends when it hits it. In a normal eye, light hits the eye
lens, bends and focuses right exactly back on your retina to make an clear image.
Your eye can be slightly misshapen from strain and this can cause the light not
to focus on your retina.
When light bends too much it
focuses before it hits your
retina and you are nearsighted
and this is called MYOPIA
When light does not bend
enough it focuses behind the
retina and you are farsighted.
This is called HYPEROPIA
Fixing the problem
With MYOPIA light bends too much so we need to bend the light out a little before it
hits the eye. We want the light to diverge a little so we put a diverging lens in front
With HYPEROPIA light bends too little so we need to bend the light in a little before it
hits the eye. We want the light to converge a little so we put a converging lens in front
AN IMPORTANT Side Note.
- These equations and rules apply to THIN
lenses in air. When lenses are thicker or
they are placed in other substances like
water, the focal points change and the math
becomes more advanced.
Experimental Laboratory Optics
-Image formation using real lenses can be performed in class
labs.
- Using a candle, an image can be projected onto a piece of paper
that is moved into the proper location to find the focused image.
- A ruler can be used to measure image and object distances and
the focal point of the lens can be calculated, or if the lens focal
point is known, we could determine an experimental value
Experimental Laboratory Optics … continued
Note: in these labs, the objects are not very far from the
lenses so the images will form in various locations based on
object distance to the lens.
IMPORTANT: Light traveling a far distance to a lens is
assumed to be all horizontal relative to the lens. For this
situation, all of the light will converge to the focal point and
the image will only be found directly at the focal point
- This is a handy way to estimate the focal point of a lens, by
focusing an image of a tree far away on a piece paper, or even
better, by focusing an image of the sun on a card, we know that
the location of that image must be at the focal point of the lens.
When you start fire with the sun and a lens, you are essentially
making an image of the sun to burn the paper.
Fini
That’s the end of the lenses
presentation. If you enjoyed this
film, look for other great
presentations such as
”How To Get Good Grades in
Physics with $100 bills ”
©2001, well not really