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4/5/2017
AP PHYSICS 2
PLANE MIRRORS
UNIT 6
Geometric and
physical optics
CHAPTER 22
Mirrors and
lenses
Plane mirrors
 The simplest mirror is a
plane mirror—a flat,
reflective surface, often
consisting of a metal
film covered in glass.
Plane mirrors
s
s’
PLANE MIRROR
 The image of the real object seen in the
mirror is located where light reflected
from the mirror to the eye of the observer
seems to originate.
 This perceived image is behind the
mirror and not on the surface of the
mirror.
 Using the ray diagram, we find that the
image is exactly the same distance behind
the plane mirror as the object is in front of
it.
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Plane mirror virtual image
What does the image look like?
 The virtual image formed by a plane mirror will be
 A plane mirror produced a virtual image
that is the same distance behind the
mirror as the object is in from of it.
 The same size as the object.
 Equidistant from the mirror perpendicularly.
 Flipped left-to-right relative to the object (mirror
image)
S
S’
 VIRTUAL: The reflected light reaching
your eyes appears to originate from the
image behind the mirror. But no light
actually leaves that image, you see light
h
h’
object
virtual image
mirror
reflected from the mirror.
CURVED MIRRORS
CURVED MIRRORS
 A curved mirror is cut from a spherically
shaped piece of glass backed by a metal
film.
CONCAVE MIRROR
Focal length
Center of curvature
 Due to its geometry, a circularly curved
mirror has a focal length that is one half
of its radius of curvature.
𝑐
𝑓=
2
Focal point
f
c
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Principal Rays (or Guiding Rays)
normal
f
Although there are essentially an infinite number
of rays emanating from the object, we can use
three principal rays to help us determine the
location of an image produced by a curved
mirror.
c
And don’t forget, the center of curvature
will show you where to draw the normal
line when a ray reflects from a curved
mirror!
c
CONCAVE MIRROR
f
Real Images
 Rather than a virtual image (which is formed
by virtual rays), a real image is formed by real
rays!
F-ray
C-ray
P-ray
Inverted
Reduced
Real
 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.
Convex mirrors
 Convex mirrors are
used as passengerside rearview
mirrors and to
provide visibility at
blind spots, such as
hallway corners and
driveway exits.
CONVEX MIRROR
Center of
curvature
Focal point
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CONVEX MIRROR
P-ray
F-ray
C-ray
Upright
Reduced
Virtual
THE MIRROR EQUATION
CURVED MIRRORS
VOCABULARY
 f - focal length
 c - center of curvature
 s - distance from the object to the
mirror.
 s’ - distance from the image to the
mirror.
 h - height of the object.
 h’ - height of the image.
 m - magnification of the image
THE MIRROR EQUATION
 The focal length is positive for concave
mirrors and negative for convex mirrors.
+
=
MAGNIFICATION
• Ratio of the image height (h’) and object
height (h)
 The image distance is positive for real
images and negative for virtual images.
IMAGE FINDINGS
 Image orientation:
 Upright, inverted
 Image size:
 Enlarged, reduced, same size
=
 Image type:
 Real, virtual
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Concave Mirrors: Summary
Convex Mirrors: Summary
Object Location
Image Orientation
Image Size
Image Type
Beyond c
Inverted
Reduced
Real
Object Location
Image Orientation
Image Size
Image Type
At c
Inverted
Same as object
Real
Anywhere
Upright
Reduced
Virtual
Between c and f
Inverted
Enlarged
Real
At f
No image
No image
No image
Closer than f
Upright
Enlarged
Virtual
This is why convex mirrors are used for seeing
large areas at once!
 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.
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!
LENSES
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!
Qualitative analysis of lenses
 A lens is a piece of glass or other
transparent material with two curved
surfaces that produces images of objects
by changing the direction of light through
refraction.
CONVEX LENS
Center of
curvature
Focal point
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CONVEX LENS
 A convex lens made of
glass is similar to a
concave mirror where
incident rays parallel to
the principal axis
intersect at a focal
point after passing
through the lens.
 How the rays
converge depends
on the curvature of
the surface of the
lens.
CONVEX LENS
F-ray
Inverted
Reduced
Real
P-ray
Photography and cameras
 Light from an object
enters the camera
through the lens,
which focuses the
light on a surface
that has lightsensitive properties
(an image sensor).
