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Photonics Handbook

Physical Constants & Conversion Factors

Physical Constants & Conversion Factors

Length [I]

1 meter (m) = 39.3700 in. = 3.280833 ft = 1.093611 yd
1 kilometer (km) = 0.6213711 mi = 0.53996 nautical mi
1 micron (µm) = 10—6 m = 10—4 cm = 104 Å = 39.3700 x 10—6 in.
1 nanometer (nm) = 10—7 cm = 10—9 m = 10—3 µm = 10 Å
1 angstrom (Å) = 10—8 cm = 10—10 m = 10—4 µm = 3.937 x 10—9 in.
1 inch (in.) = 1000 mil = 2.54 cm
1 foot (ft) = 30.48 cm = 1.89394 x 10—4 mi
1 yard (yd) = 0.9144 m
1 fathom = 6 ft = 1.828804 m
1 mile (mi) = 1760 yd = 5280 ft = 6.3360 x 104 in. = 1.609344 km = 0.868979 nautical mi
1 nautical mi = 1852 m = 6076.10333 ft = 1.15078 mi
1 light-year (l.y.) = 5.8804 x 1012 mi = 9.46073 x 1012 km = 0.307 parsec

Area [I2]

1 cm2 = 10—4 m2 = 10.764 x 10—4 ft2 = 0.15500 in.2
1 km2 = 0.3861006 mi2 = 247.1044 acres
1 circular mil = area of circle 1 mil in diameter = 0.78540 sq mil = 10—6 circular in.
1 in2 = 6.4516 cm2 = 1.27324 x 106 circular mil
1 yd2 = 9 ft2 = 0.8361274 m2
1 mi2 = 3.0976 x 106 yd2 = 640 acres = 2.589998 x 106 m2
1 acre = 43,560 ft2 = 10 sq chains = 4046.873 m2

Volume [I3]

1 cm3 = 0.061023 in.3 = 0.03381 fl oz
1 liter (L) = 1000.027 cm3 = 33.8147 fl oz = 1.05671 qt (liquid) = 0.26418 gal
1 ft3 = 1728 in.3 = 0.02831685 m3 = 7.481 gal = 0.80357 bushel
1 gallon (gal) = 231 in.3 = 0.13368 ft3 = 3.785412 L
1 quart (qt) = 32 fl oz = 0.9463529 L
1 pint (pt) (liquid) = 0.5 qt = 28.875 in.3 = 0.4731765 L
1 fluid ounce (fl oz) = 29.57353 mL

Time [t]

1 week = 7 days = 168 h = 10,080 min = 604,800 s
1 day = 1440 min = 86,400 s
1 calendar year = 365 days = 8760 h = 5.256 x 105 min = 3.1536 x 107 s
1 year sidereal = 365.256 days = 8766.14 h = 3.155815 x 107 s

Velocity [It—1]

1 m/s = 2.2369 mi/h
1 mi/h = 1.4667 ft/s = 0.8690 knots = 1.609344 km/h = 0.44704 m/s
1 knot = 1 nautical mi/h = 1.1508 st mi/h = 1.6878 ft/s = 0.5144444 m/s

Angular Velocity [t—1]

1 rad/s = 0.1592 rev/s = 9.549 rpm = 57.296 deg/s
1 rpm = 0.01667 rev/s = 0.1047198 rad/s = 6 deg/s

Acceleration [It—2]

1 ft/s2 = 30.48 cm/s2 = 0.6818 mi/h-s

Angle

1 radian (rad) = 360°/2π = 57.29608 deg = 103 angular mil
1 degree (deg) = 60 min = 0.01745329 rad
1 minute (min) = 60 s = 2.908882 x 10—4 rad
1 mil = 360/6400 deg = 0.05625 deg = 9.817477 x 10—4 rad
1 s slope = 4.848 microinch/in. = 0.001 in./17.19 ft
1 solid angle = 4π steradians = 12.566 steradians = 1 sphere
1 steradian = 0.079580 solid angle

Mass [m]

1 gram (g) = 2.20462 x 10—3 lb (av) = 0.03527 oz (av) = 15.4324 grains
1 pound (lb) avoirdupois (av) = 16 oz (av) = 7000 grains = 256 drams (av) = 453.5924 g
1 ounce (oz) (av) = 16 drams (av) = 437.5 grains = 28.34952 g
1 short ton = 2000 lb (av) = 907.1847 kg = 20 hundredweight (short)
1 long ton = 2240 lb (av) = 1016.047 kg = 20 hundredweight (long)

