ray diagramming of image formation in curved mirrors

1. Lesson 4: Image
Formation
Curved Mirrors
Objectives:
At the end of this lesson, the students should
be able to
1.Differentiate concave and convex mirrors.
2.Describe the qualitative characteristics of
images formed by curved mirrors.
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2. Terminologies
used in Curved
Mirrors
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Education and Science under the National Development Plan

3. M
O
R
I
R
R

4. Curved Mirror
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Education and Science under the National Development Plan
A mirror whose
reflective surface is
the side of the
sphere

5. ELVIRA R. CONESE

6. Principal Axis
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Education and Science under the National Development Plan
A line that intersects
at the center of the
curved mirror

8. C
T
V
A
U
R
R
U
E

9. Center of curvature
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Education and Science under the National Development Plan
A point whose
distance from the
mirror is equal to the
radius of the circle

10. Cal
Cal
Cal
Cal
.

11. Focal Point
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Education and Science under the National Development Plan
A point between the
center of curvature
and vertex

13. Vertex
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A point that
intersects to the
surface of the mirror.

14. 2 Types of
Curved
Mirrors
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Education and Science under the National Development Plan

15. Concave Mirror
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Education and Science under the National Development Plan
Mirror whose reflective
surface is the inner side
of the circle.

16. Convex Mirror
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Education and Science under the National Development Plan
Mirror whose reflective
surface is the outer side
of the circle.

17. Basic differences between concave
and convex mirrors
Descriptions Concave Convex
Reflective surface Inner surface Outer surface
Also known as
Converging mirror Diverging mirror
Uses
Make -up artists,
dentists etc
Convenience stores,
security purposes
and side mirrors.

18. Properties of an image
Type
Size
Orientation
Real Virtual
Enlarged
Reduced
Same
Upright
Laterally
Inverted
Inverted
(vertical)

19. Types of images
• Real - image appears
in front of the mirror
(could be projected
onto a screen)
• Virtual - image
appears behind the
mirror

20. Virtual
image

21. Sizes of images
• Enlarged - image is larger than the object
• Reduced - image is smaller than the object
• Same size- image is the same size as the object
a)
b)
c)

22. Orientations of images
Upright/Erect
Inverted
(vertical)
Laterally
Inverted
image is
right-side up
image is
upside-down
image is flipped
horizontally

23. Concave Mirror- Part of a sphere reflective
surface on inside
C: the center point of the sphere
r: radius of curvature (just the radius of the sphere)
F: the focal point of the mirror (halfway between C and the mirror)
f: the focal distance, f = r/2
r
f
•
C
•
F

24. optical axis
Concave Mirrors
(caved in)
•
F
•Light rays that come in parallel to the optical axis reflect through the focal
point
•Light rays that come in along the optical axis strike the mirror at 90 so reflect
back along optical axis through the focal point.

25. ƒ = focal length
u = object distance
v = image distance

26. Ray Diagrams for Mirrors
We can use three “principal rays” to construct images. In
this example, the object is “outside” of F.
Ray 1 is parallel to the axis
and reflects through F.
Ray 2 passes through F
before reflecting parallel to
the axis.
Ray 3 passes through
C and reflects back on
itself.
F
C
A fourth principal ray is the one directed at the vertex V.
V

27. Principal axis
Concave Mirror
•
F
•
c
Image formed in a concave mirror object placed outside center of curvature
Focus
Centre of Curvature
Object
Image:- Between C and F, Inverted, smaller and real
f
v
u

28. Object’s
Location
Image
Location Orientation
Inverted
vs. Upright
Size
larger,
same size
or smaller
Type
Real vs.
Virtual
Beyond
C
At C
Between
C and F
At F
Between
F and V

29. Object’s
Location
Image
Location Orientation
Inverted
vs. Upright
Size
larger,
same size
or smaller
Type
Real vs.
Virtual
Beyond
C
Between
C and F
inverted smaller real
At C
Between
C and F
At F
Between
F and V

30. Principal axis
Concave Mirror
•
F
•
c
Image formed in a concave mirror when object placed at center of curvature
Focus
Centre of Curvature
Object
Image: At C, Inverted, Same size and Real
v
f
u

31. Principal axis
Concave Mirror
•
F
•
c
Image formed in a concave mirror when object placed at center of curvature
Focus
Centre of Curvature
Object
Image: At C, Inverted, Same size and Real
v
f
u

32. Principal axis
Concave Mirror
•
F
•
c
Image formed in a concave mirror when object placed between center of
curvature & focus
Focus
Centre of Curvature
Object
Image:- Beyond C, Inverted, larger and Real
v
f
u

33. Principal axis
Concave Mirror
•
F
•
c
Image formed in a concave mirror when object placed at focus
Focus
Centre of Curvature
Object
Image: No image
f
u

34. Principal axis
Concave Mirror
•
F
•
c
Image formed in a concave mirror when object placed inside focus
Focus
Centre of Curvature
Object
Image:- Behind the mirror, upright, larger and virtual
v
f
u

35. Object’s
Location
Image
Location Orientation
Inverted
vs. Upright
Size
larger,
same size
or smaller
Type
Real vs.
Virtual
Beyond
C
Between
C and F
inverted smaller real
At C
Between
C and F
At F
Between
F and V

36. Object’s
Location
Image
Location Orientation
Inverted
vs. Upright
Size
larger,
same size
or smaller
Type
Real vs.
Virtual
Beyond
C
Between
C and F
inverted smaller real
At C At C inverted Same size real
Between
C and F
At F
Between
F and V

37. Magnification Equation
m = magnification
hi= image height
ho = object height
di = image distance
do = object distance
if the magnification is negative
the image is inverted (upside down)

38. Sign Convention for Mirrors
Quantity Positive (+) Negative (--)
Object location (u) Object is in front of
the mirror
Object is behind
the mirror
Image location (v) Image is front
mirror
Image is behind of
mirror
Focal length (f) Mirror is concave Mirror is convex
Magnification (M) Image is upright Image is inverted

39. Concave
mirror
Crosswire
Lamp-box
Screen
u
v
TO FIND THE FOCAL LENGTH OF A CONCAVE
MIRROR
Procedure
• Get the approx. focal length of mirror by focusing distant object on screen – why?
• Place the lamp-box well outside the approximate focal length – why?
• Move the screen until a clear inverted image of the crosswire is obtained.
• Measure the distance u from the crosswire to the mirror, using the metre stick.
• Measure the distance v from the screen to the mirror.
• Calculate the focal length of the mirror using - - - - - -
• Repeat this procedure for different values of u.
• Calculate f each time and then find an average value.

40. Convex Mirrors
Light rays that come in parallel to the optical axis reflect from the focal point.
optical axis
•
F
The focal point is considered virtual since sight lines, not light rays, go through it.

41. principal axis
•
C
•
F
Convex Mirrors
Image:- Behind the mirror, upright, smaller and virtual
Focus
Centre of Curvature
Object
v
f
u

42. Object’s
Location
Image
Location Orientation
Inverted
vs. Upright
Size
larger,
same size
or smaller
Type
Real vs.
Virtual
Beyond C Behind the
mirror
upright Smaller virtual
At C
Between C
and F
At F
Between F
and V
Table : Qualitative Descriptions of Images Formed by Convex Mirrors

44. END