How Mirrors form an Image?

Contributed by:

Jonathan James Fri, Jan 21, 2022 05:08 PM UTC

Plane mirror, Convex mirror, Concave mirror

1. Mirrors
Basic Optics, Chapter 25

2. 2
 Like
lenses, mirrors can affect the
vergence of light
 Also like lenses, questions and problems
involving mirrors are fair game on the OKAP

3. 3
 Likelenses, mirrors can affect the
vergence of light
 Also like lenses, questions and problems
involving mirrors are fair game on the OKAP
 Mirrors come in three flavors:
 Plane (flat)
 Concave
 Shaped like the inside of a spoon—ie, like ‘a cave’
 Convex
 Like the back surface of a spoon

4. 4
 Plane mirrors
 Change the direction of light, but do not alter its
vergence (vergence out = vergence in)

5. 5
 Plane mirrors
 Change the direction of light, but do not alter its
vergence (vergence out = vergence in)
 The only rule you need to remember is that, for
any light ray, the angle of incidence equals the
angle of reflection (with respect to the normal)
(The normal is perpendicular to the plane normal
of the mirror’s surface at that location)

6. 6
 Plane mirrors
 Change the direction of light, but do not alter its
vergence (vergence out = vergence in)
 The only rule you need to remember is that, for
any light ray, the angle of incidence equals the
angle of reflection (with respect to the normal)
normal
incidence
incidence

7. 7
 Plane mirrors
 Change the direction of light, but do not alter its
vergence (vergence out = vergence in)
 The only rule you need to remember is that, for
any light ray, the angle of incidence equals the
angle of reflection (with respect to the normal)
reflection
normal
incidence
incidence = reflection

8. 8
Mirrors
normal
incidence
Object

9. 9
Mirrors
reflection
normal
incidence = reflection
incidence
Object

10. 10
Mirrors
This
ray…
reflection
normal
incidence = reflection
incidence
Object

11. 11
Mirrors
This
ray…
reflection
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
Object

12. 12
Mirrors
This
ray…
reflection
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
incidence normal
Object

13. 13
Mirrors
This
ray…
reflection
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
incidence normal
incidence = reflection
Object reflection

14. 14
Mirrors
This
ray…
reflection
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
incidence normal
incidence = reflection
Object reflection
ay…
This r

15. 15
Mirrors
This
ray…
reflection
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection
ay…
This r

16. 16
Mirrors We’ve seen this sort of thing before…
What do you suppose is significant
about the point where the extended
rays meet?
As was the case with ray tracing
involving lenses, it determines the
This location, orientation (ie, upright vs
ray… inverted), magnification and status
reflection (ie, real vs virtual) of the image.
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection
ay…
This r

17. 17
Mirrors We’ve seen this sort of thing before…
What do you suppose is significant
about the point where the extended
rays meet?
As was the case with ray tracing
involving lenses, it determines the
This location, orientation (ie, upright vs
ray… inverted), magnification and status
reflection (ie, real vs virtual) of the image.
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection Image
ay…
This r

18. 18
Mirrors We’ve seen this sort of thing before…
What do you suppose is significant
about the point where the extended
rays meet?
As was the case with ray tracing
involving lenses, it determines the
This location, orientation (ie, upright vs
ray… inverted), magnification and status
reflection (ie, real vs virtual) of the image.
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection Image
ay…
This r
Re plane mirrors:
The image location is always ‘behind’ the mirror (ie, on the side opposite the object)

19. 19
Mirrors We’ve seen this sort of thing before…
What do you suppose is significant
about the point where the extended
rays meet?
As was the case with ray tracing
involving lenses, it determines the
This location, orientation (ie, upright vs
ray… inverted), magnification and status
reflection (ie, real vs virtual) of the image.
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection Image
ay…
This r
Re plane mirrors:
The image location is always ‘behind’ the mirror (ie, on the side opposite the object)
The image is always upright (Remember, upright means that the image has the same orientation as the object)

20. 20
Mirrors We’ve seen this sort of thing before…
What do you suppose is significant
about the point where the extended
rays meet?
As was the case with ray tracing
involving lenses, it determines the
This location, orientation (ie, upright vs
ray… inverted), magnification and status
reflection (ie, real vs virtual) of the image.
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection Image
ay…
This r
Re plane mirrors:
The image location is always ‘behind’ the mirror (ie, on the side opposite the object)
The image is always upright (Remember, upright means that the image has the same orientation as the object)
The magnification is 1.0 (ie, the image is the same height as the object)

