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Interference and Diffraction
Two Slit Interference: Constructive interference (bright fringes):
d sin ( θ ) m m-order of interference fringe
m=0, ±1, ±2, …
Destructive interference (dark fringes):
d sin θ m^1
( ) m=0, ±1, ±2, …
Single Slit Diffraction: Angular displacement of mth^ order dark fringe
mλ
sin(θ)
D
m-order of dark fringe
m=±1, ±2, … NOTE: m 0
m=0 yields central bright fringe maximum of width
L
D
All other bright fringes have widths
L
D
Diffraction Grating
Constructive interference (bright fringes):
d sin() m m=0, ±1, ±2,…
Distance between successive diffraction maxima:
x (^) m 1 x (^) m L d
^ ^ ^
where L is the distance from
diffraction grating to screen [sin()≈tan()≈]
Half-width of diffraction maxima: L N d
d= N
meters and N is the number of lines in one meter
Bright fringes get narrower as N increases.
Invariance of speed of light: The speed of light in vacuum (c=3.00 x 10^8 m/s) is the same in all inertial frames of reference and is independent of the motion of the source or observer.
Relativistic Energy
For objects with velocity approaching that of light, expression for energy of motion changes:
Total Energy of object with rest mass m:
E = K + mc 2 =
2
2 2
m c
1 v /c
Rest Energy of an object with mass m:
E = mc 2
m is the rest mass of an object that is at rest
Energy of massless particle:
E = pc where p is the momentum of particle
