Transcript Document

University Physics
Midterm Exam Overview
16. THE NATURE OF LIGHT


Speed of light
c = 3x108 m/s (in the vacuum)
v = c/n (in the media)
Formulas
c = lf = l/T , f

= 1/T
(How to memorize? Think about v=d/t.)

Refraction and Reflection

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The incident ray, the
reflected ray, the
refracted ray, and the
normal all lie on the same
plane
What is the normal?
How to find angle of
incidence and angle of
refraction?
Snell’s Law

n1 sin θ1 = n2 sin θ2

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θ1 is the angle of incidence
θ2 is the angle of refraction
As light travels from one
medium to another


its frequency (f) does
not change
But the wave speed
(v=c/n) and the
wavelength (lmed=l/n)
do change
17. THIN LENSES
1 1 1
 
Thin Lens Equation
s s' f
Magnification
h'
s'
M  
h
s
Quantity
Positive “+”
Negative “-”
s - Object Distance
Front*
Back*
s’ - Image Distance
Back*
Real
Front*
Virtual
f - Focal Length (f)
Converging “()”
Diverging “)(”
h – Image Height
Upright
Inverted
Combination of Thin Lenses
1 1 1
 
s1 s1 f1
1 1
1
 
s2 s2
f2
Spherical Mirrors

Focal length is
determined by the
radius of the mirror
R "" converging
f  

2 "" diverging 
Corrective Lenses

Nearsighted correction – bring infinity to the far
point
image distance = - far point (upright virtual image)
object distance = ∞

Farsighted correction – bring the close object
(accepted 25 cm) to the near point of farsighted
image distance = - near point (upright virtual image)
object distance = 25 cm

Power of the Lens
P=1/f (in diopters or m-1)
18. Wave Motion
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A wave is the motion of a disturbance
Mechanical waves require
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Some source of disturbance
A medium that can be disturbed
Some physical connection between or mechanism
though which adjacent portions of the medium
influence each other
All waves carry energy and momentum
Types of Waves – Traveling
Waves

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Flip one end of a long
rope that is under
tension and fixed at
one end
The pulse travels to the
right with a definite
speed
A disturbance of this
type is called a
traveling wave
Types of Waves – Transverse

In a transverse wave, each element that is disturbed
moves in a direction perpendicular to the wave
motion
Types of Waves – Longitudinal


In a longitudinal wave, the elements of the medium
undergo displacements parallel to the motion of the
wave
A longitudinal wave is also called a compression
wave
Speed of a Wave

v=λƒ


Is derived from the basic speed equation of
distance/time
This is a general equation that can be applied
to many types of waves
Speed of a Wave on a String

The speed on a wave stretched under some
tension, F
v 


F
m
where m 
m
L
m is called the linear density
The speed depends only upon the properties
of the medium through which the disturbance
travels
Waveform – A Picture of a
Wave

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The brown curve is a
“snapshot” of the wave
at some instant in time
The blue curve is later
in time
The high points are
crests of the wave
The low points are
troughs of the wave
Interference of Sound Waves

Sound waves interfere

Constructive interference occurs
when the path difference
between two waves’ motion is
zero or some integer multiple of
wavelengths
 path difference = mλ

Destructive interference occurs
when the path difference
between two waves’ motion is
an odd half wavelength
 path difference = (m + ½)λ
Mathematical Representation
A wave moves to the left with velocity v and wave length l, can
be described using
 2

D( x, t )  Dm sin  ( x  vt )  Dm sin(kx  t )
l

It can be derived by comparing the factors of x and t, that
k
2
l
and
  2
v
l
 2f
Dividing  and k gives v, that is
v

k
Doppler Effect

The doppler effect is the change in frequency
and wavelength of a wave that is perceived
by an observer when the source and/or the
observer are moving relative to each other.

If the source is moving
relative to the observer
f
f
vs
1
v
http://en.wikipedia.org/wiki/Doppler_effect
19. INTERFERENCE
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Light waves interfere with each other much
like mechanical waves do
Constructive interference occurs when the
paths of the two waves differ by an integer
number of wavelengths (Dx=ml)
Destructive interference occurs when the
paths of the two waves differ by a half-integer
number of wavelengths (Dx=(m+1/2)l)
Interference Equations
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The difference in path difference can be found as
Dx = d sinθ
For bright fringes, d sinθbright = mλ, where m = 0, ±1, ±2, …
For dark fringes, d sinθdark = (m + ½) λ, where m = 0, ±1, ±2, …
The positions of the fringes can be measured vertically from the
center maximum, y  L sin θ (the approximation for little θ)
Single Slit Diffraction

A single slit placed
between a distant light
source and a screen
produces a diffraction
pattern
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It will have a broader,
intense central band
The central band will be
flanked by a series of
narrower, less intense
dark and bright bands
Single Slit Diffraction, 2
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The light from one portion of
the slit can interfere with light
from another portion
The resultant intensity on the
screen depends on the
direction θ
Single Slit Diffraction, 3

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The general features of
the intensity distribution
are shown
Destructive interference
occurs for a single slit of
width a when
asinθdark = mλ

m = 1, 2, 3, …
Interference in Thin Films

The interference is due to the
interaction of the waves reflected
from both surfaces of the film

Be sure to include two effects when
analyzing the interference pattern from
a thin film
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Path length
Phase change
Facts to Remember
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The wave makes a “round trip” in a
film of thickness t, causing a path
difference 2nt, where n is the
refractive index of the thin film
Each reflection from a medium with
higher n adds a half wavelength l/2
to the original path
The path difference is
Dx = x2  x1


For constructive interference
Dx = ml
For destructive interference
Dx = (m+1/2)l
where m = 0, 1, 2, …
Path change
x1 = l/2
Path change
x2 = 2nt
Thin Film Summary
Dx = 2nt
x1 = 0
Dx = 2nt
x1 = l/2
x2 = 2nt+l/2
Thinnest film leads to
p2 = 2nt
High
Low
n
n
Low
Dx = 2nt + l/2
x1 = 0
x2 = 2nt + l/2
High
n
High
High
constructive
2nt = l
destructive
2nt = l/2
Dx = 2nt  l/2
x1 = l/2
x2 = 2nt
Thinnest film leads to
constructive
Low
2nt = l/2
n
destructive
Low
2nt = l
20. COULOMB’S LAW
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Coulomb shows that an electrical force has
the following properties:
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It is along the line joining the two point charges.
It is attractive if the charges are of opposite
signs and repulsive if the charges have the
q1 q2
same signs
F  ke
r2
Mathematically,
ke is called the Coulomb Constant

ke = 9.0 x 109 N m2/C2
Vector Nature of Electric
Forces

The like charges
produce a repulsive
force between them

The force on q1 is
equal in magnitude
and opposite in
direction to the force
on q2
Vector Nature of Forces, cont.
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The unlike charges
produce a attractive
force between them

The force on q1 is
equal in magnitude
and opposite in
direction to the force
on q2
The Superposition Principle

The resultant force on any one charge equals
the vector sum of the forces exerted by the
other individual charges that are present.

Remember to add the forces as vectors
Superposition Principle
Example
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The force exerted by
q1 on q3 is
F13
The force exerted by
q2 on q3 is
F23
The total force
exerted on q3 is the
vector sum of
and
F13
F23