!"#$%&'()*+$,-$.'/#0'#$/1$",1203$*4,$#5#0/031$*,$"#)6$
789$:/1',5#;$789<$-(*(;#$/0$.'/#0'#$
=<,>#;*$.'"()*?$!"#&*;#@
Mon. 1 March @ 5:45pm
!"#$#%"&'$()&"*+&*,-(./*0",123('+4(5"&2#6"#$#%3!
Wed. 3 March@ 5:45pm!
.#0781*2()&"-(5'1/-(9/3,"&,(:(;,12#+#03-('+4()1'1,
Wednesday, February 24, 2010
24
./30$(6$!8AB7C
"#$%!&'!#%!()&*!+,-../
0)*!1)*2!#%3)*1-4)%!+)%5-+56
7-&*22%!8-#.,2(!9!:;:<=;>?
7-&*22%@8-#.,2(9&1-%#5)A-B+-
Wednesday, February 24, 2010
25
Week of Feb 23-25
Experiment 3: e/m of electron
Midterm Review in Class
Monday, March 1 - send questions!
Midterm Exam
Wednesday, March 3, 7-9 pm
Chapters 18 - 22, 24, 25
20 multiple choice questions
Formula sheet provided
Wednesday, February 24, 2010
26
Seating for PHYS 1030 Midterm Exam
Wednesday, March 3, 7 - 9 pm
20 multiple choice questions
Formula sheet provided
From-To
Room
A - Fe
100 Fletcher Argue
Fl - Pa
200 Fletcher Argue
Pe - U
206 Tier
V-Z
213 Tier
Wednesday, February 24, 2010
27
Essence of chapter 24
• Visible light, x-rays, gamma-rays, radio waves, infrared, ultraviolet...
are all electromagnetic waves, contain electric and magnetic fields
• Electromagnetic waves travel at speed c = 3 ! 108 m/s in vacuum
• The relation between speed, frequency and wavelength is: c = f!
Wednesday, February 24, 2010
28
Chapter 25: Reflection of Light
• Wavefronts and rays
• Reflection of light, formation of image in a plane mirror
• Omit sections 4, 5, 6 (spherical mirrors, mirror equation)
Wednesday, February 24, 2010
29
Waves originating from a point source
The waves move out from the
source, travelling at the same
speed in all directions.
The wavefronts are surfaces on
which the wave has the same
phase. For example, where the
electric field of a light wave has
its peak value.
Source of wave
The distance between
wavefronts is the wavelength, λ.
The rays travel at right angles to
the wavefronts.
Wednesday, February 24, 2010
Source of wave close by
so the wavefronts are
curved as they diverge
from the source.
30
!
Source of wave
Source of wave far
away so that the
wavefronts are flat to
a good approximation
and the rays are
parallel – “plane waves”.
Wednesday, February 24, 2010
!
31
Specular reflection of light
“Specular reflection”, as
from a mirror.
Angle of incidence = angle of
reflection:
!i = !r
nd
ays a e
r
d
e
plan
flect
a
e
n
r
i
d
e
nt an mirror li
e
d
i
c
e
in
The
to th
l
a
m
or
the n
– the law of reflection
Wednesday, February 24, 2010
32
Diffuse reflection
The surface is irregular so that, although the law of reflection holds for
each ray, the rays are not all reflected in the same direction. Example,
reflection of light from paper, or from any surface that is not shiny.
Wednesday, February 24, 2010
33
Corner Reflector
Angle of incidence is 90º – "1
Incoming ray
θ1
Total deflection of ray by the two mirrors
θ1
θ1
Ray deflected at mirror by 2"1
= 2"1 + (180º – 2"1)
= 180º, whatever the angle "1
90º
90º – θ1
Outgoing ray
Mirrors
90º – θ1
90º – θ1
Ray deflected at mirror by
2(90º - "1) = 180º – 2"1
Add a third mirror at
right angles to these two
for rays not travelling in
the plane of the screen
Wednesday, February 24, 2010
34
The image formed by a plane mirror
The image is:
• the right way up (upright)
• the same size as the object
• the same distance behind the mirror
as the object is in front
• left and right are reversed
• virtual –"cannot show the image on a
screen
Wednesday, February 24, 2010
35
Formation of image by a plane mirror
The virtual image –
where the light appears
to be coming from
Wednesday, February 24, 2010
36
Formation of image by a plane mirror
A number of rays from the same point on the object hit the
mirror at different angles, are reflected according to the law
of reflection and reach the eye.
The light rays appear to come from the
“virtual image” which is at the same
distance behind the mirror as the
object is in front.
