Formula Sheet Physics 112 Formulas Geometric Optics, Lenses, Optical Instrument

fdd oi

111 =+ o

i

d

dm −= N

dfM

i

−= 11

oe

e

ff

NfLM

)( −−=

e

o

f

fM −=

SHM

221 kxPE =

m

k=ω L

g=ω )cos( tAx ω= )sin( tAv ωω−= )cos(2 tAa ωω−=

Av ω=max Aa 2max ω=

Waves, Intensity, Sound

fv λ= lm

Fv

/=

A

PI =

24 r

PI

π= )/(log)10( 010 IIdB=β 212

0 /100.1 mWI −×=

Beats, Standing Waves Strings and Pipes )(12 veconstructinLL λ=− L,3,2,1,0)()( 2

1 =+= nedestructivn λ

D

λθ =sin D

λθ 22.1sin =

=L

vnf n 2

n=1,2,3, …

=L

vnf n 4

n=1,3,5,… 12 fffbeat −=

Light Interfere, Diffraction, Diffraction grating, Resolving power

cf =λ 00

1

µε=c E=cB

)(12 veconstructinLL λ=− L,3,2,1,0)()( 21 =+= nedestructivn λ

Light Interfere, Diffraction, Diffraction grating, Resolving power (cont.)

d

mλθ =sin d

m λθ

)(sin 2

1+= m=0,1,2,… θtanLy =

Wm

λθ =sin m=1,2,3,…

D

λθ 22.1min ≈ d

mλθ =sin m=0,1,2,3, … for small angles θθθ ≈≈ tansin

Resolving power, Thin Film Interference

D

λθ 22.1)sin( =

dm

λθ =sin m=0,1,2,3, … θtanLy = film

vacuumfilm n

λλ =

filmmphaset λ=+2 filmmphaset λ)(2 21+=+ 0=phase or

2filmλ

Relativity

2

2

1c

v

tt o

−

∆=∆

2

2

0 1c

vLL −=

2

2

1c

v

mvp

−

=

KEcm

c

v

mco +=

−

2

2

2

2

1

220

222 )( cmcpE +=

Photoelectric Effect, Bohr Atom

hfE = ph /=λ 0max WKEhf +=

2

2

)6.13(n

ZeVEn −=

Z

nmxrn

211 )1029.5( −=

−=22

111

mnR

λ fi EEhf −=

1710097.1 −= mxR

Compton Scattering, deBroglie, Heisenburg Uncertainty

ph /=λ )cos1( θλλ −=−′mch mxmc

h 121043.2 −=

π4hpx ≥∆∆

π4htE ≥∆∆

Hydrogen Orbitals

π2)1( hllL += nl < π2h

lz mL = lml l <<− π2h

sz mS = 21±=sm S,P,D,F,…

Nuclear Physics

XAZ NZA += ( ) 3

115102.1 Amr −×≅ teNN λ−= 0 Nt

N λ−=∆∆

21

693.0

T=λ

toeAA λ−= BqA 23.00 = (1 g)

Biological Effect Ionizing Radiation

m

q

xroentgensExposure

= −41058.2

1)(

Mass

EnergyseAbsorbedDo =

RBEseAbsorbedDolentDoseicalEquivaBio ×=log

Constants Refractive Indices: nair=1.00 noil=1.20 nwater=1.33 nglass=1.50 Speed of Sound: vair=343 m/s vwater=1440 m/s vglass=1880 m/s Speed of Light: c = 3x108 m/s Visible Light: 400 nm – 750 nm Blue Red Metric Exponents: milli = 10-3 micro = 10-6 nano = 10-9 pico = 10-12 fempto = 10-15

Conversion: 1.602x10-19 Joules = 1 eV 1 light-year = 9.46x1015m 1u =1.660566x10-27 kg =931.5 MeV/c2 Navagadro=6.022x1023 molecule/mol Planck’s Constant: h=6.63x10-34 Js hc=1.24x103 eVnm Electron Charge: e=1.602x10-19C

Masses of Elementary Particles: mp=1.6726x10-27 kg =938.3 MeV/c2=1.007276u mn=1.6749x10-27 kg =939.6 MeV/c2=1.008665u me=9.11x10-31 kg =0.511 MeV/c2=0.000549u

m( H21 )=2.014102u

m( H11 ) =1.007825u

Room Temperature: T=25oC=298K

Bohr Atom (ground state): E1=-13.6 eV Radioactive Decay: Ao=0.23Bq (1 gram) Ionizing Radiation: 1 Gray= 1J/kg 1 rad=0.01Gy 1Ci=3.70x1010Bq