1. MIRROR AND LENSES Contents INTRODUCTION FLAT MIRROR SPHERICAL MIRRORS
SPHERICAL MIRROR EQUATION
SIGN CONVENTION FOR MIRRORS
THIN LENSES
THIN LENS EQUATION
SIGN CONVENTION FOR LENS
POWER OF LENSES

2. MIRROR AND LENSES At the end of this chapter you should be able to:
Describe the characteristics of plane mirrors
Distinguish between converging and diverging spherical mirrors,
describe images and their characteristics, and determine these
image characteristics using ray diagrams and the spherical mirror
equation.

3. Describe the nature of image formed by plane mirrors.

4. INTRODUCTION The images of objects formed by optical systems ( mirrors
and/or lenses ) can be either real or virtual.
real image is one formed by light rays that converge at
and pass through the image location, and can be seen or
formed on a screen.
virtual image is one for which light ray appear to emanate
from the image, but do not actually do so. Virtual images
cannot be seen or formed on screen.
The images of objects can also be upright (erect), inverted,
magnified, unmagnified, or reduced in size (diminished)

5. Contrast real image and virtual image.Give examples.
Virtual images: images formed by a plane mirror
Real Images: image formed by the LCD projector

6. PLANE MIRROR A plane mirror is a mirror with a flat surface
Mirrors are smooth reflecting surfaces and can reflect beam of light in one direction instead of either scattering it widely into many direction or absorbing it.
When one side of a piece of glass is coated with a
compound of tin, mercury or silver, its reflectivity is
increased and light is not transmitted through
the coating.
Flat mirror is a mirror with a flat surface , smooth reflecting surfaces and can reflect beam of light in one direction instead of
Either scattering it widely into many direction or absorbing it.
When one side of a piece of glass is coated with a compound of tin, , mercury or silver its reflectivity is increased.
And light is not transmitted through the coated. A mirror maybe front coated or back coated
Depending on its applications.
When you look directly in to a mirror, you will see the reflected images of yourself
And objects around you.
A mirror may be front coated or back coated
depending on its applications

7. As light ray strikes the surface of the plane mirror, what happens to the ray?
How plane mirror is produced?

8. PLANE MIRROR When you look directly into a mirror ,
what will you see ?
A mirror forms an image based on the law of reflection.
The characteristics of the images formed by a plane
mirror are virtual, upright, and unmagnified,
that is M = +1.
Flat mirror is a mirror with a flat surface , smooth reflecting surfaces and can reflect beam of light in one direction instead of
Either scattering it widely into many direction or absorbing it.
When one side of a piece of glass is coated with a compound of tin, , mercury or silver its reflectivity is increased.
And light is not transmitted through the coated. A mirror maybe front coated or back coated
Depending on its applications.
When you look directly in to a mirror, you will see the reflected images of yourself
And objects around you.
The image formed by a plane mirror appears to be
at a distance behind the mirror that is equal to the
distance of the object in front of the mirror and has
right-left or front-back reversal.

9. LEFT- RIGHT REVERSAL
AMBULANCE
Draw a ray diagram as basis.

10. Characterize the images formed in a plane mirror.
What is left-right reversal or front-back reversal?

11. 8.2.1 IMAGES FORMED BY PLANE MIRROR
Locating a mirror image
The geometry of a mirror’s surface affect the size,
orientation, and type of image.

12. What is the minimum length of a plane mirror needed
for a person to be able to see his/her complete image
( head to toe) ?

13. Kaleidoscopic effect, with multiple images formed.

14. Multiple Reflections ( 2 or more mirrors)
object
image
image
image
Web Link: Multiple reflections

15. When mirror surfaces are curved instead of flat, strange things happen……

16. SPHERICAL MIRRORS A spherical mirror is a section of a sphere.
Either the outside ( convex ) surface or
the inside ( concave ) surface of the
spherical section may be the reflecting surface.
concave mirror is called a converging mirror
convex mirror is called a diverging mirror

17. Why concave mirror is also called converging mirror?
Rays parallel to the principal axis reflect from the concave mirror and meet or converge at the real focus F.
Why convex mirror is also called diverging mirror?
Rays parallel to principal axis hit a convex mirror, the reflected ray spread out or diverge.

19. Give examples of converging mirror and diverging mirror.
Describe a concave and convex mirror.

20. SPHERICAL MIRRORS F The focal point (F) principal axis
vertex f
principal axis
The focal point (F)
center of curvature ( C )
focal length ( f )
radius of curvature ( R )

21. Principal axis is a line through the center of the
spherical mirror that intersects the mirror at the
vertex of the spherical section
Centre of curvature is the point on the optic axis
that corresponds to the center of the sphere of
which the mirror forms a section.
Radius of curvature is the distance from the vertex to
the center of curvature
Focal point is the point at which parallel rays
converge or appear to diverge.
Focal length is the distance from the focal point to the
vertex of the spherical section. It is equal to one-half of
the radius of curvature,

