Wave Nature Of Light

Question 0

Light

Answer 0

Electromagnetic wave. Time varying electric (Ex) and magnetic (By) fields. Ex and By are perpendicular

Question 1

Augustine Jean Fresnel

Answer 1

French physicist and civil engr. proponent of the wave theory of light

Question 2

Propagation constant

Answer 2

AKA wave number. 2pi/lambda

Question 4

Simplest traveling wave with propagation along z.

Answer 4

A sinusoid! Ex=E0Cos(wt-kz+phi0)

Question 5

Monochromatic plane wave

Answer 5

Described by Ex=E0Cos(wt-kz+phi0). It is a PLANE wave of infinite extent. The one above travels in the positive z direction

Question 6

Wavefront

Answer 6

A surface over which the phase of a wave is constant. Also called phase planes A plane that intersects the EM wave perpendicularly; so if the wave is traveling in the z direction the wavefront is in the x-y plane.

Question 7

Electric Field

Answer 7

A vector field generated by electric charges of time varying magnetic fields

Question 8

Faraday’s Law

Answer 8

Time varying magnetic fields result in time varying electric fields and viceversa. A time varying E fields sets up a time varying B field with the same frequency. in a monochromatic plane wave, By and Ex accompany each other and have the same freq, and propagation constant. However their direction is orthogonal.

Question 9

Optical Field refers to…

Answer 9

Electric Field

Question 10

Wave vector

Answer 10

K(vector) indicates the direction of propagation. Magnitude of propagation constant is 2pi/lambda

Question 11

Ex equation using field vector:

Answer 11

Ex=E0Cos(wt-k . r+phi0). r and k are both vectors. r is a point on plane. The dot product is the product of k and projection of r onto k.

Question 12

Using the wave vector, if propagation is along z, the dot product of k.r becomes

Answer 12

k.r=(kx)(x)+(ky)(y)+(kz)(z) since x=y=0, k.r=(kz)(z)=kz

Question 13

Equation for phase velocoty

Answer 13

V=dz/dt=w/k=(v)lambda w=2(pi)v

Question 14

Phase difference can be expressed as

Answer 14

2pi((delta z)/lambda)= k(delta z)

Question 15

Waves are in phase if:

Answer 15

Phase difference is 0 or multiple of 2pi.

Question 16

Maxwell’s Equations (in words)

Answer 16

Describe how B and E fields are generated. All EM waves obey this Describes the time and space dependence of the E-field

Question 17

Describe a perfect wave plane

Answer 17

Wavefronts are separated by 2pi or lambda (Generally). Direction of wave propagation (Kvector) is normal to the wavefront surface. So here, propagation vectors are all parallel. This plane wave has no divergence -> 0 degrees of optical divergence. The amplitude, E0, does not depend on the distance from a reference point. it is the same at all points on a given perpendicular plane to K. So it is also independent of x and y. Extends to infinity and there is infinite energy. An infinitely large EM source with infinite power is needed to generate a perfect plane wave. Light beam’s area and power depend on the extent of the e and b fields.

Question 18

Isotropic

Answer 18

Uniform

Question 19

Maxwell’s EM wave equation

Answer 19

has partial derivatives.

Question 20

Describe a spherical wave

Answer 20

A point source is needed. A traveling field emerges from this point and amplitude decays with distance r form the source. Wavefronts are spheres centered at source point O. since direction of propagation is normal to the wavefronts, K diverges outward Has 360 degrees of optical divergence.

Question 21

Optical Divergence

Answer 21

the angular separation of wave vectors on a given wavefront.

Question 22

Gaussian Beams

Answer 22

Many light beams are described like so. Beam has an expj(wt-kz) dependence (still) Amplitude varies spatial away from the beam axis and also along the beam axis. Light intensity distribution is Gaussian.

Question 23

Beam diameter

Answer 23

Only on Gaussian beams? 2w… defined so that the cross sectional area pi(w^2) at that point contains 85% the beam power. beam diameter increases as the beam travels along z.

