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 = f = f = 1/T (How to memorize? Think about v=d/t.)
Refraction and Reflection
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 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 (med=/n) do change
17. THIN LENSES
fss
1
'
11
s
s
h
hM
''Magnification
Thin Lens Equation
Quantity Positive “+” Negative “-”
s - Object Distance Front* Back*
s’ - Image DistanceBack*Real
Front*Virtual
f - Focal Length (f) Converging “()” Diverging “)(”
h – Image Height Upright Inverted
Combination of Thin Lenses
222
111
fss
111
111
fss
Spherical Mirrors
Focal length is determined by the radius of the mirror
diverging
convergingRf
""
""
2
Corrective Lenses
Nearsighted correction – bring infinity to the far pointimage distance = - far point (upright virtual image)
object distance = ∞
Farsighted correction – bring the close object (accepted 25 cm) to the near point of farsightedimage 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
A wave is the motion of a disturbance Mechanical waves require
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
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 = λ ƒ 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
is called the linear density The speed depends only upon the properties
of the medium through which the disturbance travels
F mv where
L
Waveform – A Picture of a Wave
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
)sin()(2
sin),( tkxDvtxDtxD mm
2
k fv
22
It can be derived by comparing the factors of x and t, that
and
Dividing and k gives v, that is
kv
A wave moves to the left with velocity v and wave length , can be described using
Doppler Effect
If the source is moving relative to the observer
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.
http://en.wikipedia.org/wiki/Doppler_effect
v
vf
fs
1
19. INTERFERENCE
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 (x=m)
Destructive interference occurs when the paths of the two waves differ by a half-integer number of wavelengths (x=(m+1/2))
Interference Equations The difference in path difference can be found as
x = 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 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
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
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 Path length Phase change
Facts to Remember
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 /2 to the original path
The path difference is x = x2 x1 For constructive interferencex = m For destructive interference
x = (m+1/2)where m = 0, 1, 2, …
Path change x1 = /2
Path changex2 = 2nt
Thin Film Summary
Low
Low
x = 2nt /2
n
x1 = /2x2 = 2nt
High
Low
x = 2nt
n
x1 = 0 p2 = 2nt
Low
High
x = 2nt
n
x1 = /2 x2 = 2nt+/2
High
High
x = 2nt + /2
n
x1 = 0 x2 = 2nt + /2
Thinnest film leads to
constructive 2nt =
destructive 2nt = /2
Thinnest film leads toconstructive
2nt =
destructive 2nt =
20. COULOMB’S LAW
Coulomb shows that an electrical force has the following properties: 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 same signs
Mathematically, ke is called the Coulomb Constant
ke = 9.0 x 109 N m2/C2
2
21e r
qqkF
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.
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
The force exerted by q1 on q3 is
The force exerted by q2 on q3 is
The total force exerted on q3 is the vector sum of
and
13F
13F
23F
23F