From Mirrors to Lenses
c
f
real image
Real Images
Rather than a virtual image (which is formed by
virtual rays), a real image is formed by real rays!
It can only be produced by a concave mirror, and
only if the object is further than the focal point.
Since the image is formed by actual rays of light in
front of the mirror, it can be projected onto a screen.
You need to see it to believe it..
Concave Mirror – Object further than c
Color Code
P-ray
F-ray
C-ray
c
f
The image is real, inverted, and reduced.
Concave Mirror – Object at c
Color Code
P-ray
F-ray
C-ray
f
c
The image is real, inverted, and the same size as
the object.
Concave Mirror – Object between c and f
Color Code
P-ray
F-ray
C-ray
f
c
The image is real, inverted, and enlarged.
Concave Mirror – Object at focal point
Color Code
P-ray
F-ray
C-ray
c
f
NO IMAGE IS FORMED!!!
Concave Mirror – Object closer than f
Color Code
P-ray
F-ray
C-ray
f
c
The image is virtual, upright, and enlarged.
This is why concave mirrors with large focal
lengths are used as makeup mirrors!
Concave Mirrors: Summary
Object Location
Image Orientation
Image Size
Image Type
Beyond c
Inverted
Reduced
Real
At c
Inverted
Same as object
Real
Between c and f
Inverted
Enlarged
Real
At f
No image
No image
No image
Closer than f
Upright
Enlarged
Virtual
If the object is further than f, the image will be inverted and real.
If the object is closer than f, the image will be upright and virtual.
Convex Mirror – Object anywhere
Color Code
P-ray
F-ray
C-ray
f
c
The image is virtual, upright, and reduced.
Convex Mirrors: Summary
Object Location
Image Orientation
Image Size
Image Type
Anywhere
Upright
Reduced
Virtual
This is why convex mirrors are used for
seeing large areas at once!
Real vs Virtual Images
Real images are formed by actual light rays (not virtual rays).
They are able to be seen directly with the human eye, and can
also be projected onto a screen!
Virtual images are formed by virtual rays.
A virtual image is the appearance of light originating from a
certain location, although the light never actually did (it was
redirected by a mirror or lens to look like it did!)
When a virtual image is formed, it can be seen by the human eye.
However, it cannot be projected onto a screen!
What is a lens?
A lens is a piece of transparent material that is shaped such that the
outside is curved on at least one side.
There are many types of lenses, and the two that we will concentrate
on in this course are convex lenses and concave lenses.
Convex lens
Concave lens
The types of lenses that we will be learning about are
circular in curvature on both sides.
Convex Lens
focal point
c
Incoming rays that are parallel to the principal axis will all
pass through the focal point!
This type of lens is sometimes called a converging lens.
Focal point depends on n of lens and
medium that it is in!
Lenses actually have a focal point on both
sides.
f
f
We will be Working with Thin Lenses
This means that you don’t need to worry about light refracting as it enters and as it
leaves the lens. You only need to know how to use concepts to draw principal rays.
It also means that a light ray passing through the center of the lens (at any angle)
will pass directly through the lens, undeflected!
The thin lens assumption allows us to draw this ray.
With thick lenses, a more complex approach is required.
Principal Rays for Lenses!
The principal rays used to locate the image
formed by a lens are very similar to the ones
used with curved mirrors!
The concepts are also very similar.
Make sure to pay attention to the concepts, as
well as the specific rules for each ray.
P-Ray (Parallel Ray)
Emitted by the object, traveling parallel to the principal axis.
It is then refracted through the focal point!
f
f
F-Ray (Focal Ray)
Emitted by the object, traveling through the focal point.
It is then refracted parallel to the principal axis!
f
f
C-Ray (Center Ray)
Emitted by the object, traveling toward the center of the lens.
It passes through undeflected!
f
f
Concave Lens
antifocal point
Incoming rays that are parallel to the principal axis will
diverge directly away from the antifocal point!
This type of mirror is sometimes called a diverging lens.
P-Ray: Concave Version
Emitted by the object, traveling parallel to the principal axis.
It is then refracted directly away from the antifocal point!
f’
f’
F-Ray: Concave Version
Emitted by the object, toward the antifocal point on the other side
of the lens.
It is then refracted parallel to the principal axis!
f’
f’
C-Ray: Concave Version
Emitted by the object, traveling toward the center of the lens.
It passes through undeflected!
f’
f’
Concave Lens – Object at any location
Color Code
P-ray
C-ray
c
f
f
c
The image is virtual, upright, and reduced.
Virtual Images in Mirrors vs Lenses
For mirrors, a virtual image will
always be on opposite side as the
object. Convex mirrors always
produce virtual images.
f
c
Rays appear to
diverge from behind
the mirror.
For lenses, a virtual image will
always be on the same side as the
object. Concave lenses always
produce virtual images.
c
f
f
c
Rays appear to
diverge from in front
of the lens.
Concave Lenses: Summary
Object Location
Image Orientation
Image Size
Image Type
Anywhere
Upright
Reduced
Virtual
This is the same as for a convex mirror!
Converging lenses and converging mirrors have the same image properties.
Diverging lenses and diverging mirrors have the same image properties.
Convex Lens – Object further than c
Color Code
P-ray
F-ray
C-ray
c
f
f
c
The image is real, inverted, and reduced.
Real Images in Mirrors vs Lenses
For mirrors, a real image can
only be produced by a concave
mirror, and the image is on the
same side as the object.
c
f
Rays converge in
front of the mirror.
