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University Physics. Midterm Exam Overview. 16. THE NATURE OF LIGHT. Speed of light c = 3x10 8 m/s (in the vacuum) v = c/n (in the media) Formulas c = l f = l/T , f = 1/T (How to memorize? Think about v=d/t.). Refraction and Reflection.

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university physics

University Physics

Midterm Exam Overview

16 the nature of light
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
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
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
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
17. THIN LENSES

Thin Lens Equation

Magnification

spherical mirrors
Spherical Mirrors
  • Focal length is determined by the radius of the mirror
corrective lenses
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
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
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
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
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
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
Speed of a Wave on a String
  • The speed on a wave stretched under some tension, F
    • 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
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
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
Mathematical Representation

A wave moves to the left with velocity v and wave length l, can be described using

It can be derived by comparing the factors of x and t, that

and

Dividing w and k gives v, that is

doppler effect
Doppler Effect
  • If the source is moving relative to the observer
  • The doppler effectis 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

19 interference
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 (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
Interference Equations
  • 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
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
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
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
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
Facts to Remember

Path change x1 = l/2

Path changex2 = 2nt

  • 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 interferenceDx = ml
    • For destructive interferenceDx = (m+1/2)l

where m = 0, 1, 2, …

thin film summary

Dx = 2nt + l/2

Dx = 2nt l/2

Dx = 2nt

Dx = 2nt

x1 = l/2

x1 = l/2

x1 = 0

x1 = 0

x2 = 2nt + l/2

x2 = 2nt+l/2

p2 = 2nt

x2 = 2nt

Low

High

Low

High

n

n

n

n

Low

High

Low

High

Thin Film Summary

Thinnest film leads to

constructive 2nt = l

destructive2nt = l/2

Thinnest film leads toconstructive 2nt = l/2

destructive2nt = l

20 coulomb s law
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
vector nature of electric forces
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
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 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
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