22. ______________is a line through the center of the
spherical mirror that intersects the mirror at the
vertex of the spherical section
______________is the point on the optic axis
that corresponds to the center of the sphere of
which the mirror forms a section.
______________ is the distance from the vertex to
the center of curvature
______________ is the point at which parallel rays
converge or appear to diverge.
______________ is the distance from the focal point to the
vertex of the spherical section. It is equal to one-half of
the radius of curvature,

23. SPHERICAL MIRRORS The images formed by spherical mirrors can be
studied from geometry ( ray diagrams/ ray tracing ).
Three important rays are used to determine the
images in a ray diagram:
a parallel ray is a ray incident along a path parallel
to the optic axis and reflected through the focal point F ( or appear to go through )
a chief ( radial ) ray is a ray incident through the
center of curvature C ( or appear to go though )
and reflected back along its incident path through C
a focal ray is a ray which passes through ( or appear to go through ) the focal point and is reflected parallel to the optic axis.

24. SPHERICAL MIRRORS
CONCAVE MIRROR

25. SPHERICAL MIRRORS
CONVEX MIRROR

26. IMAGE FORMATION BY A CONCAVE MIRROR
SPHERICAL MIRRORS
IMAGE FORMATION BY A CONCAVE MIRROR
a) The image is real, inverted, reduced in size,
same side as object
b) The image is real, inverted, enlarged,
same side as object

27. 8.3 SPHERICAL MIRRORS c) The image is virtual, upright, enlarged,
behind the mirror.
What are the characteristics of an image formed,
when the object is at F ?

29. IMAGE FORMATION BY A CONVEX MIRROR
SPHERICAL MIRRORS
IMAGE FORMATION BY A CONVEX MIRROR
a) The image is always virtual, upright, reduced,
behind the mirror.

30. SPHERICAL MIRRORS

31. IMAGING CHARACTERISTICS OF CONVEX
SPHERICAL MIRRORS
Convex Mirror
Object location
Image orientation
Image size
Image type
Arbitrary upright reduced virtual

32. 8.3 (b) IMAGING CHARACTERISTICS OF CONCAVE SPHERICAL MIRRORS
Concave Mirror
Object location
Image orientation
Image size
Image type
Beyond C
Inverted
Reduced
Real
At C
Same as object
Between F and C
Enlarged
Just beyond F
Approaching infinity
Just inside F
Upright
Virtual
Between mirror and F

33. How would you compare the images formed in a side mirror of the car with that of a plane mirror?
Plane mirror: virtual, upright, unmagnified.
Car’s side mirror: virtual, upright, diminished

34. Spherical Mirrors
(Mirror Formulae)
concave side
convex side

35. Group 1 Group 3 Group 2 Group 4 C F C F
Review: Construct ray diagrams to locate and describe the image formed by the spherical mirrors.
Group 1 Group 3
C F C F
Group 2 Group 4
C F C F

36. : Construct ray diagrams to locate and describe the image formed by the spherical mirrors.
Group 5 Group 6 C F C F

37. Recall:
2. How will you describe the image formed by convex mirror in all location of the object?
3. What are the 3 specific rays drawn used to find location, size, and orientation of the image in a curved mirrors?

38. Starter:
How would you explain an inverted image using the ray diagram?
How would you be able to distinguish a virtual image from a real image using the ray diagrams?

39. SPHERICAL MIRROR EQUATION
Position and size can be determined by
analytical method.
di : the image distance (from the image to the vertex)
do : the object distance (from the object to the vertex)
f : the focal length.

40. SPHERICAL MIRROR EQUATION
To determine the magnification and orientation of the object

41. SIGN CONVENTION FOR MIRRORS
do is + (do > 0) if the object is in front of the mirror (real object )
do is – (do < 0) if the object is in back of the mirror (virtual object )
di is + (di > 0) if the image is in front of the mirror (real image)
di is - (di < 0) if the image is in back of the mirror (virtual image)
Both f and R are + if the center of curvature is in front of the mirror
(concave mirror)
Both f and R are - if the center of curvature is in back of the mirror
(convex mirror)
If m is +, the image is upright
If m is -, the image is inverted

42. SIGN CONVENTION FOR MIRRORS

43. Sample Problems:
1. Santa checks himself for soot, using his reflection in a shiny silvered Christmas tree ornament m away. The diameter of the ornament is 7.20 cm. Standard reference work state that he is “ right jolly old elf,” so we estimate his height too be 1.6 m. where and how tall is the image of Santa formed by the ornament? Is it erect or inverted?
2. A magnified, inverted image is located a distance of 32.0 cm from a concave mirror with a focal length of 12.0 cm. Determine the object distance and tell whether the image is real or virtual.

44. QUIZ
True or false?
(a) The image of an object placed in front of a concave mirror is always upright. (b) The height of the image of an object placed in front of a concave mirror must be smaller than or equal to the height of the object.
(c) The image of an object placed in front of a convex mirror is always upright and smaller than the object.

45. Quiz
1. Determine the image distance and image height for a 5.00-cm tall object placed 45.0 cm from a concave mirror having a focal length of 15.0 cm. 2. A concave mirror forms an image on a wall 3.00 m from the mirror of the filament of a head light lamp 10.0 cm in front of the mirror. (a) What are the radius of curvature and focal length of the mirror? (b) What is the height of the image if the height of the object is 5.0 mm?

