Formulae 2112 Exam 4 Fall17.pdf - Formula Sheet for LSU...

Formula Sheet for LSU Physics 2112, EXAM 4, Fall 2017
Constants:
0
= 8 . 85 × 10
- 11
C
2
/Nm
2
1
4 π
0
= 8 . 99 × 10
9
Nm
2
/C
2
μ
0
4 π
= 10
- 7
Tm/A
μ
0
= 1 . 26 × 10
- 6
Tm/A e = 1 . 602 × 10
- 19
C c = 3 . 0 × 10
8
m/s
Electromagnetic Waves:
Plane waves propagating in the ± x -direction:
~
E ⊥
~
B
E = E
m
cos ( kx ∓ ωt ) B = B
m
cos ( kx ∓ ωt ) E
m
= cB
m
k =
2 π
λ
λ =
c
f
=
2 πc
ω
Poynting Vector, Intensity, Energy Flux:
~
S =
1
μ
0
~
E ×
~
B I = S
avg
=
1
2 cμ
0
E
2
m
=
1
cμ
0
E
2
rms
E
rms
=
E
m
√
2
I =
P
4 πr 2
Law of Reflection: θ
r
= θ
i
Snell’s Law of Refraction: n
1
sin θ
1
= n
2
sin θ
2
Total Internal reflection: θ
c
= sin
- 1
n
2
n
1
Mirror/Thin Lens:
1
p
+
1
i
=
1
f
f =
r
2
, Lens maker’s equation:
1
f
= ( n - 1)
1
r
1
-
1
r
2
!
Concave mirror: f > 0 , Convex mirror: f < 0 ; Converging lens: f > 0 , Diverging lens: f < 0 ,
Magnification: m = -
i
p
, if m > 0, the image is upright, if m < 0, inverted.
Interference:
Constructive: phase difference, Δ φ = 2 πm ; path-length diff., Δ L = mλ , ( m = 0 , 1 , 2 , · · · )
Destructive: phase difference, Δ φ = (2 m + 1) π ; path-length diff., Δ L = (2 m + 1)
λ
2
, ( m = 0 , 1 , 2 , · · · )
Index of Refraction: n =
c
v
, λ
n
=
λ
n
, v : speed of light in a medium f
n
=
c/n
λ/n
= f
Phase change due to distance, L , traveled: Δ φ =
2 π
λ
n
L =
2 πn
λ
L
Phase difference when traveling through different media with same length: