Drawing Ray Diagrams

1
Drawing Ray Diagrams

• Concave and Convex Mirrors and Double Concave and
  Double Convex Lenses
• By Vincent Sapone

2
Concave Mirror

1. First ray goes parallel to the mirror and then
   reflects back down through the focus.
2. Second Ray goes through the focus and into the
   mirror and then reflected back parallel to axis.
3. Ray drawn to center of lens and reflects back
   downwards at an equal angle (symmetric)
4. If at or within the focal length you an draw a
   line perpendicular to the mirror so that it goes
   back through itself and into the center of
   curvature (R 2f). This can replace the second
   ray above which now cannot be drawn.

3
Concave Mirror

• Rule 1 First ray goes parallel to the mirror and
  then reflects back down through the focus.

F
C
4
Concave Mirror

• Second Ray goes through the focus and into the
  mirror and then reflected back parallel to axis.

Ray 1
F
C
Ray 2
5
Concave Mirror

• Ray drawn to center of lens and reflects back
  downwards at an equal angle (symmetric)

Ray 1
F
C
Ray 2
Ray 3
6
Concave Mirror

• Lets draw ray diagrams for the following cases
• do f
• fltdoltR
• dogtR
• dogtf
• doR

7
Concave Mirror

• Object is on the Focal Point
• Do F

8
Concave Mirror
F
C
9
Concave Mirror

• do f

F
C
10
Concave Mirror

• do f

F
C
11
Concave Mirror

• do f

F
C
12
Concave Mirror

• do f

Ray 1
F
C
13
Concave Mirror

• do f

Cannot Draw 2nd ray from Object through focus.
Ray 1
F
C
14
Concave Mirror

• do f

Cannot Draw 2nd ray from Object through focus.
Ray 1
F
C
Ray 3
15
Concave Mirror

• do f

Cannot Draw 2nd ray from Object through focus.
Ray 1
F
C
They do not Cross No Image!
Ray 3
16
Concave Mirror

• do f

Cannot Draw 2nd ray from Object through focus.
Ray 1
Ray 4
F
C
Even a fourth ray will not cross the others.
They do not Cross No Image!
Ray 3
17
Concave Mirror

• Object is Between Focal Point and Center of
  Curvature
• fltdoltR

18
Concave Mirror

• fltdoltR

F
C
19
Concave Mirror

• fltdoltR

Ray 1
F
C
20
Concave Mirror

• fltdoltR

Ray 1
F
C
Ray 2
21
Concave Mirror

• fltdoltR

Ray 1
F
C
Ray 2
Ray 3
22
Concave Mirror

• fltdoltR

Ray 1
F
C
Ray 2
Real Image Magnified
Ray 3
23
Concave Mirror

• Object distance is Greater than or outside the
  radius of curvature (C)
• dogtR

24
Concave Mirror

• dogtR

F
C
25
Concave Mirror

• dogtR

Ray 1
F
C
26
Concave Mirror

• dogtR

Ray 1
F
C
Ray 2
27
Concave Mirror

• dogtR

Ray 1
F
C
Ray 2
Ray 3
28
Concave Mirror

• dogtR

Ray 1
F
C
Ray 2
Image Real and Demagnified
Ray 3
29
Concave Mirror

• Object distance is smaller than or within the
  radius of curvature (C)
• doltf

30
Concave Mirror

• doltf

F
C
31
Concave Mirror

• doltf

Ray 1
F
C
32
Concave Mirror

• doltf

Ray 1
F
C
Ray 2
33
Concave Mirror

• doltf

Ray 1
F
C
Ray 3
Ray 2
34
Is there an Image? What do you think?
35
Concave Mirror

• doltf

Ray 1
F
C
Ray 3
Ray 2
36
Concave Mirror

• doltf

Ray 1
F
C
Ray 3
Ray 2
37
Concave Mirror

• doltf

Ray 1
F
C
Ray 3
Ray 2
38
Concave Mirror

• doltf

Ray 1
F
C
Image is Virtual, Right side up and Magnified
Ray 3
Ray 2
39
Compare this to the First Example with no
Image. Why Didnt that one have a virtual image?
40
Concave Mirror

• do f

Cannot Draw 3rd ray from Object through focus.
Ray 1
Ray 2
F
C
Ray 4
41
The Rays appear to be pretty much parallel.
Therefore they will not cross on either side so
there is no image, virtual or real.
42
Concave Mirror

• Object distance is equal to radius of curvature
• do R

43
Concave Mirror

• do R

F
C
44
Concave Mirror

• do R

F
C
45
Concave Mirror

• do R

Ray 1
F
C
46
Concave Mirror

• do R

Ray 1
F
C
47
Concave Mirror

• do R

Ray 1
Ray 2
F
C
48
Concave Mirror

• do R

Ray 1
Ray 2
F
C
49
Concave Mirror

• do R

Ray 1
Ray 2
F
C
Ray 3
50
Concave Mirror

• do R

Ray 1
Ray 2
F
C
Ray 3
51
Concave Mirror

• do R

Ray 1
Ray 2
F
C
Ray 3
Image is Real, upside down and demagnified.
52
Cosmetics

• This is a cosmetics mirror.
• Up close (do ltf) you are right side up and appear
  magnified.
• As you move away your image will eventually
  invert and become smaller.

53
Convex Mirror

1. First ray goes parallel to the mirror and then
   reflects back up (dotted image line goes through
   focus on the other side).
2. Second Ray is aimed directly at the center of
   curvature on the other side but once it hits the
   mirror it reflects back through itself with the
   dotted image line going through C).
3. Ray drawn aimed at focus on the other side and
   reflect off the mirror parallel to the axis
   (dotted line drawn parallel in the other
   direction)

54
Convex Mirror

• We shall now draw Convex Mirror Diagrams for the
  following cases
• dogtR
• fltdogtR
• doltf

55
Convex Mirror

• Distance to Object is greater than radius of
  curvature
• do gt R

56
Convex Mirror
F
C
57
Convex Mirror
dogtR
F
C
58
Convex Mirror
dogtR
F
C
59
Convex Mirror
dogtR
F
C
60
Convex Mirror
dogtR
Ray 1
F
C
61
Convex Mirror
dogtR
Ray 1
F
C
62
Convex Mirror
dogtR
Ray 1
F
C
63
Convex Mirror
dogtR
Ray 1
F
C
64
Convex Mirror
dogtR
Ray 1
Ray 2
F
C
65
Convex Mirror
dogtR
Ray 1
Ray 2
F
C
66
Convex Mirror
dogtR
Ray 1
Ray 2
F
C
67
Convex Mirror
dogtR
Ray 1
Ray 2
Ray 3
F
C
68
Convex Mirror
dogtR
Ray 1
Ray 2
Ray 3
F
C
69
Convex Mirror
dogtR
Ray 1
Image Virtual, Right Side up Demagnified
Ray 2
Ray 3
F
C
70
Convex Mirror

• Distance to Object is in between focus and radius
  of curvature.
• fltdoltR

71
Convex Mirror
FltdoltR
F
C
72
Convex Mirror
FltdoltR
F
C
73
Convex Mirror
FltdoltR
F
C
74
Convex Mirror
FltdoltR
F
C
75
Convex Mirror
FltdoltR
Ray 1
F
C
76
Convex Mirror
FltdoltR
Ray 1
F
C
77
Convex Mirror
FltdoltR
Ray 1
F
C
78
Convex Mirror
FltdoltR
Ray 2
Ray 1
F
C
79
Convex Mirror
FltdoltR
Ray 2
Ray 1
F
C
80
Convex Mirror
FltdoltR
Ray 2
Ray 1
F
C
81
Convex Mirror
FltdoltR
Ray 2
Ray 1
F
C
82
Convex Mirror
FltdoltR
Ray 2
Ray 1
Ray 3
F
C
83
Convex Mirror
FltdoltR
Ray 2
Ray 1
Ray 3
F
C
84
Convex Mirror
FltdoltR
Ray 2
Ray 1
Ray 3
F
C
85
Convex Mirror
fltdoltR
Ray 2
Image Virtual, right side up, demagnified.
Ray 1
Ray 3
F
C
86
Convex Mirror

• Distance to Object less than the distance to the
  focus
• doltf

87
Convex Mirror
doltf
F
C
88
Convex Mirror
doltf
F
C
89
Convex Mirror
doltf
F
C
90
Convex Mirror
doltf
F
C
91
Convex Mirror
doltf
F
C
92
Convex Mirror
doltf
Ray 1
F
C
93
Convex Mirror
doltf
Ray 1
F
C
94
Convex Mirror
doltf
Ray 1
F
C
95
Convex Mirror
doltf
Ray 1
F
C
96
Convex Mirror
doltf
Ray 1
Ray 2
F
C
97
Convex Mirror
doltf
Ray 1
Ray 2
F
C
98
Convex Mirror
doltf
Ray 1
Ray 2
F
C
99
Convex Mirror
doltf
Ray 1
Ray 2
Ray 3
F
C
100
Convex Mirror
doltf
Ray 1
Ray 2
Ray 3
F
C
101
Convex Mirror
doltf
Ray 1
Ray 2
Ray 3
F
C
102
Convex Mirror
doltf
Image Virtual, right side up, demagnified
Ray 1
Ray 2
Ray 3
F
C
103
Convex or Converging Lens

• For the Following Conditions
• dof fltdolt2f dogt2f
  doltf do2f
• Note the lens thickness is to be assumed small so
  that refraction is not a concern.

104
Convex Lens Rules

• First ray is drawn parallel to principal axis
  until it strikes the center of the mirror. It
  then converged down on through the focal point on
  the other side of the lens.
• The second ray has a straight line drawn from the
  object to the focus to the lens on the same side
  and then it refracts parallel to the principal
  axis on the other side.
• The third ray is usually drawn in a direction
  from the object through the center of the lens
  itself into the other side.

105
Convex or Converging Lens
Ray 1
F
F
First ray is drawn parallel to principal axis
until it strikes the center of the mirror. It
then converged down on through the focal point on
the other side of the lens
106
Convex or Converging Lens
Ray 1
F
F
The second ray has a straight line drawn from the
object to the focus to the lens on the same side
and then it refracts parallel to the principal
axis on the other side.
Ray 2
107
Convex or Converging Lens
Ray 1
F
F
Ray 3
The third ray is usually drawn in a direction
from the object through the center of the lens
itself into the other side.
Ray 2
108
Convex or Converging Lens

• Distance to Object is in between focus and radius
  of curvature.
• dof

109
Convex or Converging Lens
dof
F
F
110
Convex or Converging Lens
dof
F
F
111
Convex or Converging Lens
dof
F
F
112
Convex or Converging Lens
dof
Ray 1
F
F
113
Convex or Converging Lens
dof
Ray 1
F
F
Ray 2
114
Convex or Converging Lens
dof
Ray 1
F
F
Cannot Draw Ray Three Through Focus as the object
is on the focus.
Ray 2
115
Convex or Converging Lens
dof
Ray 1
No Image!
F
F
Cannot Draw Ray Three Through Focus as the object
is on the focus.
Ray 2
116
Convex or Converging Lens
fltdolt2f
F
F
117
Convex or Converging Lens
fltdolt2f
F
F
118
Convex or Converging Lens
fltdolt2f
Ray 1
F
F
119
Convex or Converging Lens
fltdolt2f
Ray 1
F
F
Ray 2
120
Convex or Converging Lens
fltdolt2f
Ray 1
F
F
Ray 3
Ray 2
121
Convex or Converging Lens
fltdolt2f
Ray 1
F
F
Ray 3
Ray 2
122
Convex or Converging Lens
fltdolt2f
Ray 1
Real Image, Inverted and Magnified
F
F
Ray 3
Ray 2
123
Convex or Converging Lens
dogt2f
F
F
124
Convex or Converging Lens
dogt2f
Ray 1
F
F
Ray 2
125
Convex or Converging Lens
dogt2f
Ray 1
Ray 3
F
F
Ray 2
126
Convex or Converging Lens
dogt2f
Ray 1
Image is Real Upside Down Demagnified
Ray 3
F
F
Ray 2
127
Convex or Converging Lens
doltf
F
F
128
Convex or Converging Lens
doltf
Ray 1
F
F
129
Convex or Converging Lens
doltf
Ray 1
F
F
Ray 2
130
Convex or Converging Lens
doltf
Ray 1
F
F
Cannot Draw Ray 3 but there is an image still!
Ray 2
131
Convex or Converging Lens
doltf
Ray 1
F
F
Cannot Draw Ray 3 but there is an image still!
Ray 2
132
Convex or Converging Lens
doltf
Ray 1
F
F
Cannot Draw Ray 3 but there is an image still!
Ray 2
133
Convex or Converging Lens
doltf
Ray 1
F
F
Image is Virtual Upside Down and really magnified
Ray 2
134
Convex or Converging Lens
do2f
F
F
135
Convex or Converging Lens
do2f
Ray 1
F
F
136
Convex or Converging Lens
do2f
Ray 1
F
F
Ray 2
137
Convex or Converging Lens
do2f
Ray 1
F
F
Ray 3
Ray 2
138
Convex or Converging Lens
do2f
Ray 1
Image Real Upside Down Magnified
F
F
Ray 3
Ray 2
139
Magnifying Glass

• This double convex lens is how a magnifying glass
  works.
• When at the focus (dof) there is no image (very
  blurry).
• When close (doltf) it magnifies an image which
  appears normal (right side up).
• As you move farther the image will appear to be
  upside down buy magnified.
• As you move even farther the image will stay
  inverted but get smaller.
• Try it out next time you have a magnifying
  glass!!!!

140
Concave or Diverging Lens

• For the Following Conditions
• dof fltdolt2f dogt2f
  doltf
• Note the lens thickness is to be assumed small so
  that refraction is not a concern.

141
Rules for Concave Lenses

• 1st ray is drawn parallel to principle axis and
  hits the lens. It will refract upwards with its
  reversibility going through the focal point on
  the same side.
• 2nd ray is drawn from the object in a direction
  diagonal to the focal point on the other side but
  goes parallel to the principal axis once it
  crossed the lens.
• 3rd ray is drawn from the object straight through
  the center of the lens.

142
Concave or Diverging Lens
Ray 1
F
F
Rule One Parallel to axis once it hits lens.
Goes diagonally upwards with reversisibility
going through focus on same side.
143
Concave or Diverging Lens
Ray 1
Ray 2
F
F
Rule Two Toward focus on other side but
parallel to axis once it hits lens.
144
Concave or Diverging Lens
Ray 1
Ray 2
F
F
Ray 3
Rule Three Straight through the center of the
lens into the other side.
145
Concave or Diverging Lens
dof
F
F
146
Concave or Diverging Lens
dof
Ray 1
F
F
147
Concave or Diverging Lens
dof
Ray 1
Ray 2
F
F
148
Concave or Diverging Lens
dof
Ray 1
Ray 2
F
F
Ray 3
149
Concave or Diverging Lens
dof
Ray 1
Ray 2
F
F
Ray 3
150
Concave or Diverging Lens
dof
Ray 1
Ray 2
F
F
Ray 3
151
Concave or Diverging Lens
dof
Ray 1
Ray 2
F
F
Image Virtual Right Side Up Demagnified
Ray 3
152
Concave or Diverging Lens
dogt2f
F
F
153
Concave or Diverging Lens
dogt2f
Ray 1
F
F
154
Concave or Diverging Lens
dogt2f
Ray 1
Ray 2
F
F
155
Concave or Diverging Lens
dogt2f
Ray 1
Ray 2
F
F
Ray 3
156
Concave or Diverging Lens
dogt2f
Ray 1
Ray 2
F
F
Ray 3
157
Concave or Diverging Lens
dogt2f
Ray 1
Ray 2
F
F
Ray 3
158
Concave or Diverging Lens
dogt2f
Ray 1
Ray 2
F
F
Ray 3
Image Virtual Right Side Up Demagnified
159
Concave or Diverging Lens
fltdolt2f
F
F
160
Concave or Diverging Lens
fltdolt2f
Ray 1
F
F
161
Concave or Diverging Lens
fltdolt2f
Ray 1
Ray 2
F
F
162
Concave or Diverging Lens
fltdolt2f
Ray 1
Ray 2
F
F
Ray 3
163
Concave or Diverging Lens
fltdolt2f
Ray 1
Ray 2
F
F
Ray 3
164
Concave or Diverging Lens
fltdolt2f
Ray 1
Ray 2
F
F
Ray 3
165
Concave or Diverging Lens
fltdolt2f
Ray 1
Ray 2
F
F
Image Virtual Right Side Up Demagnified
Ray 3
166
Concave or Diverging Lens
doltf
F
F
167
Concave or Diverging Lens
doltf
Ray 1
F
F
168
Concave or Diverging Lens
doltf
Ray 1
Ray 2
F
F
169
Concave or Diverging Lens
doltf
Ray 1
Ray 2
F
F
Ray 3
170
Concave or Diverging Lens
doltf
Ray 1
Ray 2
F
F
Ray 3
171
Concave or Diverging Lens
doltf
Ray 1
Ray 2
F
F
Ray 3
172
Concave or Diverging Lens
doltf
Ray 1
Ray 2
F
F
Image Virtual Right side Up Demagnified
Ray 3
173
Sign Conventions (Spherical Mirrors Lenses) Sign Conventions (Spherical Mirrors Lenses) Sign Conventions (Spherical Mirrors Lenses)
Quantity Conditions Sign
Focal Length f Concave Mirror
Remember one remember all Convex Mirror -
CCM is Positive Convex Lens
Concave Lens -

Object Distance (do) Mostly Always

Image Distance (di) Image Real
Does not depend on side it is on. Image Virtual -

Magnification (M) Image Upright
Image Inverted -
174
Spherical Mirrors Spherical Mirrors Spherical Mirrors Spherical Mirrors Spherical Lenses Spherical Lenses Spherical Lenses Spherical Lenses
Concave Concave Convex Convex Convex (Converging) Convex (Converging) Concave (Diverging) Concave (Diverging)
Condition Results Condition Results Condition Results Condition Results
dof No Image dogtR Virtual Right side up Demagnified dof No image dof Virtual Right Side Up Demagnified
fltdoltR Real Upside down. Magnified. fltdoltR Virtual Right side up Demagnified fltdolt2f Real Upside Down Magnified dogt2f Virtual Right Side Up Demagnified
dogtR Real Demagnified Upside Down doltf Virtual Right side up Demagnified dogt2f Real Upside Down Demagnified fltdolt2f Virtual Right Side Up Demagnified
doltf Virtual Magnified Right Side up doltf Virtual Right Side up Magnified doltf Virtual Right Side Up Demagnfied
doR Real Upside Down Demagnified do2f Real Upside Down Magnified
175
Concave Mirror Convex Mirror
First ray goes parallel to the mirror and then reflects back down through the focus. Second Ray goes through the focus and into the mirror and then reflected back parallel to axis. Ray drawn to center of lens and reflects back downwards at an equal angle (symmetric) If at or within the focal length you an draw a line perpendicular to the mirror so that it goes back through itself and into the center of curvature (R 2f). This can replace the second ray above which now cannot be drawn. First ray goes parallel to the mirror and then reflects back up (dotted image line goes through focus on the other side). Second Ray is aimed directly at the center of curvature on the other side but once it hits the mirror it reflects back through itself with the dotted image line going through C). Ray drawn aimed at focus on the other side and reflect off the mirror parallel to the axis (dotted line drawn parallel in the other direction)
Concave Lens Convex Lens
1st ray is drawn parallel to principle axis and hits the lens. It will refract upwards with its reversibility going through the focal point on the same side. 2nd ray is drawn from the object in a direction diagonal to the focal point on the other side but goes parallel to the principal axis once it crossed the lens. 3rd ray is drawn from the object straight through the center of the lens. First ray is drawn parallel to principal axis until it strikes the center of the mirror. It then converged down on through the focal point on the other side of the lens. The second ray has a straight line drawn from the object to the focus to the lens on the same side and then it refracts parallel to the principal axis on the other side. The third ray is usually drawn in a direction from the object through the center of the lens itself into the other side.