Question 24

waist/waist radius/spot size

Answer 24

the finite width 2w0, where the wavefronts are parallel w0 is the waist radius 2w0 is the spot size.

Question 25

Beam divergence

Answer 25

2theta. increase in beam diameter with distance is linear, and makes an angle 2theta at O. eq on pg 6.

Question 26

What slows down an EM field wave?

Answer 26

The interaction between the field and the dipoles. The stronger the interaction, the slower the propagation of a wave. (since energy gets transferred when field polarizes molecules in the medium it is traveling. )

Question 27

Relative permitivity, what does it do, symbol?

Answer 27

Measures the ease with which the medium become polarized. Or you can say that: Indicates the extent of interaction between the field and induced poles. symbol: epsilon_r

Question 28

phase vel. for EM wave traveling in medium with relative permitivity epsilon_r

Answer 28

V=1/sqrt(epsilon_r epsilon µ₀)

Question 29

epsilon_r in free space

Answer 29

1

Question 30

phase velosity in vacuum V=

Answer 30

V=1/sqrt(epsilon₀ X µ₀)= c

Question 31

C, speed of light in vaccum (numerical)

Answer 31

3X10⁸ms^-1

Question 32

refractive index

(definiton and equation)

Answer 32

def: the ratio of the speed of light it its speed in a medium
eq: n=c/v=sqrt(epsilon_r)

Question 33

when light progapagets to another medium, what happens to the speed, and the frequency?

Answer 33

the speed changes, slows down if the medium is more dense.

the frequency **remains the same **

Question 34

wave vector and wavelength in a medium (equations)

Answer 34

k_medium=nk

lambda_medium=lambda/n

*n=refractive index

Question 35

In which materials does the refractive index stay the same in all directions? ( ie. is isotropic? )

Answer 35

non-crystaline materials

(glasses, liquids)

Question 36

which materials have anisotropic properties?

Answer 36

Crystals .

depending on the structure, the relative permitivity is different along different crystal directions.

Question 37

optically isotropic means

Answer 37

the refractive index remains the same in a material for all directions.

Question 38

when two perfectly harmonic waves with diferent frequencies, and wave vectors travel along the same direction the form….

Answer 38

A wave paket

Question 39

group velocity is…

Answer 39

a wave paket’s velocity

V_g=dw/dk

V_g(vacuum)= dw/dk=c=phase vel.

Question 40

group vel on a medium

Answer 40

n is a function of wavelength: n(lambda)

V_g(medium)=c/N_g

N_g=n-lambda(dn/dlambda)

Ng= group index

Question 41

group index of medium

Answer 41

N_g=n-lambda(dn/dlambda)

Question 42

is epsilon_r frequency dependent?

Answer 42

YES

Question 43

Dispersive medium

Answer 43

when both the phase velocity and group velocity depend on hte wavelength

Question 44

S used to represent

Answer 44

S=v²epsilln₀epsilon_r (E X B)

Energy flow per unit area

Question 45

total internal reflection

Answer 45

everything gets reflected. When theta_c reaches 90.

theta_c=n₂/n₁

Question 46

Poyting vector

Answer 46

S. represents thenergy flow per unit time per unit area in a direction determined by E X B

Question 47

irradiance

Answer 47

Poynting vector’s magnitude.

Power flow per nit area.

Question 48

intensity is sometimes used to mean

Answer 48

Irradiance!

Question 49

refracted light

Answer 49

when light is traveling through one medium, then reaches the boundary and gets transmitted on to medium 2. this transmited light is also known as refracted light,

Question 50

the magnitudes of Kr and Ki are the same beause

Answer 50

they are on the same medium

Kr=Ki

Question 51

if A_i and B_i are both incident rays parallel to each other and are in phase, the only way that the light can be reflected qith equal intensity for both rays is if:

Answer 51

theta_i = theta_r

this way, A_r and B_r are in phase and don’t destructively interfere with one another.

Question 53

A _t and B_t have diferent velocities than A_i and B_i because….

Answer 53

they are on a different mediium