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Chapter 26
Reflection and Refraction
A Brief History of Light

1000 AD
• It was proposed that light consisted of tiny
particles

Newton
• Used this particle model to explain reflection
and refraction

Huygens
• 1670
• Explained many properties of light by
proposing light was wave-like
A Brief History of Light, cont

Young
• 1801
• Strong support for wave theory by
showing interference

Maxwell
• 1865
• Electromagnetic waves travel at the
speed of light
A Brief History of Light, final

Planck
• EM radiation is quantized

Implies particles
• Explained light spectrum emitted by hot
objects

Einstein
• Particle nature of light
• Explained the photoelectric effect
Geometric Optics – Using a Ray
Approximation



Light travels in a straight-line path
in a homogeneous medium until it
encounters a boundary between
two different media
The ray approximation is used to
represent beams of light
A ray of light is an imaginary line
drawn along the direction of travel
of the light beams
Ray Approximation


A wave front is a
surface passing
through points of a
wave that have the
same phase and
amplitude
The rays,
corresponding to the
direction of the wave
motion, are
perpendicular to the
wave fronts
Reflection of Light


A ray of light, the incident ray,
travels in a medium
When it encounters a boundary with
a second medium, part of the
incident ray is reflected back into the
first medium
• This means it is directed backward into
the first medium
Specular Reflection



Specular reflection
is reflection from a
smooth surface
The reflected rays
are parallel to each
other
All reflection in this
text is assumed to
be specular
Diffuse Reflection



Diffuse reflection is
reflection from a
rough surface
The reflected rays
travel in a variety
of directions
Diffuse reflection
makes the road
easy to see at
night
Law of Reflection

The normal is a line
perpendicular to the
surface
• It is at the point where
the incident ray strikes
the surface


The incident ray
makes an angle of θ1
with the normal
The reflected ray
makes an angle of θ1’
with the normal
Law of Reflection, cont


The angle of reflection is equal to the
angle of incidence
θ1= θ1’
When we talk about an image, start from an ideal point light source.
Every object can be constructed as a collection of point light sources.
VIRTUAL
IMAGE
p
|q|
Image forms at the point where the light rays converge.
When real light rays converge  Real Image
When imaginary extension of L.R. converge  Virtual Image
Only real image can be viewed on screen placed at the spot.
VIRTUAL
IMAGE
p
|q|
For plane mirror: p = |q|
How about left-right?
Let’s check?
Spherical Mirror
R: radius of curvature
focal Point
f: focal length = R/2
Optical axis
concave
convex
Parallel light rays: your point light source is very far away.
Focal point:
(i) Parallel incident rays converge after reflection
(ii) image of a far away point light source forms
(iii) On the optical axis
Reflected rays do not converge:
Not well-defined focal point
 not clear image
Spherical Aberration
f = R/2 holds strictly for a very
narrow beam.
Parabolic mirror can fix this problem.
Spherical Aberration:
some mirrors were ground wrong by
1/50th of human hair thickness.
Notation for Mirrors

The object distance is the distance from
the object to the mirror
• Denoted by p

The image distance is the distance from
the image to the mirror
• Denoted by q

The lateral magnification of the mirror is
the ratio of the image height to the object
height
• Denoted by M
Types of Images for Mirrors

A real image is one in which light
actually passes through the image point
• Real images can be displayed on screens

A virtual image is one in which the light
does not pass through the image point
• The light appears to diverge from that point
• Virtual images cannot be displayed on
screens
More About Images

To find where an image is formed, it
is always necessary to follow at least
two rays of light as they reflect from
the mirror
Flat Mirror




Simplest possible
mirror
Properties of the
image can be
determined by
geometry
One ray starts at P,
follows path PQ and
reflects back on itself
A second ray follows
path PR and reflects
according to the Law
of Reflection
Properties of the Image Formed
by a Flat Mirror

The image is as far behind the mirror as
the object is in front
• |q| = p

The image is unmagnified
• The image height is the same as the object
height



h’ = h and M = 1
The image is virtual
The image is upright
• It has the same orientation as the object

There is an apparent left-right reversal in
the image
Case 1: p > R
p
f
P>q
Real Image
q
Case 2: p = R
p=q
Real Image
Case 3: f < p < R
p<q
Real Image
Case 4: p = f
q = infinite
Case 5: p < f
q<0
Virtual Image
Mirror Equation
1/p + 1/q = 1/f
For a small object, f = R/2 (spherical mirror)
1/p + 1/q = 2/R
Alert!!
Be careful with the sign!!
Negative means that it is inside the mirror!!
p can never be negative (why?)
negative q means the image is formed inside the mirror
VIRTUAL
How about f?
For a concave mirror: f > 0
Focal point inside the mirror
f < 0
1/p + 1/q = 1/f < 0 : q should be negative.
1/p + 1/q = 1/f < 0 : q should be negative.
All images formed by a convex mirror are VIRTUAL.
Magnification, M = -q/p
Negative M means that the image is upside-down.
For real images, q > 0 and M < 0 (upside-down).
Sign Conventions for Mirrors
Quantity
Positive
When
Object location Object is in
(p)
front of the
mirror
Image location Image is in
(q)
front of mirror
Image height
Image is
(h’)
upright
Focal length (f) Mirror is
and radius (R) concave
Magnification
Image is
(M)
upright
Negative
When
Object is
behind the
mirror
Image is
behind mirror
Image is
inverted
Mirror is
convex
Image is
inverted
Ex. 26.1 An object is placed at the center of curvature of a
Mirror. Where is the image formed? Describe the image?
1/p + 1/q = 1/f
f = R/2
Object is at the center: p = R
1/q = 1/f – 1/p
= 2/R – 1/R
= 1/R
q = R > 0 (Real Image)
M = -q/p = -R/R = -1
No magnification but upside-down
Ex. 26.2 A concave mirror has a 30 cm radius of curvature.
If an object is placed 10 cm from the mirror, where will the
image be found?
f = R/2 = 15 cm, p = 10 cm
Case 5: p < f
1/p + 1/q = 1/f  1/10 + 1/q = 1/15
3/30 + 1/q = 2/30
1/q = -1/30
q = -30 cm
Real or Virtual
M = -q/p = 3
q < 0
Magnified or Reduced
Up-right or Upside-down
Q. An upright image that is one-half as large as an object is
needed to be formed on a screen in a laboratory experiment
using only a concave mirror with 1 m radius of curvature.
If you can make this image, I will give you $10. If you can’t
you should pay me $10. Deal or no deal? Why?
1/p + 1/q = 1/f = 2/R > 0
M = -q/p = ½ > 0
should be a real image: q > 0
M = -q/p cannot be positive, if q > 0.
No deal!!!