University Physics

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# University Physics - PowerPoint PPT Presentation

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

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
• 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 (lmed=l/n) do change
17. THIN LENSES

Thin Lens Equation

Magnification

Spherical Mirrors
• Focal length is determined by the radius of the mirror
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
• 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
• 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
• 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

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

and

Dividing w and k gives v, that is

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
• 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
• 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
• 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

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, …

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

constructive 2nt = l

destructive2nt = l/2

Thinnest film leads toconstructive 2nt = l/2

destructive2nt = l

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
• 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