For lenses, a real image can only
be produced by a convex lens,
and the image is on the opposite
side as the object.
c
f
f
c
Rays converge behind
the lens.
Convex Lens – Object at c
Color Code
P-ray
F-ray
C-ray
c
f
f
c
The image is real, inverted, and the same size.
Convex Lens – Object between c and f
Color Code
P-ray
F-ray
C-ray
c
f
f
c
The image is real, inverted, and enlarged.
Convex Lens – Object at f
Color Code
P-ray
F-ray
C-ray
c
f
f
No image is formed!
c
Convex Lens – Object closer than f
Color Code
P-ray
F-ray
C-ray
c
f
f
c
The image is virtual, inverted, and enlarged.
You now have all of the tools necessary to locate
an image formed by any curved mirror or lens.
Geometric optics is covered on the AP test,
so you should go over this again in your AP
review book in the next few weeks.
Go forth and make me a proud physics teacher :)
(and get college credit for this course)
Convex Lenses: Summary
Object Location
Image Orientation
Image Size
Image Type
Beyond c
Inverted
Reduced
Real
At c
Inverted
Same as object
Real
Between c and f
Inverted
Enlarged
Real
At f
No image
No image
No image
Closer than f
Upright
Enlarged
Virtual
This is the same as for a concave mirror!
This is why convex lenses held close to an object make good
magnifying glasses!
Concave Lenses: Summary
Object Location
Image Orientation
Image Size
Image Type
Anywhere
Upright
Reduced
Virtual
This is the same as for a convex mirror!
Converging lenses and converging mirrors have the same image properties.
Diverging lenses and diverging mirrors have the same image properties.
Enlightening Concept!
A large lens is used to focus an image of an
object onto a screen. If the left half of the lens is
covered with a dark card, which of the following
occurs?
(A) The left half of the image disappears.
(B) The right half of the image disappears.
(C) The image becomes blurred.
(D) The image becomes dimmer.
(E) No image is formed.
Although principal rays help guide us to locate the image, we cannot forget
the important fact that each point on the object emits rays in all directions.
The lens is completely filled with rays from every point of the object!
(The image is also formed by infinite rays from the
middle of the object, the bottom of the object, etc.)
So, if we cover half of the lens...
The entire image would still exist!
However, less light would be forming the image.
Therefore the image would be dimmer.
Which three of the glass lenses above, when placed
in air, will cause parallel rays of light to converge?
(A) I, II, and III
(B) I, III, and V
(C) l, IV, and V
(D) II, III, and IV
(E) II, IV, and V
I, III, and V are more convex than concave –
they will cause light rays to converge.
II and IV are more concave than convex –
they will cause light rays to diverge.
Geometric Optics Equation #1
1 1 1
+ =
di do f
Applies to both mirrors and lenses.
di is the distance from the image to the mirror or lens
do is the distance from the object to the mirror or lens
f is the focal length of the mirror or lens
Focal length can be positive or negative!
Mirrors and lenses that have a focal point will have a
positive focal length.
Mirrors and lenses that have an antifocal point will
have a negative focal length.
Converging lenses and mirrors (concave mirrors and
convex lenses) have a positive focal length.
Diverging lenses and mirrors (convex mirrors and
concave lenses) have a negative focal length.
A Point of Possible Confusion
• Real images have a positive di
• Virtual images have a negative di
If you end up with a negative di when you do
the calculations, it means that a virtual image
is produced!
This applies to both mirrors and lenses, and
you must be consistent!
Whiteboard Problem Solving I
A postage stamp is placed 30 centimeters to the left
of a converging lens of focal length 60 centimeters.
Where is the image of the stamp located?
(A) 60 cm to the left of the lens
(B) 20 cm to the left of the lens
(C) 20 cm to the right of the lens
(D) 30 cm to the right of the lens
(E) 60 cm to the right of the lens
Whiteboard Problem Solving II
A concave mirror with a radius of curvature
of 1.0 m is used to collect light from a
distant star. The distance between the
mirror and the image of the star is nearly
(A) 0.25 m (B) 0.50 m (C) 0.75 m
(D) 1.0 m (E) 2.0 m
Solution!
A star is so far away that we can comfortably use
the approximation do = ∞!
This gives
1 1 1
+ =
di ¥ f
Since 1/∞ = 0, this results in di = f
Geometric Optics Equation #2
hi
di
=ho
do
hi is the height of the image
ho is the height of the object
A negative image height means that the image is inverted.
Memorize both of these equations
(don’t forget the negative sign!)
Attack of the Whiteboard
15 cm
5 cm
f’
f’
10 cm
10 cm
Where will the image be located and what will it look like?
do = 15 cm
f = -10 cm
1 1
1
+ =
di 15 -10
di = -6 cm
ho = 5 cm
hi
-6cm
=5 cm
15 cm
hi = 2 cm
f’
(Virtual image
6 cm from
lens)
(Inverted and
reduced image)
f’
Deep Whiteboard Thoughts!
do
ho
An object of height h0
is located at a distance
do from a plane mirror.
1 1 1
+ =
Using the mathematical models
and
di do f
hi
di
=- ,
ho
do
determine the location and height of the
image formed by the plane mirror!
Hint: What is the radius of curvature of a plane mirror?
do
fplane mirror = ∞
ho
1 1 1
+ = = 0!
di do ¥
di = -do
This means that the mirror will
produce a virtual image
(negative image distance) that
is equidistant from the mirror.
hi
di
=ho
do
Since di = -do 
-di / do = 1
Therefore hi / ho = 1
hi = ho
The image is the same height as
the object!