Density [ml—3]

1 lb/ft3 = 5.787 x 10—4 lb/in.3 = 16.01846 kg/m3 = 1.6018 x 10—2 g/cm3
1 g/cm3 = 0.03613 lb/in.3 = 64.23 lb/ft3

Pressure [ml—1t—2]

1 atmosphere (atm) = 1.0133 bar = 14.696 lb/in.2 = 1.01325 x 106 dyn/cm2 = 760 Torr = 1033.2 g/cm2 (0 °C) = 760
     mm Hg (0 °C) = 29.921 in./ Hg (0 °C) = 33.903 ft water (0 °C) = 1.01325 x 105 Pa
1 dyn/cm2 = 1.01971 x 10—3 g/cm2 = 1.4504 x 10—5 lb/in.2 = 0.1 Pa
1 bar = 1.0 x 106 dyn/cm2 = 0.98692 atm
1 pound-force per square inch (psi) (lbf/in.2) = 70.307 g/cm2 = 6.894757 x 104 dyn/cm2

Temperature

temperature differences: Δ1 °Celsius (C) = Δ1.8 °Fahrenheit (F) = Δ1.8°Rankine (R) = Δ1 kelvin (K) = Δ0.8
    Δ1.8°Rankine (Ra) = Δ1 kelvin (K) = Δ0.8°Réaumur (Re)
0 °C = 273.15 K = 32 °F = 492 °R = 0°Re
100 °C = 373.15 K = 212 °F = 671.67 °Ra = 80 °Re
0 K = 273.15 °C = -459.67 °F = 0°Ra = -218.52 °Re

Force [mIt—2]

1 Newton = 1 x 105 dyn = 0.22481 lbf
1 dyn = 2.2481 x 10—6 lbf = 7.2330 x 10—5 poundal (pdl) = 0.0010197 g wt
1 g wt = 0.07932 pdl = 980.665 dyn = 2.2046 x 10—3 lb wt
1 lbf = 32.174 pdl = 453.59 g wt = 4.4482 N
1 pdl = 0.031081 lbf = 14.098 g wt = 1.382550 x 10—1 N

Work and energy [ml—2t—2]

1 Joule (J) = 1 N meter (N•m) 1 x 107 ergs = 1 x 107 dyn cm = 1 W•s = 1 V coulomb = 0.73756 ft lbf = 2.3889 x
     10—4 kg cal (mean) = 9.4708 x 10—4 Btu (mean) = 23.730 ft pdl = 2.778 x 10—7 kWh - 3.725 x 10—7 hp h
1 calorie (International Table) = 4.1868 J
1 calorie (thermochemical) = 4.184 J
1 calorie (15°C) = 4.18580 J (abs) = 0.003968 Btu
1 kWh = 3413.0 Btu (mean) = 2.6552 x 106 ft lb = 1.3410 hp h = 3.6 x 106 J
1 liter atm (normal) = 3.7745 x 10—5 hp h = 24.206 g cal (mean) = 101.328 J
1 atomic mass unit (amu) = 931.16 MeV = 1.65983 x 10—24 g mass (energy equiv.)
1 electon volt (eV) = 1.60207 x 10—19 J

Power [ml—2t—3]

1 Btu (mean)/min = 0.023575 hp = 17.580 W (abs) = 778.0 ft•lbf/min
1 erg/s = 1 x 10—7 W = 1.34 x 10—10  hp = 5.688 x 10—9 Btu (mean)/min = 1.4333 x 10—9 kg cal (mean)/min =
     7.3756 x 10—8 ft•lbf/s
1 hp (U.K.) = 0.70696 Btu (mean)/s = 550 ft•lbf/s = 745.70 W = 10.688 kg-cal (mean)/min
1 hp (electric) = 746 W

Torque [ml2t—2]

1 dyn•cm = 1.0197 x 10—8 kfg•m = 7.3756 x 10—8 lbf•ft = 8.8507 x 10—7 lbf•in
1 kgf•m = 9.8066 x 107 dyn•cm
1 lbf•ft = 1.355818 x 107 dyn•cm
1 pdl•ft = 4.2140 x 105 dyn•cm
1 lbf•in = 1.1298 x 106 dyn•cm
1 lbf•ft = 1.3558 N•m

