This document provides an overview of geometric optics, including the ray model of light, reflection, refraction, and image formation using plane mirrors, spherical mirrors, and thin lenses. Key concepts covered include the types of images that can be formed (real or virtual), sign conventions, lateral magnification, focal points and lengths, and graphical methods for solving problems involving mirrors and lenses. Sample problems are worked through as examples.

1. GEOMETRIC OPTICS

2. To understand images and image
formation, all we need are the RAY
MODEL OF LIGHT, the LAWS OF
REFLECTION and REFRACTION, and some
simple geometry and trigonometry.

3. GEOMETRIC OPTICS
• The study of how light rays form images

4. REFLECTION AND REFRACTION AT A
PLANE SURFACE

5. OBJECT
• Anything from which light rays radiate
• Could be:
–Light emitted by the object itself (self-
luminous)
–Light emitted by another source and then
reflected from the object

6. • POINT OBJECT has no
physical extent.
• EXTENDED OBJECT has
length, width and
height.

7. • Point P an object
point
• Point P’ an image
point
“The reflecting surface
forms an image of
point P.”

8. TYPES OF IMAGES
• Virtual image  if the outgoing rays
don’t actually pass through the image
point
• Real image  the outgoing rays do pass
through an image point.

9. Image formation by a Plane Mirror

10. SIGN RULES

15. Lateral Magnification
• The ratio of image height to object
height
• If the image is erect, m is positive
• If the image is inverted, m is negative

16. REFLECTION AT A SPHERICAL
SURFACE
Concave and Convex Mirrors

17. CONCAVE MIRRORS

18. • Center of Curvature (C)
• Radius of Curvature (R)
• Vertex, the center of
the mirror surface (V)
• Optic axis, the line CV

21. Focal Point and Focal Length

22. • Where:
f = focal length
R = radius of curvature

23. • Where:
s = object distance
s’= image distance
f = focal length

24. Lateral Magnification (m)

25. SAMPLE PROBLEM
• A 4.00-cm tall light bulb is placed a
distance of 45.7 cm from a concave
mirror having a focal length of 15.2
cm. Determine the image distance
and the image size.

26. SAMPLE PROBLEM

28. CONVEX MIRRORS
• The center of curvature (C) is on the opposite
side to the outgoing rays

33. Sample Problem

35. CONCAVE AND CONVEX MIRROR

36. CONCAVE MIRROR
• has the capability of
forming images that can
be smaller or larger in
size and virtual or erect,
depending on the
position of the object.
CONVEX MIRROR
• always produces a
smaller, virtual, and
erect image of an
object.
• In convex mirror, the
length of the image is
shorter than that of the
object.

37. CONCAVE MIRROR
• doctors use this mirror for obtaining a
relatively larger image of teeth, ear, skin etc.

38. CONVEX MIRROR

39. SW : REFLECTION ON SPHERICAL
SURFACE
½ c.w. DO NOT COPY THE PROBLEM. SHOW COMPLETE SOLUTION

40. 1. A luminous object is 4.00 m from a wall.
You are to use a concave mirror to
project an image of the object on the
wall, with the image 2.25 times the size
of the object. How far should the mirror
be from the wall? What should the
radius of curvature be?

41. 1. Determine the image distance and
image height for a 5.00-cm tall object
placed 20.0 cm from a concave mirror
having a focal length of 15.0 cm.

42. 2. Find the focal length of a convex
mirror of an object 0.30 m from the
mirror forms an image of 0.10 m
behind the mirror.

43. GRAPHICAL METHOD FOR MIRRORS

44. Concave Mirror
• The center C of a concave mirror is outside the
mirror.
• Focal point F is also outside the mirror, half way
between the center and the surface of the mirror.
• The focal length f is half of the radius.

45. case 1:case 1: The object is placed at a distanceThe object is placed at a distance
greater than the C. The image formed isgreater than the C. The image formed is
real, inverted and smaller in size.real, inverted and smaller in size.
Step 1 Step 2
Step 3 Step 4

46. case 2: The object is placed at a distance
equal to C. The image formed is real,
inverted and the same size as the object.

47. Case 3: The object is placed between C
and f. The image formed is real, inverted
and magnified in size.

48. Case 4: The object is located at f.
No image is formed.

49. Case 5: The object is placed between
the principal focus and the mirror. The
image formed is virtual, upright and
magnified.

50. CONVEX MIRRORS

51. PRINCIPAL RAYS:

52. PRINCIPAL RAYS:

53. PRINCIPAL RAYS:

54. PRINCIPAL RAYS:

55. PRINCIPAL RAYS:

63. THIN LENSES

64. THIN LENS
• A lens is an optical system with two
refracting surfaces
• The simplest lens has two spherical
surfaces close enough together that we
can neglect the distance between them
(the thickness of the lens)

66. CONVERGING LENS
• Has the property that when a beam of
rays parallel to the axis passes through
the lens, the rays converge to a point F2
and form a real image at that point.
• Similarly, rays passing through point F1
emerge from the lens as a beam of
parallel rays.
• A positive lens (F1 and F2 are both
positive)

68. DIVERGING LENS
• The beam of parallel rays incident on
this lens diverges after refraction.
• Is called a negative lens
• The focal length of a diverging lens is
a negative quantity

72. GRAPHICAL METHOD FOR LENSES

73. GRAPHICAL METHOD FOR LENSES

74. GRAPHICAL METHOD FOR LENSES

80. Sample Problem
• An object 5.0 cm high is placed 24
cm away from a lens of focal length
8.0 cm.
a.Calculate the location of the image
b.Calculate the height of the image

81. SHORT QUIZ
OPEN NOTES (1/2 CW) DO NOT COPY THE PROBLEM…
SHOW GIVEN AND COMPLETE SOLUTION

82. 1. An object 5.0 cm high is placed 24.0 cm away