46. 3. In a laboratory experiment, it is desired to form an image that is one-half as large as an object. How far must the object be held from a diverging mirror of radius 40 cm? 4. What is the magnification of an object if it is located 10 cm from a mirror and its image is erect and seems to be located 40 cm behind the mirror? Is the mirror diverging or

47. QUICK QUIZ :ANSWER
a) False. A concave mirror forms an inverted image when the object distance is greater than the focal length. b) False. The magnitude of the magnification produced by a concave mirror is greater than 1 if the object distance is less than the radius of curvature. c) True

48. Example: 1 A 2.0 cm high object is situated 15.0 cm
in front of a concave mirror that has radius
of curvature of 10.0 cm. Using ray diagram
drawn to scale , measure
the location and
the height of the image

49. Example: 2 Repeat problem 1 for a concave mirror with
focal length of 20.0 cm, an object distance of
12.0 cm and a 2.0 cm high object.

50. Example: 3 Find the location and describe the characteristic
of the image formed by a concave mirror of radius
20.0 cm if the object distance is
30.0 cm
5.0 cm

51. Example: 4 A concave mirror has a focal length of 20.0 cm .
What is the position ( in cm ) of the resulting image if the image is inverted and four times smaller than the object?

52. 8.4. THIN LENSES Made from some transparent material,
ex: glass, plastic, crystal, etc.
Biconvex lens
( Converging )
Biconcave lens
( Diverging )
Prism base to base
Prism point to point

53. 8.4. THIN LENSES A lens forms an image based on the law of refraction
( Snell's law ).
spherical biconvex lens is a converging lens
spherical biconcave lens is a diverging lens

54. THIN LENSES

55. Three important rays are used to determine the images:
THIN LENSES
Image is real: when formed on the side of the lens opposite the object
Image is virtual: when formed of the same side of the lens as the object
Three important rays are used to determine the images:
a parallel ray is a ray incident along a path parallel to the optic axis and refracted through the focal point F ( or appears to go through )
a chief ( radial ) ray is a ray incident through the center of the lens
( or appears to go through ) and refracted undeviated a focal ray is a ray which passes through ( or appears to go through ) the focal point and is refracted parallel to the principal/optic axis.
The intersection of any two of the rays at a point
locates the image

56. THIN LENSES

57. THIN LENSES
CONVERGING LENS

58. THIN LENSES
DIVERGING LENS .

59. IMAGE FORMATION BY A CONVEX LENS
THIN LENSES
IMAGE FORMATION BY A CONVEX LENS
The image is real
The image is inverted

60. IMAGE FORMATION BY A CONVEX LENS
THIN LENSES
IMAGE FORMATION BY A CONVEX LENS
The image is virtual
The image is upright

61. IMAGE FORMATION BY A CONCAVE LENS
8.4 THIN LENSES
IMAGE FORMATION BY A CONCAVE LENS
The image is virtual
The image is upright

62. THIN LENS EQUATION
The thin lens equation is identical in form to the spherical mirror equation

63. THIN LENS EQUATION
The lateral magnification is also defined the same way as for spherical mirrors.

64. 8.4.2 SIGN CONVENTION FOR THIN LENS
di +ve: real image
do +ve: real object
do -ve: virtual object
di -ve: virtual object
Both f and R are +ve : convex lens ( concave mirror ) .
Both f and R are -ve : concave lens ( convex mirror )
M is +ve: image is upright and on the same side as object
M is -ve: image is inverted and on the side of the lens
opposite to the object

65. 8.4.2 SIGN CONVENTION FOR THIN LENS
Quantity
Positive When
Negative When
Object location (p)
Object is in front of the lens
Object is in back of the lens
Image location (q)
Image is in back of the lens ( real image )
Image is in front of the lens ( virtual image )
Image height (h’)
Image is upright and on the same side as object
Image is inverted and opposite the object
R1 and R2
Center of curvature is in back of the lens
Center of curvature is in front of the lens
Focal length (f)
Converging lens
Diverging lens .

66. Problem Solving Strategy
Be very careful about sign conventions
Do lots of problems for practice
Draw confirming ray diagrams .

67. POWER OF LENSES
Power of lens , .
Unit: Diopters

68. Example: 5
An object , O, 4.0 cm high is 20 cm in front of a thin
convex lens of focal length +12 cm . Determine the
position and height of its image
By construction
By computation

69. Example: 6
An object , 9.0 cm high is 27 cm in front of a concave lens of focal length -18 cm . Determine the position and height of its image by the construction and computation.

70. Example: 7
A converging lens ( f=20 cm ) is placed 37 cm in front of a screen. Where should the object be placed if its image is to appear on the screen?

71. Example: 8
Compute the position and focal length of the converging lens which will project the image of a lamp, magnified 4 times, upon a screen 10.0 cm from the lamp.
M= l di / d0 l = 4
di=+4do
do+di=10
d0+4d0=10
do=10/5=2, di=10-2=8cm

72. END OF CHAPTER 8 .