CHAPTER 13-14
Reflection and Refraction of Light
A is A
“Something cannot be itself and something else at
the same time.”
Aristotle
Light exhibits wave-like properties when studied
under certain conditions.
Light exhibits particle-like properties when studied
under certain conditions.
Light does not exhibit wave-like and particle-like
properties simultaneously.
Properties of Light
Speed:
In a vacuum (c):
2.997924574x108m/s
c = 3.00x108m/s
In other mediums: Speed of light is less than c.
Nothing can travel faster than the speed of light.
Direction: Light travels in a straight line path until it
encounters a boundary between two different
mediums.
Ray Model of Light
Reflection: Light rays reflect (bounce) off the surface of a
new medium that it encounters in a very
predictable fashion.
The “Normal” is a line perpendicular to the surface of
the second medium.
1 = 1’
Angle of Incidence (1) = Angle of Reflection (1’)
Angles are measured from the Normal.
I = r
Always!!
This law is obviously true in some situations and not
so obviously true in other situations.
Light rays reflect from
the smooth surface in
only one direction
because all the Normal
lines are parallel to each
other. All i are the same
 All r are the same.
Light rays reflect in
many directions from a
rough surface because
each ray encounters the
surface with a Normal
not parallel to the other
Normals.
However, for each ray:
i = r
Flat (Plane) Mirrors
Terms:
Plane Mirror:
Flat Mirror
Object:
Physical thing placed in front of the mirror
Object Distance (do): Distance of object from the front of the
mirror
Image:
The form of the object takes “in the mirror”
Image Distance (di): Distance of image from the front of the mirror
Virtual Image:
Located behind mirror. Rays appear to come
from it.
Real Image:
Located in front of mirror. Rays converge to
form real images.
Flat Mirror (con’t)
Image:
Real or Virtual?
Virtual
Upright or Inverted?
Upright
Magnification?
None (M=1)
Image Distance (di) and Object Distance (do)?
Ray Diagrams:
Follow the Law of Reflection.
Follow Snell’s Law (with lenses).
Rays can be traced forward or backward.
Same
Spherical Mirrors
Concave:
Principle Axis:
Line formed by point C and F. It runs to the
center of the mirror and is perpendicular to
the surface at the mirror’s center.
Center of Curvature (C): A point equidistant from all points on
the mirrors surface. Distance from C
to mirror equals “radius of
curvature” of the sphere (from which
the mirror is formed)
Focal Point (F):
A point where all rays parallel to the
Principle Axis converge after striking the
mirror. (F=.5C)
NOTE: Relatively flat or small spherical mirrors are an
approximation of a parabolic mirror.
With regard to a concave spherical mirror, describe the 3
general locations of interest where an object might be
placed.
1. between mirror and focal point
2. between focal point and center of curvature
3. outside of center of curvature
Ray Diagrams (Case 2)
The purpose of ray diagrams is to find the location of an
image and determine its characteristics.
Rules:1. Rays originate at the tip of object in all directions.
2. The ray parallel to the principle axis reflects back
through the focal point (focal point definition).
3. The ray going directly through the focal point
reflects back parallel with principle axis (rays can be
traced forward or backward).
Ray Diagram (Case 1)
Notes:1. Three rays of interest can be drawn.
2. Two rays determine a point. Three rays rarely
come to a point even when they should.
3. Use only two rays to find the tip of the image
(Use Rays 1 and 2.)
The rays diverge in front of the mirror, but converge
behind the mirror.
Result
Virtual Image
Read the book and draw
Upright
the 3rd case yourself.
Magnified
Convex Mirrors
Rays of Interest:
1. Ray parallel to Principle Axis
2. Ray reflected perpendicularly off the surface
(appear to come from center of curvature).
“Objects in mirror are closer than they appear.”
Mirror Equation (for Concave and Convex Mirrors)
1
1
+
=
do
di
1
f
f=½c
di
hi
M=
=
do
ho
do = + ALWAYS
di = + if image is in front of mirror (real image)
di = - if image is behind the mirror (virtual image)
f and c = + if they are in front of mirror (concave)
f and c = - if they are behind the mirror (convex)
M = + if upright
Ray Model of Light
Refraction: The tendency for light ray to bend when
traveling from one medium into another medium.
Examples: Rays traveling from:
air to water
air to glass
water to glass
Law of Reflection 1 = 1’
v1 = speed of light in air (still
approximately 3.0x108m/s)
v2 = speed of light in glass
v1  v2
1 = Incident Angle
1’ = Reflected Angle
2 = Angle of Refraction
Light takes the quickest path between two points.
Only 1 Medium  Straight Line Path
2 Mediums Encountered  Bent Line Path
The bent line path allows light to travel relatively more
distance in the medium in which it travels faster and less
distance in the slower medium.
