!"#$%&'()'*+,(-"#(../( 01'&(+2'$ ( .( ( ) U = - - PDF document

SLIDE 1

!"#$%&'()'*+,(-"#(../( 01'&(+2'$ (

.(

SLIDE 2

x(t) = Acos 2 t T

• = Acos t

( )

F

SHM = kx

SHM

2

= k m

• =

k m T = 2 m k

sin

• mgsin mg

F

restoring = mg = mg

L

• s

s = L

(displacement = arc on circle of radius R)

k = mg L

• T = 2

m k

• T = 2

L g U = 1 2 kx2 = 1 2 kA2 cos t

( )

( )

2

K = 1 2 mv2 = 1 2 kA2 sin t

( )

( )

2

E = U + K = 1 2 kA2

I0 = 1012 W/m2 = 1016 W/cm2 IPain = 1013 I0

f ' = f 1+ uOBS c

• (stationary source)

f ' = f 1 1 uSRC / c

• (stationary observer)

f ' = 1± uOBS c

• 1 uSRC

c

• (source and/or obs moving)

waves on a string:

1 = 2L1

• L1 = 1

2

• f1 = v

1 = v 2L1 n = 1 n , Ln = L1 n , fn = v n = n f1 y1 t

( ) = Acos 2 f1t

( ),

y2 t

( ) = Acos 2 f2t

( )

y1 + y2 = 2Acos 2 f1 f2 2

• t
• cos 2

f1 + f2 2

• t
• fBEAT = f1 f2 fOSC = f1 + f2

2

dB]

[ ] = 10log10

I I0

• I0 = reference level

3(

SLIDE 3

Doppler effect for EM waves : f ' = f 1± u c

• (u = relative speed, use + for approaching, - for moving apart)

c = f E = cB uE = 1 2 0E2, uB = 1 2 B2 µ0 , uE = uB ERMS = EMAX 2 , BRMS = BMAX 2 uAVG = 0E2

RMS OR uAVG = B2 RMS

µ0

I = u c = c 0E2

• = c

B2 µ0

• absorption: p = U

c = I area

( )t

c reflection: p = 2U / c FAVG = I area

( )

c pAVG = IAVG c

I = I0 cos2 (Malus)

Spherical mirrors: f = R / 2 , 1 dO + 1 dI = 1 f m = dI dO

• (4,()",456+(-"#(7"17'6+($4##"#,8(1+*'56+(-"#(7"16+28(410149+(-"#()&'1+(

(:;(4,()",456+(4-(4$'*+(4,(41(-#"19("-($4##"#8(1+*'56+(4-(<+=41:(( (:>(4,()",456+(4-(4$'*+(4,(41(-#"19("-($4##"#8(1+*'56+(4-(<+=41:( n1sin1 = n2 sin2 sin2 = n1 n2 sin1 cMEDIUM = c nMEDIUM

Total internal reflection critical angle: sinc = n2 n1 Total polarization of reflection (Brewster angle): tanB = n2 n1

Angular magnification: M = '

• refractive power, diopters =

1 f ,meters f - number = f D

1 dO + 1 dI = 1 f m = dI dO

Magnifiers: N = near point distance for image viewed at : M = N f , at near point : M = 1+ N f Compound microscope : MTOTAL = dI N fOBJ fEYEP Telescope : MTOTAL = fOBJ fEYEP , L = fOBJ + fEYEP

c = 3108 m s2, µ0 = 4 107T m A1 0 = 8.85 1012C2 N 1 m2 e = 1.60 1019C, k = 8.99 109 N m2 / C2

?(

SLIDE 4

c = 3108 m s2 h = 6.631034 J s = 4.135 1015eV s; 1 eV = 1.60 1019J Constructive interference: = m, m = 0,1,2… 2-slit pattern, slit spacing d, bright fringes: sin = m d Fringe position on screen at distance L: ym = L tanm Path diff for constructive: = mVACUUM = 2nt or = mn = 2t where n = VACUUM /n

( )

n = film index, t = film thickness, m = integer Use m +1/ 2

( ) for destructive.

Add / 2

( ) to for a reflection with phase change.

Single slit of width W, angle m to order-m minimum: W = m sinm

Rayleigh criterion: min = 1.22 D Separation at distance L : y = L tanmin Lmin

Angle of mth bright fringe for grating with N lines/unit length : = sin mN

t = t0 1 v2 c2 L = L0 1 v2 c2

p = mv 1 v2 c2 m = m0 1 v2 c2 , E = mc2

K = m0c2 1 1 v2 c2 1

• fpeak = 5.88 1010 s1 K1

( )T

E = hf = hc

• Kmax = hf W0

p = h

• 1 rad = 57.296

c = f melectron = 9.111031kg, 5.49 104u, 8.19 1014J, 0.511 MeV K = p2 2m = h2 2m2

xp h 2 E t h 2

@(

SLIDE 5

1 = R 1 22 1 n2

• R = 1.097 107 m1

rn = h2 4 2mkZe2

• n2

En = 13.6 eV

( ) Z 2

n2

pn = mvn = m 2ke2 nh

• E = Ef Ei = 13.6 eV

1 ni

2 1

nf

2

• n = h

pn = h mvn

= 0,1,2...max where max = n 1; m = , …–1, 0, 1, … 1, L = +1

( ) h / 2 ( )

E = hf = hc

• deBroglie : n n = 2rn

E = m c2 931.5 MeV/c2 = 1 u

Z

AX : Z=number of protons,

A=number of nucleons, number of neutrons N = A- Z Isotope = same Z, different A alpha decay: Z Z - 2, A A- 4. beta-minus or -plus decay: Z Z +1 or Z 1, A = unchanged.

= ln 2 T

1/2

N(t) = N0et R = N

hadron = strongly interacting, not fundamental: constituents = quarks quark+antiquark = meson, 3 quarks = baryon lepton = weak interaction, fundamental particle boson = integer spin, carrier of forces ( ,W±,Z 0) fermion = half-integer spin, matter (eg, electrons, nucleons)

A(