Wednesday, February 24, 2010
37
Image distance = object distance
At the mirror: angle of incidence = angle of reflection
!="
So, !1 = !2 and di = do
(do = h tan β1, di = h tan β2)
That is, the image is the same
distance behind the mirror as the
object is in front of it.
h
Wednesday, February 24, 2010
38
Prob. 25.6/2: A person whose eyes are 1.7 m above the floor stands in
front of a plane mirror. The top of her head is 0.12 m above her eyes.
a) What is the height of the shortest mirror in which she can see her
entire image?
b) How far above the floor should
the bottom edge of the mirror
be placed?
0.85 m
1.7 m
a) 91 cm
b) 85 cm off floor
Wednesday, February 24, 2010
0.85 m
39
Clicker Question
The drawing shows a light ray undergoing multiple reflections from
a mirrored corridor. The walls of the corridor are either parallel or
perpendicular to one another. If the initial angle of incidence is
35°, what is the angle of reflection when the ray makes its last
reflection?
A) 25o
B) 35o
C) 45o
D) 55o
E) 65o
o
o
90
35o
5
-3
90o
35o
D) 55o
Wednesday, February 24, 2010
40
Clicker Question:
A wave front __________
A) is a surface on which all points of the wave are in the same phase of
motion.
B) is always a plane surface.
C) is parallel to a ray.
D) is always a spherical surface.
E) is a surface that contains one cycle of the wave.
Ans: A)
Wednesday, February 24, 2010
41
Clicker Question:
When diffuse reflection from a surface occurs, __________
A) an individual ray of light does not obey the law of reflection.
B) there are no reflected rays.
C) the reflected rays are parallel to each other.
D) the reflected rays are not parallel to each other.
Ans: D)
Wednesday, February 24, 2010
42
Clicker Question:
The drawing shows a top view of an object to the right of a plane mirror.
An observer looks into the mirror. At what location, A, B, C, or D, does the
observer see the image?
A) A
B) B
C) C
D) D
E) The observer does not see an
image because the observer is
closer to the mirror than is the
object.
Ans: A)
Wednesday, February 24, 2010
43
Clicker Question:
A friend is standing 2 m in front of a plane mirror. You are standing 3 m
directly behind your friend. What is the distance between you and the
image of your friend?
A) 2 m
B) 10 m
C) 3 m
D) 5 m
E) 7 m
3m
You
2m
Friend
Image of Friend
Mirror
Ans: E) 2 + 2 + 3 m
Wednesday, February 24, 2010
44
Prob. 25.5/5: What is the angle θ?
90º– 35º = 55º
180º– (25º+120º) = 35º
65º
90º–65º = 25º
Wednesday, February 24, 2010
45
Prob. 25.9/36: A ray of light strikes a mirror at 45º. The mirror is then rotated
by 15º into the position shown in red, while the incident ray is kept fixed.
a) Through what angle φ does the reflected ray rotate?
b) What is the answer if the initial angle of incidence is 60º instead of 45º?
New position
of normal
15º
a) 300, b) 300
Wednesday, February 24, 2010
46
Prob. 25:4/43
Suppose that you are walking with a velocity of +1.5 m/s directly toward a
stationary plane mirror. What is the velocity of your image relative to
you? The direction in which you walk is the positive direction.
You
Image
Mirror
Ans: 3 m/s to left
Wednesday, February 24, 2010
47
What is the angle θ between the incident and outgoing rays?
Angle of
incidence = "2
θ1
! 2!2
θ1
α
2!1
! Angle of incidence = "1
! + " + 50◦ = 180◦, so ! + " = 130◦
Also, ! + "1 = # + "2 = 90◦
! = 2!1 + 2!2
so (! + "1) + (# + "2) = 180◦
Therefore, (! + ") + (#1 + #2) = 180◦
→ ! = 100◦
130◦ + !/2 = 180◦
Wednesday, February 24, 2010
48
Multiple reflections
3 3
(image 1 reflected
in mirror 2)
1
2
3
1
Wednesday, February 24, 2010
3# (image 2 reflected
in mirror 1)
2
49
At what angle must the laser be fired from P toward mirror C to hit
the upper left corner at X?
B
X
Image of X in C
L
L
C
L
A
Light paths can be
reversed – light
travelling from X to P
follows the same path
and the light appears
to come from C
L
Aim the laser toward
the image of X in
mirror C.
tan ! =
"
L/2
L
2
=
L/2 + L 3
! = 33.7◦
Wednesday, February 24, 2010
50
Summary of Chapter 25
• Specular and diffuse reflectors
• Angle of incidence = angle of reflection
• Formation of an image by a plane mirror – virtual image
• In a plane mirror, the image is the same distance behind
the mirror as the object is in front
Wednesday, February 24, 2010
51