Sand
A
B
Shoreline
Ocean
Draw how you would travel if you were a lifeguard at
point A trying to quickly reach a person at point B.
Light bends toward the Normal when passing from fast
medium to a slow medium…just like the lifeguard.
Light bends away from the Normal when passing from a
slow to a fast medium…just like you in the ocean if you
noticed someone stealing from your possessions on shore.
Your possessions
2
Normal
1
You
Law of Refraction
speed of light in vacuum
Index of Refraction (n) = speed of light in medium
c
n = v
Index of Refraction is another physical property of a
substance (medium)
n  1 because c  v
Always!
However nair  1.00 (to 3 sig.figs.)
f1 = f 2
Waves don’t “pile up” at the
boundary.
v1  v2
1  2
The wavelength changes at
the boundary.
Law of Refraction (Snell’s Law)
sin1
v1
sin2 = v2 = constant (for two given mediums)
c
c
v2 = n
v1 = n
2
1
sin1
c/n1
sin2 = c/n2
sin1
n2
sin2 = n1
n1 sin1 = n2 sin 2
Snell’s Law
Example (Snell’s Law)
1=60
air
water
30
41
Find the angle (relative to the Normal) of the ray in the water.
Strategy:
Draw the Normal and measure 1 relative to the normal.
Look up n1 and n2
n1 = 1.00 (air)
n2 = 1.33 (water)
Plug into Snell’s Law and Solve for 2
1.00 sin60 = 1.33 sin2
sin2 = .651
2 = sin-1(.651)
2 = 41
Example (Snell’s Law and “Critical Angles”)
Normal
air n=1.00
water n=1.33
C
Find the “critical angle” where light travels parallel to the
surface of the water upon leaving the water.
Apply Snell’s Law
1.33 sinC = 1.00 sin90
sinC = .75
C = sin-1(.75)
C = 49
Question:
What happens to the light leaving the water if the incident
angle is greater than C?
Total Internal Reflection
Normal
air n=1.00
water n=1.33
C=49
Where will the
red ray travel?
=60
60
Apply Snell’s Law
1.33 sin60 = 1.00 sin2
sin2 = 1.15
2 = sin-1(1.15)
ERROR
The red ray is reflected internally as if the air/water surface
acted like a mirror.
The law of reflection is followed: 1 = 2
Fiber Optics
(Total Internal Reflection Application)
Core:
Cladding:
Transparent material about the diameter of a
piece of spaghetti.
Light travels through the core.
High or Low value for ncore??
High
Jacket
Encases the core.
Cladding
Light is not supposed to travel
through cladding.
High or Low value for ncladding??
Low
Core
Jacket:
Protective Coating
End View
Lenses
Flat “Lens”
Flat Thin “Lens”
Flat Lens is really a contradiction in terms.
Lenses are not flat!
“Thin” implies no “offset” from the original path.
Converging Lenses
Lens Factors
More Curvature
Larger Index of Refraction
Immerse glass (n=1.5)
lens in water (n=1.33)
Affect on Focal Length
Shortens focal length
Shortens focal length
Lengthens focal length
Lenses
Terms:
Thin lens:
Thin compared to focal length
Converging lenses:Parallel rays entering the lens converge
at a focal point behind the lens.
Diverging lenses: Parallel rays entering a lens diverge
away from each other behind the lens.
They appear to all come from a focal
point in front of the mirror.
Converging Lenses
Ray Diagrams
Purpose:
Determine the location and characteristics of
an image formed by a lens.
Rules:
1. Rays parallel to the principle axis strike
the lens and bend towards the focal point
behind the lens. (Definition of focal point)
2. Rays passing through the focal point in
front of the lens exit from the lens parallel to
the principle axis.
3. Rays going through the center of the lens
(at any angle) continue straight through the
“thin” lens.
Example (Objects outside focal point)
Converging Lenses Location of Interest
Lens
2f
f
1. Object is between lens and f.
2. Object is between f and 2f.
3. Object is outside of 2f.
Summary
Object
Image
location (do)
location
Type Magnification Upright
do  f
Front of lens Virtual
Positive
Yes
2f  do  f
Behind lens
Real
Positive
No
do  2f
Behind lens
Real
Negative
No
Diverging Lenses
Ray Diagram Rules
1. Rays parallel to principle axis diverge through
the lens and appear to originate at focal point in
front of lens.
2. Rays striking center of lens pass through lens
without bending.
3. Ray directed towards focal point behind the lens
emerges from lens parallel to principle axis.
Lens Equation
1
1
+
=
do
di
1
f
d
hi
M= - i =
do
ho
Exactly the same
as with mirrors
Converging Lens (Sign Convention)
f = positive
do = positive if object in front of lens (real object)
di = positive if image is in back of lens (real image)
ho = positive if object is upright
hi = positive if image is upright
Diverging Lens
f = negative
do = positive
di = positive if image is in back of the lens (not typical)