Shiva Ka Insaaf - Jackie Shroff, Vinod Mehra & Poonam Dhillon - Bollywood Superhit Action Movie - HQ

Uploaded by cfurse on 17.08.2009

Transcript:

Today's lecture is going to be how to analyze plane waves that

come on to a boundary between two media in an oblique fashion. So

here's a separation between two different materials: Material

number one and material number two. This is the normal to that

boundary, the perpendicular to the boundary, and here's a plane

wave that's coming in at a direction that is not perpendicular to

the boundary. We call this oblique incidence, just because it is

not perpendicular. This represents the frontal plane waves as

they are moving through space. There are two aspects of this

plane wave that are going to be particularly important to us. One

is the direction of propagation. We're going to call that KI,

with a unit vector, because that's representing the direction the

wave is propagating. Here's the angle theta I relative to the

normal that tells us the direction of that plane wave. There's

also going to be a reflected wave that comes off like this, the

angle of the reflected wave, theta R, is equal to the angle of the

incident wave, regardless of the two materials. We're going to

call this vector KR with a hat over it. That's a unit vector in

the reflected direction. And then finally there's going to be a

transmitted vector. We're going to call this KT, for

transmission. And there's going to be an angle here, theta T. We

use Snell's law to be able to find all of the angles. The first

thing that we indicated was that theta I and theta R are equal.

The second thing is depending on these two materials and theta I,

we'll be able to find theta T. This is how it works. We can say

that the index of refraction N, this is not eta, this is N. N1

times the sine of theta 1 is N2 sine of theta 2. This is material

1 and this is material number 2. This is N1 sine of theta

incident equals N2 sine of theta 2. And for a lossless material

is the square root of epsilon R. Square root of epsilon R1,

square root of epsilon R2. So this tells us that the angle of

incidents affects the angle of transmission in a lossless -- this

is lossless-- nonmagnetic material. Nonmagnetic means that UR is

equal to 1. This helps us analyze the different directions of

propagation, and there's one other factor that's going to be very

important. And that is the polarization of the plane wave. The

polarization is defined by the electric field vector. So I'm

going to draw two different choices for electric field vector

here. One of them would be if the electric field vector came out

of the board or the electric field vector went into the board. In

this case the electric field would be perpendicular to the board.

We call the board the plane dissonance because it includes the

direction of the propagation and it includes the normal boundary

between the two materials. So if you have an electric field in

either of these directions, this is a perpendicular polarized

plane wave. On the other hand, you might have an electric field

vector that is either up or down. And this electric field vector

can be drawn on the plane of incidence, the blackboard, and this

is therefore parallel to the plane of incidence. So we're going

to do two different cases. One of them is going to be for a plane

wave that is propagating in the perpendicular polarization and the

other one is the plane wave propagating in the parallel

polarization. And now let's also look at where the magnetic field

vector is. If I had a direction of propagation such as my

incident field here, and I had a perpendicular polarized electric

field vector, let's figure out where the magnetic field vector is.

The magnetic field vector can be found using the right-hand rule.

We put our thumb in the direction of propagation. We put our

first finger in the direction of E, and then our third finger

shows us where H is. So H in this case is down like so. Let's

look at this case. We put our thumb in the direction of

propagation. We put our finger in the direction of E. Our third

finger will show us where H is. So for the electric field vector

going up like so, H would be in this direction. So the two things

we've looked at so far are how to define the angles, how to define

the direction of the propagation, how to determine if we are

perpendicular or parallel polarize d and how to find the magnetic

field vector.

come on to a boundary between two media in an oblique fashion. So

here's a separation between two different materials: Material

number one and material number two. This is the normal to that

boundary, the perpendicular to the boundary, and here's a plane

wave that's coming in at a direction that is not perpendicular to

the boundary. We call this oblique incidence, just because it is

not perpendicular. This represents the frontal plane waves as

they are moving through space. There are two aspects of this

plane wave that are going to be particularly important to us. One

is the direction of propagation. We're going to call that KI,

with a unit vector, because that's representing the direction the

wave is propagating. Here's the angle theta I relative to the

normal that tells us the direction of that plane wave. There's

also going to be a reflected wave that comes off like this, the

angle of the reflected wave, theta R, is equal to the angle of the

incident wave, regardless of the two materials. We're going to

call this vector KR with a hat over it. That's a unit vector in

the reflected direction. And then finally there's going to be a

transmitted vector. We're going to call this KT, for

transmission. And there's going to be an angle here, theta T. We

use Snell's law to be able to find all of the angles. The first

thing that we indicated was that theta I and theta R are equal.

The second thing is depending on these two materials and theta I,

we'll be able to find theta T. This is how it works. We can say

that the index of refraction N, this is not eta, this is N. N1

times the sine of theta 1 is N2 sine of theta 2. This is material

1 and this is material number 2. This is N1 sine of theta

incident equals N2 sine of theta 2. And for a lossless material

is the square root of epsilon R. Square root of epsilon R1,

square root of epsilon R2. So this tells us that the angle of

incidents affects the angle of transmission in a lossless -- this

is lossless-- nonmagnetic material. Nonmagnetic means that UR is

equal to 1. This helps us analyze the different directions of

propagation, and there's one other factor that's going to be very

important. And that is the polarization of the plane wave. The

polarization is defined by the electric field vector. So I'm

going to draw two different choices for electric field vector

here. One of them would be if the electric field vector came out

of the board or the electric field vector went into the board. In

this case the electric field would be perpendicular to the board.

We call the board the plane dissonance because it includes the

direction of the propagation and it includes the normal boundary

between the two materials. So if you have an electric field in

either of these directions, this is a perpendicular polarized

plane wave. On the other hand, you might have an electric field

vector that is either up or down. And this electric field vector

can be drawn on the plane of incidence, the blackboard, and this

is therefore parallel to the plane of incidence. So we're going

to do two different cases. One of them is going to be for a plane

wave that is propagating in the perpendicular polarization and the

other one is the plane wave propagating in the parallel

polarization. And now let's also look at where the magnetic field

vector is. If I had a direction of propagation such as my

incident field here, and I had a perpendicular polarized electric

field vector, let's figure out where the magnetic field vector is.

The magnetic field vector can be found using the right-hand rule.

We put our thumb in the direction of propagation. We put our

first finger in the direction of E, and then our third finger

shows us where H is. So H in this case is down like so. Let's

look at this case. We put our thumb in the direction of

propagation. We put our finger in the direction of E. Our third

finger will show us where H is. So for the electric field vector

going up like so, H would be in this direction. So the two things

we've looked at so far are how to define the angles, how to define

the direction of the propagation, how to determine if we are

perpendicular or parallel polarize d and how to find the magnetic

field vector.