Notes for December 15, 2004 



Today we used a magnifying glass and burned paper. This was possible becuase a magnifing glass makes an exact replaca of the image. 

Huyghens says that the center spot is s1-s2=0 and s1'-s2' = +_ n lamda 

units 
kilo = 10^3
mega = 10^6 
micro = 10^-6 
milli = 10^-3 
pico = 10^-12 

greek letters 
sigma 
omega 
alpha 
lamda 
theta 
Delta 
delta 
mu 
beta 
Lamda 
nu 
Omega 

Mu = micrometer symbol 

Intensity of light 
Energy / Area = intesity 
energy of sunlight is 1000w/m^2 
set something on fire the concentration of sunlight must be greater then 50 kw/m^2

complex numbers 
i= (-1)^1/2 
i^1= i 
i^2 = -1 
i^3 = -i 
i^4 = 1

multiplying two complex numbers 
(a+bi)(c+di) = ac+adi+bci+bdi^2 = (ac-bd)+(ad+bc)i = e+if
(a+bi)(a-bi)= a^2-abi+abi-b^2i^2 = a^2+b^2 = distance from the origin^2 
e = a+bi 
e* = a-bi 
(ee*)^1/2 = magnitude of the point 
cartesian cordinates are 2D with two variables 
Polar cooridinates are 3D coordinates with three variables 
e^x
e^1= 2.718281828459045
e^itheta = cos(theta)+isin(theta) 
Euler's formula e^ipie + 1 =0 Best math formula