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1. Chapter 35
Mirrors
Lenses
Images

2. We will use geometrical optics: light propagates in straight
lines until its direction is changed by reflection or refraction.
When we see an objectdirectly, light comes to us straight from
the object.
When we use mirrors and lenses, we see light that seems to
come straight from an objectbut actually doesn’t.
Thus we see an image (of the object), which may have a
different position, size, or shape than the actual object.
Image Formation

3. Images Formed by Plane Mirrors
(the ray reaching your
eye doesn’t really come
from the image)
object
image
virtual image
But…. the brain thinks the ray came from the image.
When we use mirrors and lenses, we see light that seems to come
straight from the objectbut actually doesn’t. Thus we see an
image, which may have a different position, size, or shape than
the actual object.

4. Images Formed by Plane Mirrors
You can locate each point on the image with two rays:
1. A ray normal to the mirror
Image is reversed
front to back
object image

5. Images Formed by Plane Mirrors
You can locate each point on the image with two rays:
1. A ray normal to the mirror
2. The ray that reaches the observer’s eye
Image is reversed
front to back
object image

6. Images Formed by Plane Mirrors
object image
Image is reversed
(front to back)
You can locate each point on the image with two rays.

7. Images Formed by Plane Mirrors
object image
Image is reversed
(front to back)
You can locate each point on the image with two rays.

8. Images Formed by Plane Mirrors
object image
The distance from the image to the mirror equals
the distance from the object to the mirror: p = i
p i
Also, the height of
the image equals the
height of the object

9. Parabolic Mirrors
•Shape the mirror into a
parabola of rotation (In one
plane it has cross section
given by y = x
2
).
•All light going into such a
mirror, parallel to the para-
bola’s axis of rotation, is
reflected to pass through a
common point -the focus.
•What about the reverse?
•

10. •These present the concept of a focal point -
the point to which the optic brings a set of
parallel rays together.
•Parallel rays come from objects that are very
far away (and, after reflection in the parabolic
mirror, converge at the focal point or focus).
•Parabolas are hard to make. It’s much easier
to make spherical optics, so that’s what we’ll
examine next.
Parabolic Mirrors

11. To analyze how a spherical mirror works we draw
some special rays, apply the law of reflection where
they strike the spherical surface, and find out where
they intersect.
Spherical Mirrors
c
f
A ray parallel to the mirror axis reflects through the focal point f
A ray passing through the focus reflects parallel to the axis
A ray that strikes the center of the mirror reflects symmetrically
A ray passing through the center of curvature c, returns on itself

12. When the object is beyond c, the image is:
real (on the same side as the object), reduced,
and inverted.
Spherical Mirrors
c
f

13. c
f
Object between c and f.
Spherical Mirrors -Concave
Image is real, inverted, magnified

14. Object between f and the mirror.
Spherical Mirrors
c
f
Image is virtual, upright, magnified

15. c
The Mirror Equation
f
i
p
Here f = R / 2

16. c
f
Magnification
h
h’
The magnification is given by the ratio M = h’ / h = -i/p

17. Curved Mirrors
mirror equation
focal length
magnification
Sign conventions:
Distance in front of the mirror positive
Distance behind the mirror negative
Height above center line positive
Height below center line negative

18. Positive and Negative Mirrors
•You can fill a positive mirror with water.
•You can’t fill a negative mirror.
positive
mirror is
concave
negative
mirror is
convex

19. Image With a Convex Mirror
c
f
Here the image is virtual (apparently positioned behind
the mirror), upright, and reduced. Can still use the mirror
equations (with negative distances for f, c=R, and i).

