©Rutgers, The State University of New Jersey. Department of Physics & Astronomy
Physics 228 Equation Sheet #1
Propagation of Light
Wave Optics
θi = θr
[Law of Ref lection]
c
nmedium =
[Index of Ref raction]
vmedium
λF =
λair
nF
n2
n1
Geometric Optics
(5)
[Brewster0 s Angle]
tanθP =
[P lane M irror]
1
= (n − 1)
f
m = 0, 1, 2, · · ·
φ
φ
sin ωt +
Ep = 2E0 cos
2
2
πdsinθ
πd
I = I0 cos2
y
≈ I0 cos2
λ
λ`
(8)
Phase Shift for Adjacent Slits
(9)
2πd
sinθ
λ
Thin Film Interference
1
1
1
+
=
do
di
f
(11)
∆ef f ective = ∆ref lect 1 + 2t + ∆ref lect 2
hi
di
=−
h0
do
(12)
1
f
[Lens P ower]
(13)
[Lensmaker0 s Equation] (14)
sinθ = m
λ
a
N
M=
+1
f
N
f
Intensity of Two-Slit Diffraction
2
sin (πasinθ/λ)
πdsinθ
I = I0 cos2
λ
πasinθ/λ
Limits of Resolution
λ
θmin =
[Slit of W idth a]
a
[Eye f ocused at ∞]
(15)
[Eye f ocused at near point, N ]
M =−
M = Me m o ≈
N`
fe fo
f0
fe
[T elescope]
[Compound M icroscope]
[Destructive Interf erence]
m = ±1, ±2, ±3, · · ·
2
2
sinβ/2
sin (πasinθ/λ)
I = I0
= I0
β/2
πasinθ/λ
Magnifying Glass
M=
(19)
(20)
(21)
(22)
(23)
Diffraction
M=
1
1
+
R1
R2
dsinθ = mλ [Constructive]
1
λ [Destructive]
dsinθ = m +
2
(7)
(10)
(18)
m = 0, ±1, ±2, · · ·
(6)
r
2
fmirror =
[Destructive]
∆φ =
|do | = |di |
P =
[Constructive]
2-Slit Interference
n2
n1
I = I1 cos2 θ
∆ef f = mλ
1
∆ef f = m +
λ
2
(3)
(4)
Polarization
1
I1 = Iunpolarized
2
General Condition For Interference In terms of Effective
Phase Difference (∆ef f )
(2)
[Snell0 s Law]
n1 sinθ1 = n2 sinθ2
sinθc =
(1)
(16)
1.22λ
D
λ
RP ≈
2
θmin =
(24)
(25)
(26)
(27)
[Circular Aperture Diameter D]
[M icroscope Resolving P ower]
(28)
Diffraction Grating
(17)
dsinθ = mλ
[Constructive Interf erence]
m = 0, ±1, ±2, · · ·
(29)
©Rutgers, The State University of New Jersey. Department of Physics & Astronomy