Light field photography
 In light field photography, the image sensor
records all the light entering the camera, not just
the light that would produce a sharp image on
the focal plane.
 A photographer can choose an object to focus
on after the picture has been taken, because
the camera effectively focuses on all objects at
once.
c
f
C-ray
Seeing a sharp image on a screen
 A screen must be
placed where the
image is located to
view a sharp image.
f
c
CONCAVE LENS
Center of
curvature
Focal
point
Focal point
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CONCAVE LENS
CONCAVE LENS
 For concave lenses, light seems to diverge
from a single point on the axis—the virtual
focal point.
P-ray
F-ray
C-ray
THIN LENS EQUATION
c
f
f
c
Upright
Reduced
Virtual
THIN LENS EQUATION
 A thin lens has a radii of curvature much
larger than the size of the lens.
 The focal length f is positive for convex
lenses and negative for concave lenses.
 The image distance s’ is positive for real
images and negative for virtual images.
=
+
Linear magnification in lenses
 Lenses can produce images that are larger
or smaller in size than the original objects.
=
Objects far away from the lens
 If an object is extremely far away along
the principal axis, we can assume that
rays from the object reaching the lens are
parallel to the principal axis.
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Convex Lenses: Summary
Concave Lenses: Summary
Object Location
Image Orientation
Image Size
Image Type
Beyond c
Inverted
Reduced
Real
Object Location
Image Orientation
Image Size
Image Type
At c
Inverted
Same as object
Real
Anywhere
Upright
Reduced
Virtual
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 convex mirror!
This is the same as for a concave mirror!
Converging lenses and converging mirrors have the same image properties.
This is why convex lenses held close to an object make good
magnifying glasses!
Diverging lenses and diverging mirrors have the same image properties.
Lenses with water
Ray diagrams for various lenses
Ray diagrams for various lenses
Optics of the human eye
 Light from an object enters the cornea and
passes through a transparent lens.
 An iris in front of the lens widens or narrows, like
the aperture on a camera that regulates the
amount of light entering the device.
 The retina plays the role of the film.
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Optics of the human eye
 When the eye looks
at distant objects,
muscles around the
lens of the eye relax,
and the lens
becomes less
curved.
 As the object moves
closer, the eye
muscles contract,
increasing the
curvature of the lens
and reducing the
focal length.
Corrective lenses
 The two most common
vision abnormalities
corrected with lenses
are myopia
(nearsightedness) and
hyperopia
(farsightedness).
Corrective lenses (Cont'd)
LENSES
PRACTICE
Conceptual Exercise 22.1
 You place a lamp in front of a mirror and
tilt it so that the top and the bottom of the
lamp are at different distances from the
mirror, at the position shown. Where do
you see the image of the lamp produced
by the mirror?
Conceptual Exercise 22.3
 You hold a convex mirror 0.7R behind a
pencil.
A. Approximately where is the image of
the pencil?
B. What are the properties of the image?
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Example 22.4
 You place a candle 0.80 m from a concave
mirror with a radius of curvature of 0.60
m. Where should you place a paper screen
to see a sharp image of the candle?
Example 22.5
 A friend's face is 0.60 m from a convex
mirror with a 0.50-m radius. Where does
the image of her face appear to you when
you look at the mirror?
1 1 1
+ =
𝑆 𝑆′ 𝑓
1
1
1
=
−
𝑆′ 0.3 0.8
1 1 1
+ =
𝑆 𝑆′ 𝑓
1
1
1
=
−
𝑆′ −0.25 0.6
1 1 1
= −
𝑆′ 𝑓 𝑆
𝑆 ′ = 0.48 𝑚
1 1 1
= −
𝑆′ 𝑓 𝑆
𝑆 ′ = −0.176 𝑚
Example 22.6
 You use a concave mirror with a radius of
curvature of 0.32 m for putting on makeup or
shaving. When your face is 0.08 m from the
mirror, what are the image size and
magnification
of
a
0.0030-m-diameter
birthmark on your face?
1 1 1
+ =
𝑆 𝑆′ 𝑓
1
1
1
=
−
𝑆′ 0.16 0.08
1 1 1
= −
𝑆′ 𝑓 𝑆
𝑆 ′ = −0.16 𝑚
WHITEBOARD - LENSES
 You take a picture of a carpenter ant with an old
fashioned camera with a lens 18 cm from the
film.
 a) At what places can the 4.0 cm focal length
convex camera lens be located so you see a
sharp image of the ant on the film?
 b) What is the magnification of the ant?
 c) If the length of the carpenter ant is 2.5 cm,
what is the size of the image?
