Adhi Harmoko S
LCD
Nature wave of light
Polarization
Liquid Crystal Display (LCD)
y Liquid Crystals are unpolarized in the absence of an external voltage, and will easily transmit light. When an external voltage is applied, the crystal become polarized and no longer transmit; they appear dark
Ray Approximation in Geometric Optics
Wave front
y Wave front usually refer to simply as a wave
y All the pointss along the wave forming the wave crest
y Ray : A line drawn in the direction of motion, perpendicular to the wave front
Reflection
Specular Reflection
Diffuse Reflection
Reflection and Transmission
y The law of reflection: the angle of reflection equals the angle of incidance
θi = θr
Double Reflection
Refraction
y When any wave strikes a boundary
y Some of energy is reflected
y Some of energy is transmitted or absorbed
y Different velocity
sinθ r v r
= = constant
sinθ i v i
y The index of refraction is defined as the speed of light in vacuum divided by the speed of light in the medium. c
n=
v
Snell's Law
y Snell's Law relates the indices of refraction n of the two media to the directions of propagation in terms of the angles to the normal.
sinθ r n1
=
sinθ i n2
Light Propagation Through a Slab
h
sinθ 2 =
n1
sinθ 1
n2
sinθ 3 =
n2
sinθ2
n1
sinθ 3 =
n2 n1
sinθ1 = sinθ1
n1 n2
θ1
x=
h
cosθ 2
θ2 α
d = x sinα
x
α = θ1 − θ2
h
d
d=
h
sin(θ 1 − θ 2 )
cos θ2
Dispersion and Prisms
angle of deviation
n = n(λ )
Measuring n Using a Prism
θ2 =
Φ
2
Φ δ min
θ1 = θ 2 + α = +
2
2
sinθ1 = n sinθ 2
⎛ Φ + δ min ⎞
⎛Φ⎞
sin⎜
⎟ = n sin⎜ ⎟
2
⎝
⎠
⎝2⎠
⎛ Φ + δ min ⎞
sin⎜
⎟
2
⎠
n= ⎝
sin(Φ 2 )
Angle of Deviation
α
δ
θ1
θ4
δ = θ1 + θ 4 − α
Total Internal Reflection
Critical Angle, θc
n1 sinθ c = n2 sin 90°
n2
sinθ c =
n1
Only for n1 > n2
View From a Fish Eye
n2
1
sinθ c = =
= 0.752
n1 1.33
θ c = 48.8°
For θ<θc: The fish sees above the water
For θ=θc : The fish sees the shoreline
For θ>θc : The fish sees the pond bottom
Polarization of Light Wave
y An ordinary beam of light consists of a large number of waves emitted by the atoms of the light source.
y Each atom produces a wave having some particular orientation of the electric field vector E, corresponding to the direction of atomic vibration.
y The direction of polarization of each individual wave is defined to be the direction in which the electric field is vibrating.
Polarization
y An important and useful property of light
y Transverse waves on a rope polarized
y Place an obstacle containing slit in the path of the wave
y A vertical polarized waves passes through
Polaroid
y Obtaining plane polarized light from unpolarized light
y Using crystal : tourmaline
y Intensity of a plane polarized beam transmitted by polarizer
I = Io cos2 θ
Polarizer
Polarization Equation
y Pada gelombang transversal, arah simpangan dapat ke segala
arah asal tegak lurus pada arah rambat .
y Karena gel EM merupakan gabungan gelombang transversal, maka arah arah simpangan medan listrik E dinyatakan sebagai
arah polarisasi gelombang EM.
y Secara umum komponen medan listrik E dapat dinyatakan
dalam bentuk sbb :
E = E x ˆi + E y ˆj
= E ox cos(kz − ωt + α ox )ˆi + E oy cos(kz − ωt + α oy ) ˆj
Type of polarization
Linier Polarization
y Bila αoy ‐ αox =0,π maka proyeksi E terhadap bidang yang tegak
lurus arah perambatan akan membentuk garis lurus
E = E ox cos(kz − ωt)ˆi + E oy cos(kz − ωt ) ˆj
Circular Polarization
y Bila αoy ‐ αox =±nπ/2, n=bil. ganjil maka proyeksi E terhadap
bidang yang tegak lurus arah perambatan akan membentuk
lingkaran
E = E ox cos(kz − ωt )ˆi + E oy sin(kz − ωt) ˆj
Fresnel's Equations
y Fresnel's equations describe the reflection and transmission of electromagnetic waves at an interface
y That is, they give the reflection and transmission coefficients for waves parallel and perpendicular to the plane of incidence. y For a dielectric medium where Snell's Law can be used to relate the incident and transmitted angles, Fresnel's Equations can be stated in terms of the angles of incidence and transmission.
