Transcript Diffraction - umanitoba.ca

Refraction
n1 = 1
1
1
1
2
n2 > 1
2
2
Radius = vT = (c/n)T
Triangle hce sin 1 = 1/hc
Triangle hcg sin 2 = 2/hc
sin 1 /sin 2 = 1 /2 = (v1/f) / (v2/f) = v1/v2 = (c/n1)/(c/n2) = n2/n1
n1 sin 1 = n2 sin 2
Snell’s Law
n1 sin 1 = n2 sin 2
2=/2 ==>
sin c = n2/n1
Water n=1.5
Air
n=1.
c= 41.80
Reflection
refraction
Halo
1
2
3
4
Sun Dogs
1
n sin2=sin 1
2
3
4
1200
n sin3=sin 4
2 + 3 = 600
Deflection = 1 + 4 - 600
n=1.33
nred < nblue
vred=c/nred > vblue =c/nblue
prism
Fermat’s Principle
• The path taken by light in travelling from
one point to another is such that the time of
travel is a minimum


Refraction
L L
nL n L
t 1 2  1 1 2 2
v1 v2
c
c
L12  a 2  x 2
L22  b 2  ( d  x ) 2
• Minimize t with respect to x
• dt/dx=0 using dL1/dx=x/L1 =sin1
and dL2/dx=(x-d)/L2 = -sin2
• dt/dx=(n1sin 1 - n2 sin 2)/c = 0
Time?