Upright
Enlarged
Virtual
𝑆′
𝑚=−
𝑆
𝑚=−
−0.16′
0.08
h′ = 𝑚 ∙ ℎ
𝑚=2
h′ = 2 ∗ 0.003
ℎ′ = 0.006 𝑚
ℎ′ = 0.6 𝑐𝑚
1 1 1
+ =
𝑆 𝑆′ 𝑓
1 1 1
= −
𝑆 𝑓 𝑆′
1 1 1
= −
𝑆 4 18
𝑆 = 5.14 𝑐𝑚
𝑚=−
𝑆′
𝑆
𝑚=−
18
5.14
Inverted
Enlarged
Real
𝑚 = −3.5
h′ = 𝑚 ∙ ℎ
h′ = −3.5 ∗ 2.5
ℎ′ = −8.75 𝑐𝑚
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WHITEBOARD - LENSES
 A secret agent uses a camera with 5 cm focal
length lens to photograph a document whose
height is 10 cm.
 a) What is the magnification so that an image 2.5
cm high is produced on the screen? (note: the
real image is inverted)
 b) At what distance from the lens should the
agent hold the camera?
a)m=-0.25, b) s=25 cm
WHITEBOARD - LENSES
 A 20 cm tall bottle of water is placed in front of
concave lens of focal length 30 cm.
 a) At what distance must the bottle of water be
placed so the image will be virtual and 0.25 times
the original size?
 b) What is the distance to the image?
 c) what is the height of the image?
a)S=90 cm, S’=-22.5 cm, h’=5 cm
WHITEBOARD - LENSES
 You use a convex lens of focal length
+10.0 cm to look at a tiny insect on a
book page. The lens is 5.0 cm from the
paper.
A. Where is the image of the insect?
B. If the insect is 1.0 cm in size, how
large is the image?
Telescopes
 A common
telescope has two
convex lenses
separated by a
distance slightly
less than the sum
of their focal
lengths.
a)S’=-10 cm, B) m=2, h’=2 cm
WHITEBOARD - TELESCOPES
 A 1.2-m-tall lion stands 50 m from the
first lens of a telescope.
 Locate the image of the Lion created by
the first lens (f=20 cm).
 Image, magnification, height of the image.
1 1 1
+ =
𝑆 𝑆′ 𝑓
1 1 1
= −
𝑆′ 𝑓 𝑆
1
1
1
=
−
𝑆′ 20 5000
𝑆 ′ = 20.08 𝑐𝑚
𝑚=−
𝑆′
𝑆
𝑚=−
20.08′
5000
Inverted
Reduced
Real
𝑚 = −0.004
h′ = 𝑚 ∙ ℎ
h′ = −0.004 ∗ 120
ℎ′ = 0.48 𝑐𝑚
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WHITEBOARD - TELESCOPES
 A 1.2-m-tall lion stands 50 m from the first
lens of a telescope.
 Locate the NEW image of the Lion created
by the second lens (f=5 cm).
 Image, magnification, height of the image.
1 1 1
+ =
𝑆 𝑆′ 𝑓
𝑚=−
𝑆′
𝑆
1 1 1
= −
𝑆′ 𝑓 𝑆
𝑚=−
−38.10′
4.42
1 1
1
= −
𝑆′ 5 4.42
𝑚 = 8.62
𝑆 ′ = −38.10 𝑐𝑚
WHITEBOARD - TELESCOPES
LENS 1
LENS 2
S = 5000 cm
F = 20 cm
S’ =20.08 cm
S = 4.42 cm
F = 5 cm
S’ =-38.1 cm
m = -0.004
h = 120 cm
h’ = 0.482 cm
m = 8.62
h = 0.482 cm
h’ = 4.155 cm
Angular magnification
 The angular magnification M of an optical
system is defined as:
upright
Enlarged
Virtual
h′ = 𝑚 ∙ ℎ
h′ = 8.62 ∗ 0.48 cm
ℎ′ = 4.15 𝑐𝑚
Angular magnification and
magnifying glasses
 The impression of an object's size is
quantified by its angular size:
Angular size of the object as seen
with the unaided eye
 The maximum angular
size of an object viewed
by the unaided eye is:
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