3. 3
Chapter 4
At the end of this chapter you should be able to:
Define semantically and operationally reflection, and refraction
Explain the laws of reflection and refraction
Predict the direction of reflected light using the law of reflection
Characterize different kinds of mirrors and lenses
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.
Differentiate converging and diverging lenses, describe
images and their characteristics, and find image characteristics
using ray diagram and the thin-lens equation
Explain how lenses can be combined and how optical instruments
can be made
Calculate the power of a lens
4. The Reflection of Light
If a stone is dropped into a pond, circular waves
emanate from the point where it landed. Rays,
perpendicular to the wave fronts, give the direction in
which the waves propagate.
5. The Reflection of Light
As one moves farther from the source point, the wave
fronts become more nearly flat.
17. 17
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)
18. 18
All these characteristics can be determined from
the lateral magnification
o
i
o
i
d
d
h
h
height
object
height
image
M
For real objects ( these are the only ones with which
we will deal );
M < 0 (negative) the image is real and inverted
M > 0 (positive) the image is virtual and upright
|M| > 1 the image is magnified
|M| = 1 the image is unmagnified
|M| < 1 the image is reduced
19. 19
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.
A mirror may be front coated or back coated
depending on its applications
A plane mirror is a mirror with a flat surface
20. 20
•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.
•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.
When you look directly into a mirror ,
what will you see ??
21. 21
The geometry of a mirror’s surface affect the size,
orientation, and type of image.
Locating a mirror image
22. 22
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) ?
23. 23
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
24. 24
principal axis
center of curvature ( C )
radius of curvature ( R )
focal length ( f )
The focal point (F)
Focal point
F
vertex
f
R
25. 25
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,
2
R
f
26. 26
The images formed by spherical mirrors can be
studied from geometry ( ray diagrams ).
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.
35. 35
Concave Mirror
Object location Image orientation Image size Image type
Beyond C Inverted Reduced Real
At C Inverted Same as object Real
Between F and C Inverted Enlarged Real
Just beyond F Inverted Approaching
infinity
Real
Just inside F Upright Approaching
infinity
Virtual
Between mirror and
F
Upright Enlarged Virtual
4.3 (b) IMAGING CHARACTERISTICS OF
CONCAVE SPHERICAL MIRRORS
36. 36
R
f
d
d i
o
2
1
1
1
Position and size can be determined by
analytical method.
f
d
f
d
d
or
o
o
i
do : the object distance (from the object to the vertex)
di : the image distance (from the image to the vertex)
f : the focal length.
38. 38
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
40. 40
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.
QUICK QUIZ
41. 41
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
42. 42
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
a) the location and
b) the height of the image
Answer: 7.5 cm in front of the mirror
Image height : 1.0 cm
43. 43
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.
Answer: 30.0 cm behind the mirror
Image height : 5.0 cm , upright
44. 44
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
a) 30.0 cm
b) 5.0 cm
Answer: a) +15 cm , real, M = -1/2 , inverted , reduced in
b) - 10 cm , virtual, M = + 2 , upright , magnifie
45. 45
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?
Answer: 25 cm
cm
d
d
cm
d
cm
d
d
cm
d
d
f
d
d
M
cm
f
i
i
i
i
i
o
o
i
i
25
4
100
4
4
1
20
1
1
4
1
20
1
1
1
1
4
1
20
46. 46
Made from some transparent material,
ex: glass, plastic, crystal, etc.
1
R 2
R
1
R
2
R
Biconvex lens
( Converging )
Biconcave lens
( Diverging )
Prism base to base Prism point to point
47. 47
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
50. 50
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
57. 57
• The thin lens equation is identical in form to
the spherical mirror equation
f
d
f
d
d
f
d
d
o
o
i
i
o
1
1
1
58. 58
• The lateral magnification is also defined the
same way as for spherical mirrors.
o
i
o
i
d
d
h
h
height
object
height
image
M
59. 59
.
do +ve: real object
do -ve: virtual object
di +ve: real image
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
60. 60
.
Quantity Positive When Negative When
Object location (do) Object is in front of the
lens
Object is in back of the
lens
Image location (di) Image is in back of the
lens ( real image )
Image is in front of the
lens ( virtual image )
Image height (hi) 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
61. 61
.
Problem Solving Strategy
• Be very careful about sign conventions
– Do lots of problems for practice
• Draw confirming ray diagrams
63. 63
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
a) By construction
b) By computation
Answer: di=+30 cm, hi=6.0 cm
64. 64
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.
Answer: di= - 10.8 cm, hi= 3.6 cm
65. 65
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?
Answer: 43.5 cm from the lens.
66. 66
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.
Answer: do= 2cm, di=8cm f = +1.6cm
