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