20. A simple lens is an optical device which takes
parallel light rays and focuses them to a point.
This point is called the focus or focal point
The Simple Lens
Snell’s Law applied at each surface will show where
the light comes to a focus.
•

21. Each point in the image can be located using two rays.
Image Formation in a Lens
Ray tracing:
1. A ray which leaves the object parallel to the axis, is refracted to
pass through the focal point.
2. A ray which passes through the lens’s center is undeflected.
3. A ray passing through the focal point (on the object side) is
refracted to end up parallel to the axis.
f
f

22. Some Simple Ray Traces
2f
2f
f
f
2f
2f
f
f
Object between 2f and f
Image is inverted, real
enlarged.
Object between f and lens
Image is upright, virtual,
and enlarged.

23. Some Simple Ray Traces (diverging lens)
2f
2f
f
f
2f
2f
f
f
Object beyond 2f.
Image is upright,
virtual, reduced.
Object between
f and lens.
Image is upright,
virtual, reduced.
A ray parallel to the axis diverges such that
its extension passes through the focal point.

24. Sign Conventions
1. Converging or convex lens
focal length is positive
image distance is positive when on the other side
of the lens (with respect to object)
height upright is positive, inverted is negative
2. Diverging or concave lens
focal length is negative
image distance is always virtual and negative
(on the same side of the lens as the object)
height upright is positive, inverted is negative

25. The Thin Lens Equation
2f
2f
f
f
f
p i
h’
h
M = h’/h = -i/p Magnification
1/p+ 1/i= 1/fThe thin lens equation

26. About the Thin Lens Formula
•When p = f, i = infinity
•When p = 2f , i = 2f and the magnification is 1.
•When f > p > 0, i is negative
–This means that the image is virtual, and so it is on the
same side of the lens as the object.
•If f < 0, i is always negative
–A negative lens can not produce a real image. It
always produces a virtual image.
1/p + 1/i = 1/f

27. The lens formula gives the image distance as a function of the
object distance and the focal distance [1/f -1/p = 1/i]
The lensmaker’s formula gives the focal distance f as a function
of R
1and R
2, the radii of curvature of the two surfaces of the
lens.
The Lensmaker’s Formula

11
n1
1
R
1
R
1
f
n1
1
R
1
R
1 2
1 2



 






 






Lensmaker’s Formula

28. The Eye: A Simple Imager
•A simple lens focuses
the light onto the retina
--the photosensor
•The retina sends
signals to the brain
about which sensor is
illuminated, what color
the light is, and how
much of it there is.
•The brain interprets.
Your eye’s lens is a simple
refracting lens which you can
deform to change focus.
The retina senses the light.

29. The Eye: Near & Farsightedness
Far-sighted: Near-sighted:
Eye too short:
correct with a
converging lens
Eye too long:
correct with a
diverging lens

30. Image Forming Instruments
•Cameras are much like the eye except for
having a shutter and better lenses.
•Binoculars and telescopes create magnified
images of distant objects.
•Microscopes create magnified images of
very small objects.

31. The UCF Robinson Observatory
The telescope here is a 66 cm (26 in) dia.
Schmidt-Cassegrain reflecting telescope.
Telescopes are described by their diameter since that describes its
ability to collect light from distant stars and glaxies; and that’s more
important than magnification.
Florida is not ideal for most observational astronomy. Why?

32. Image-Forming Instruments: the Telescope
When we look at distant objects, we judge their sizes
from their angular size. In the case of stars, what we
observe is their angular separation.
a
A telescope magnifies the angular size
(or separation) of objects.

33. The Telescope
f
o
a
“Objective”
f
o
The “objective” lens first creates an image, in the focal plane,
of a point at infinity.

34. The Telescope
f
o
a
“Objective”
f
o
The “objective” lens first creates an image, in the focal plane,
of a point at infinity. The “eypiece” is placed f
o+ f
e from the
objective, so that it produces parallel rays into the eye, at angle b.
f
e
f
e
“Eyepiece”
EYE
b

35. The Telescope
f
o
a
“Objective”
f
o f
e
f
e
“Eyepiece”
EYE
b
The eye sees an image at infinity, but at an angle of binstead of a.
The magnification is therefore:M = b/a = f
o /f
e.
h
tan b/ tan a= (h/f
e)/(h/f
o)