Physical Constants

h = Planck's constant = 6.62606957 x 10—34 J s
Ro = molar gas constant = (8.314472±0.000015) J/K•mol
k = Boltzmann constant = (1.3806505±0.0000024) x 10—23 J/K
σ = Stefan-Boltzmann constant = (5.670400±0.000040) x 10—8 w/m2K4
c = speed of light in a vacuum = 2.99792458 x 108 m/s = 186,284 mi/s
F = Faraday constant = (96,485.3383±0.0083) C/mol
e = elementary charge = (1.60217653±0.00000014) C
e/m = specific elementary charge = (1.75888±0.00005) x 1011 abs coulombs/kg
Na = Avogadro constant = (6.0221415±0.0000010) x 1023/mol
αo = h2/4πme2 = Bohr radius = (5.29177±0.0000000018) x 10—10 m
εo = 1/µoc2 = electric constant = 8.854187817 x 10—12 farad/m
µo = permeability of free space = 4π:(4)(3.14) = 12.5664 x 10—7 henry/m

Miscellaneous Constants & Conversions

Density of water 3.98 °C, 760 mm Hg = 0.03613 lb/in.3 = 62.43 lb/ft3 = 1 g/ml = 0.999973 g/cm3
Density of air (STP) = 1.293 x 10—3 g/cm3
STP = standard temperature & pressure = 0 °C & 760 mm Hg
Water heat of fusion (0 °C) = 79.71 g-cal (15 °C)/g
Water heat of vaporization (100 °C) = 539.55 g-cal (15 °C)/g
Molar volume (STP) = 359 ft3/lb-mole = (22.4207±0.0006) liters/g-mole (physical scale)
Velocity of sound: in air (STP) = 331.7 m/s = 1088 ft/s
                              in water (20 °C) = 1470 m/s = 4823 ft/s
Attenuation of sound in air (STP-37% RH) = δ≅6 x 10—14 dB (kc)2/ft
Viscosity of water (20 °C) = 1.002 centipoise = 0.01002 dyn-s/cm2
1 curie activity = 3.7 x 1010 disintegrations/s = 3.7 x 104 Rutherford
1 roentgen (r) radiation damage = ionization by x- or gamma rays producing 1 esu of charge in 1 cm3 air (STP)
1 barn cross section = 10—24 cm2
Ratio physical (016  = 16) to chemical scale (0 = 16) of atomic weights = 1.000272±0.000005
M = mass of earth = 5.983 x 1024 kg = 6.595 x 1021 tons
Interference fringe = 11.6 microinches/fringe (He line = 5875.6a)
π = 3.1415926535+
e = 2.7182818284+
Logen = loge 10 x log10n = 2.3026 log10n
1 kWh ≅4.2 x 10—5 g U235 in fission
           ≅6.4 x 10—6 g H3 in H3 (d,n) He4 reaction
           ≅average noon insolation in 1 h on horizontal plane of 1 m2
           ≅0.74 lb (highest power station efficiency on 12,500 Btu/lb coal)
Zo(µo/εo)1/2 = impedance of free space = (376.731±0.001) ohm (Ω)
G = Newton's grav constant = (6.670±0.005) x 10—8 cm3/g-s
g = acceleration due to gravity (standard) = 32.174 ft/s2 = 980.665 cm/s2 = 386.09 in./s2 = 21.94 mi/ h-s
Rest energy of the electron = 0.51098 MeV
Electron mass = (9.1085±0.0006) x 10—28 g = 0.51098 MeV = 5.48760 x 10—4 AMU
Proton mass = (1.67243±0.00010) x 10—24 g = 938.232 MeV = 1.007593 AMU
Neutron mass = (1.67474±0.00010)± 10—24 g = 939.526 MeV = 1.008982 AMU
α particle mass = (6.6442±0.0012) x 10—24 g = 3727.377 MeV = 4.00294 AMU
H1 atom mass = (1.67335±0.00010) x 10—24 g = 938.743 MeV = 1.008142 AMU
GLOSSARY
torque
A calculated measure of the ability of an incident force to cause an object to spin. The spin speed of any given object is a direct function of the duration of the torque application.
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