Fresnel's Equations
y The reflection coefficients:
RII =
E r ,II
E i ,II
n1 cos θt − n2 cos θ i
=
n1 cos θ t + n2 cos θ i
R⊥ =
E r ,⊥
T⊥ =
E t ,⊥
E i ,⊥
n1 cos θ i − n2 cos θ t
=
n1 cos θ i + n2 cos θ t
y The transmission coefficients
TII =
E t ,II
E i ,II
2n1 cos θ t
=
n1 cos θ t + n2 cos θ i
E i ,⊥
=
2n1 cosθ i
n1 cosθ i + n2 cos θt
y Reflectance and transmittance
rII =
t II =
Ir ,II
Ii ,II
= RII r ⊥=
2
I r ,⊥
I i ,⊥
= R⊥ 2
n cos θt
n2 cos θt
TII t ⊥ = 2
T⊥
n1 cos θ i
n1 cosθ i
rII + tII = 1
r⊥ + t ⊥ = 1
Polarization by reflection
y Photograph of river
Allowing all light into camera lens
Using a polarizer
Fresnel's Equations
y Sudut Brewster terjadi saat RII=0 atau Er hanya terdiri dari E⊥
RII =
E r ,II
E i ,II
n1 cos θt − n2 cos θ i
=
n1 cos θ t + n2 cos θ i
n=
sinθ1 sinθ P
=
sinθ2 sinθ 2
R⊥ =
E r ,⊥
E i ,⊥
n1 cos θ i − n2 cos θ t
=
n1 cos θ i + n2 cos θ t
n = tanθ P
Derajat Polarisasi P
IP
Imax − Imin
Imax − Imin
P=
=
=
IP + Ia Imax − Imin + 2Imin Imax + Imin
y
y
y
y
y
IP = intensitas cahaya yang terpolarisasi linier
Ia = intensitas cahaya alamiah
Gel terpolarisasi linier Imax=I dan Imin=0 maka P =1
Gel terpolarisasi lingkaran Imax= Imin = I maka P=0
Gel terpolarisasi elips Imax < I < Imin
Polarization by Double Refraction
y Unpolarized light incident on a calcite crystal splits into an ordinary (O) ray and an extraordinary (E) ray. These two rays are polarized in mutually perpendicular directions (drawing not to scale).
Quiz
y Tentukan persamaan gelombang EM terpolarisasi linear yang merambat pada arah y positif dengan simpangan membentuk
sudut 30o terhadap bidang YZ dan diketahui pada t=0 dan y=0 simpangan =0.
y Tentukan jenis polarisasi, arah rambat dan arah simpangan
dari persamaan dibawah ini :
π
π
E = 0,6 cos(kz − ωt + )ˆi + 0 ,8 cos(kz − ωt + ) ˆj
3
3
y Tentukan persamaan gelombang EM yang merambat pada
arah z dengan amplitudo simpangan E0 polarisasi lingkaran
y putar kanan, pada t=0 dan z=0 :E= E0 i
y Putar kiri, pada=t=0, z=0, E=E0 i
y Putar kanan pada t=0, z=0, E0x = ½ Eoy
Quiz
y Fungsi gelombang sebuah gelombang elektromagnetik sebagai
berikut :
π⎞
π⎞
)
)
⎛
⎛
E (y , t ) = −E o z cos⎜ ky + ωt + ⎟ + 3E o x cos⎜ ky + ωt + ⎟
3⎠
3⎠
⎝
⎝
y Tentukan jenis polarisasi dan gambar sketsa gelombangnya!
y Suatu sinar datang (cahaya alamiah) datang dengan sudut 30 jatuh pada ke suatu media n = 1,5 y Berapa persenkah bagian yang dipantulkan
y Berapa persenkah bagian yang diteruskan
y Bila amplitudo gelombang awal E, carilah amplitudo gelombang refleksi dan transmisi
y Bila sudut datang gelombang dirubah sehingga gelombang pantulnya terpolarisasi sempurna, carilah sudut datang gelombang sekarang