21. 21
Mirrors We’ve seen this sort of thing before…
What do you suppose is significant
about the point where the extended
rays meet?
As was the case with ray tracing
involving lenses, it determines the
This location, orientation (ie, upright vs
ray… inverted), magnification and status
reflection (ie, real vs virtual) of the image.
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection Image
ay…
This r
Re plane mirrors:
The image location is always ‘behind’ the mirror (ie, on the side opposite the object)
The image is always upright (Remember, upright means that the image has the same orientation as the object)
The magnification is 1.0 (ie, the image is the same height as the object)
The image is always virtual (so you will always have to use extended ‘dashed’ rays to create it)

22. 22
Mirrors
This
ray…
reflection
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection Image
ay…
This r
Additionally, for plane mirrors: Image-to-mirror distance =

23. 23
Mirrors
This
ray…
reflection
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection Image
ay…
This r
Additionally, for plane mirrors: Image-to-mirror distance = Object-to-mirror distance

24. 24
Mirrors
This
ray…
reflection
normal
incidence = reflection …ap
pear
s to
incidence com
e fro
m ov
er h
e re
re
om o ver he
incidence o me f r
normal ear s to c
incidence = reflection …app
Object reflection Image
ay…
This r
Additionally, for plane mirrors: Image-to-mirror distance = Object-to-mirror distance
(Note that this is just another way to say ‘Vergence out = Vergence in’ as mentioned previously)

25. 25
 Concave/convex mirrors
 Change the direction of light, but also alter its
vergence
 The rules governing reflection are equivalent to
the ray-tracing rules for lenses we encountered in
Chapter 19

26. 26
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side

27. 27
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think
of it as analogous to the nodal point of
a lens.
C
Center of curvature for the lens

28. 28
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think
of it as analogous to the nodal point of
a lens.
r
r C
Center of curvature for the lens;
ie, every line from here to the
mirror’s surface is a radius

29. 29
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think
of it as analogous to the nodal point of no
rm
a lens. al
C
Center of curvature for the lens;
al ie, every line from here to the
m
nor mirror’s surface is a radius,
and every line through the
surface is a ‘normal’

30. 30
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think
of it as analogous to the nodal point of
a lens.
The next aspect we should note are the
focal points of the mirror.
F C

31. 31
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think
of it as analogous to the nodal point of
a lens.
The next aspect we should note are the
focal points of the mirror. Like a lens, a
mirror has a primary focal point
F1 C

32. 32
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think
of it as analogous to the nodal point of
a lens.
The next aspect we should note are the
focal points of the mirror. Like a lens, a
mirror has a primary focal point, and a
secondary focal point.
F1,2 C

33. 33
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think
of it as analogous to the nodal point of
a lens.
The next aspect we should note are the
focal points of the mirror. Like a lens, a
mirror has a primary focal point, and a r = Focal length x 2
secondary focal point. Conveniently,
they are located in the same place— Focal length = r/2
exactly halfway between the center of
curvature and the surface of the mirror.
F1,2 C

34. 34
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think
of it as analogous to the nodal point of
a lens.
The next aspect we should note are the
focal points of the mirror. Like a lens, a
mirror has a primary focal point, and a
secondary focal point. Conveniently,
they are located in the same place—
exactly halfway between the center of
curvature and the surface of the mirror.
F1,2 C
(Technically it’s not the same location, in that
the primary focal is located in what is known
as ‘object space,’ whereas the secondary
focal point is located in ‘image space.’)

35. 35
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think
of it as analogous to the nodal point of
a lens.
The next aspect we should note are the
focal points of the mirror. Like a lens, a
mirror has a primary focal point, and a r = Focal length x 2
secondary focal point. Conveniently,
they are located in the same place— Focal length = r/2
exactly halfway between the center of
curvature and the surface of the mirror.
F1,2 C
Thus, if you know the location of either the
center of curvature or the focal point(s),
you can determine the location of the other.

36. 36
Mirrors (The ‘2’ simply reflects the fact that
the radius is exactly twice as large
as the focal length)
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think 1 2
of it as analogous to the nodal point of D= Focal
= r
a lens. length
The next aspect we should note are the
focal points of the mirror. Like a lens, a
mirror has a primary focal point, and a r = Focal length x 2
secondary focal point. Conveniently,
they are located in the same place— Focal length = r/2
exactly halfway between the center of
curvature and the surface of the mirror.
F1,2 C
Thus, if you know the location of either the
center of curvature or the focal point(s),
you can determine the location of the other.
Likewise, because the distance from the
focal point(s) to the mirror (ie, the focal
length) is the reciprocal of the converging
power of the mirror in diopters, you can
also determine the power of the mirror.

37. 37
Mirrors Note: Because mirrors always reverse the
direction of light, you may see the power
The shiny side is shaped like the back of a expressed thusly, with a minus sign:
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think 1 2
of it as analogous to the nodal point of D= Focal
= r
a lens. length
The next aspect we should note are the
focal points of the mirror. Like a lens, a
mirror has a primary focal point, and a r = Focal length x 2
secondary focal point. Conveniently,
they are located in the same place— Focal length = r/2
exactly halfway between the center of
curvature and the surface of the mirror.
F1,2 C
Thus, if you know the location of either the
center of curvature or the focal point(s),
you can determine the location of the other.
Likewise, because the distance from the
focal point(s) to the mirror (ie, the focal
length) is the reciprocal of the converging
power of the mirror in diopters, you can
also determine the power of the mirror.

38. 38
The shiny side is shaped like the back of a
spoon, so we know this is a convex mirror.
shiny side
The first aspect we should note is the
center of curvature for the mirror. Think 1 2
of it as analogous to the nodal point of D= Focal
= r
a lens. length
The next aspect we should note are the
focal points of the mirror. Like a lens, a
mirror has a primary focal point, and a r = Focal length x 2
secondary focal point. Conveniently,
they are located in the same place— Focal length = r/2
exactly halfway between the center of
curvature and the surface of the mirror.
F1,2 C
Thus, if you know the location of either the
center of curvature or the focal point(s),
you can determine the location of the other.
Likewise, because the distance from the
focal point(s) to the mirror (ie, the focal
length) is the reciprocal of the converging
power of the mirror in diopters, you can
also determine the power of the mirror.
Note that the same facts hold true for both convex…and concave mirrors

39. 39
Mirrors
The shiny side is shaped like the front of a
spoon, so we know this is a concave mirror.
( )
1 2
D= Focal
= r The first aspect we should note is the
length
center of curvature for the mirror. Think
of it as analogous to the nodal point of
a lens.
r = Focal length x 2
The next aspect we should note are the
Focal length = r/2 focal points of the mirror. Like a lens, a
mirror has a primary focal point, and a
secondary focal point. Conveniently,
they are located in the same place—
F1,2 C exactly halfway between the center of
curvature and the surface of the mirror.
Thus, if you know the location of either the
center of curvature or the focal point(s),
you can determine the location of the other.
shiny side Likewise, because the distance from the
focal point(s) to the mirror (ie, the focal
length) is the reciprocal of the converging
power of the mirror in diopters, you can
also determine the power of the mirror.
Note that the same facts hold true for both convex…and concave mirrors

40. 40
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
Object
F1,2 C
0.5 m 0.5 m

41. 41
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
A ray directed toward the center of curvature…
Object
F1,2 C
0.5 m 0.5 m

42. 42
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
A ray directed toward the center of curvature…
is reflected back in the direction from whence
it came.
Object
F1,2 C
0.5 m 0.5 m

43. 43
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
A ray parallel to the optical axis 4) Is the image magnified/minified?
will be reflected as if it originated from
the secondary focal point.
Object
F1,2 C
0.5 m 0.5 m

44. 44
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
Note that we now have enough information to
locate the image. Nevertheless, let’s add one
more defining ray for completeness’ sake.
Object
F1,2 C
0.5 m 0.5 m

45. 45
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
Object
F1,2 C
A ray directed toward the primary focal
point will be reflected parallel to the
optical axis.
0.5 m 0.5 m

46. 46
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula.
Object Image
F1,2 C
?
0.5 m 0.5 m

47. 47
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula.
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
?
incoming light
U + P = V
0.5 m 0.5 m

48. 48
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula.
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
?
incoming light
U + P = V
-1/.5 + -1/.25 = V
0.5 m 0.5 m

49. 49
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula.
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
?
incoming light
U + P = V
-1/.5 + -1/.25 = V
(Remember, the power of a mirror
is 1/f, and f is ½ the radius)
0.5 m 0.5 m

50. 50
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula.
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
?
incoming light
U + P = V
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

51. 51
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula. The image is
.17m to the right of the mirror.
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

52. 52
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is upright.
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

53. 53
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is virtual (note that
we had to use dashed lines to
determine its location).
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

54. 54
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is obviously minified.
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

55. 55
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is obviously minified.
However, we can determine the
exact image/object ratio by using
the similar triangles method:
(Review Chapter 20 if the term ‘similar
triangles method’ seems unfamiliar)
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

56. 56
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is obviously minified.
However, we can determine the
exact image/object ratio by using
the similar triangles method:
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V Image size
Object size
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

57. 57
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is obviously minified.
However, we can determine the
exact image/object ratio by using
the similar triangles method:
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V Image size
= Image distance
Object size Object distance
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

58. 58
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is obviously minified.
However, we can determine the
exact image/object ratio by using
the similar triangles method:
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V Image size
= Image distance
= .17m
Object size Object distance 0.5m
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

59. 59
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is obviously minified.
However, we can determine the
exact image/object ratio by using
the similar triangles method:
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V Image size
= Image distance = .17m
= 0.33
Object size Object distance 0.5m
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

60. 60
Mirrors An object is located 50 cm from the
surface of a convex mirror with a
radius of curvature of 50 cm.
shiny side 1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is obviously minified.
However, we can determine the
exact image/object ratio by using
the similar triangles method:
Thus the image is ~1/3
the size of the object
Object Image
Vergence of Vergence added Vergence of light
F1,2 C
by the mirror leaving the mirror
1/6=.17m
incoming light
U + P = V Image size
= Image distance = .17m
= 0.33
Object size Object distance 0.5m
-1/.5 + -1/.25 = V
-2 + -4 = -6
0.5 m 0.5 m

61. 61
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
Object
C F1,2
55 cm
1m

62. 62
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
A ray directed toward the center of curvature
is reflected back in the direction from whence
it came.
Object
C F1,2
55 cm
1m

63. 63
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
A ray parallel to the optical axis 4) Is the image magnified/minified?
will be reflected as if it originated from
the secondary focal point.
Object
C F1,2
55 cm
1m

64. 64
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
A ray directed toward the primary focal
point will be reflected parallel to the
optical axis.
Object
C F1,2
55 cm
1m

65. 65
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula.
Image
Object
C F1,2
?
55 cm
1m

66. 66
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula.
Image
Object
C F1,2 Vergence of Vergence added Vergence of light
incoming light by the mirror leaving the mirror
?
U + P = V
55 cm
1m

67. 67
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula.
Image
Object
C F1,2 Vergence of Vergence added Vergence of light
incoming light by the mirror leaving the mirror
?
U + P = V
-1/1 + 1/.275 = V
(Again, the power of a mirror
is 1/f, and f is ½ the radius)
55 cm
1m

68. 68
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula.
Image
Object
C F1,2 Vergence of Vergence added Vergence of light
incoming light by the mirror leaving the mirror
?
U + P = V
-1/1 + 1/.275 = V
-1 + 3.64 = 2.64
55 cm
1m

69. 69
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is located here. However, we can
determine its exact distance from the mirror
via the Vergence Formula. The image is .38m
(38 cm) to the left of the mirror.
Image
Object
C F1,2 Vergence of Vergence added Vergence of light
incoming light by the mirror leaving the mirror
1/2.64 = 38cm
U + P = V
-1/1 + 1/.275 = V
-1 + 3.64 = 2.64
55 cm
1m

70. 70
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is inverted.
Image
Object
C F1,2 Vergence of Vergence added Vergence of light
incoming light by the mirror leaving the mirror
1/2.64 = 38cm
U + P = V
-1/1 + 1/.275 = V
-1 + 3.64 = 2.64
55 cm
1m

71. 71
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is real (note no dashed lines).
Image
Object
C F1,2 Vergence of Vergence added Vergence of light
incoming light by the mirror leaving the mirror
1/2.64 = 38cm
U + P = V
-1/1 + 1/.275 = V
-1 + 3.64 = 2.64
55 cm
1m

72. 72
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is minified.
Image
Object
C F1,2 Vergence of Vergence added Vergence of light
incoming light by the mirror leaving the mirror
1/2.64 = 38cm
U + P = V
-1/1 + 1/.275 = V
-1 + 3.64 = 2.64
55 cm
1m

73. 73
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is minified. To determine by
how much, we again employ the method
of similar triangles:
Image
Object
C F1,2
1/2.64 = 38cm
55 cm
1m

74. 74
Mirrors An object is located 1 m from the
surface of a concave mirror with a
radius of curvature of 55 cm.
1) Where is the image located?
2) Is the image upright or inverted?
shiny side 3) Is the image real or virtual?
4) Is the image magnified/minified?
The image is minified. To determine by
how much, we again employ the method
of similar triangles:
Image
Object
C F1,2
1/2.64 = 38cm
Image size
= Image distance = .38m
= 0.38
Object size Object distance 1m
55 cm
1m

75. 75
shiny side
Object
C F1,2
An object is located 25 cm from the
surface of a concave mirror with a
radius of curvature of 1 m.
1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
1m 4) Is the image magnified/minified?
25cm

76. 76
shiny side
A ray directed toward the center of curvature
is reflected back in the direction from whence
it came.
Object
C F1,2
An object is located 25 cm from the
surface of a concave mirror with a
radius of curvature of 1 m.
1) Where is the image located?
2) Is the image upright or inverted?
3) Is the image real or virtual?
1m 4) Is the image magnified/minified?
25cm

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