Intensity of a reflected and transmitted light

[sapz]

Homework Statement

Hello!

This is really a simple question about how to use reflection and transmittance coefficients.

I have a light ray of intensity I0 coming (S-polarized) to a glass surface at a certain angle, like in the picture:

I want to find the intensity of the reflected wave and of the transmitted-into-the-glass wave.

I have calculated the coefficient $T_{\perp}$. Is it true to say, that the intensity of the transmitted wave is $I_0*T_{\perp}$, and the intensity of the reflected wave is $I_0*R_{\perp} = I_0*(1-T_{\perp})$?

Homework Equations

This is how I calculated the coefficient:
$t_{\perp} = \frac{2n_1Cos\theta_i}{n_iCos\theta_i+n_tCos\theta_t}$

$T_{\perp} = \frac{n_tCos\theta_t}{n_iCos\theta_i}t_{\perp}^2$

Where n-i, n-t are the indexes of the air and glass, and the angles are as in the picture: theta-i is the hitting angle, and theta-t is the transmittance angle.

Thank you (:

 

[Simon Bridge]

Sounds like you don't really know what the coefficients actually are, what they mean physically, or just the definition would answer those questions. i.e. why are the coefficient indexed by a "perpendicular to" symbol?

Revise:
http://en.wikipedia.org/wiki/Fresnel_equations
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/freseq.html

there are two of each coefficient.

 

[sapz]

I am aware there are two coefficients of each, actually there are 4: Rs,rs,Rp,rp,Ts,ts,Tp,tp.
And yeah, I'm not sure of how to use the coefficients... this is why I ask it here.

I've already seen these links before I asked and they refer to lower-case-coefficients which I think are proportional to the amplitudes , except the Wiki link from which I could not deduce anything about how to use it to get the intensity.
I ask about the upper case coefficient Tp because I think it should be proportional to the intensities.
I know I don't know, and I did a fare share of googling before posting here.

 

[ehild]

The power transmission coefficient (or transmittance) is defined as the ratio of the transmitted and incident light intensities: T=I(transmitted)/I(incident) . In the same way, the power reflection coefficient or reflectance is R=I(reflected)/I(incident).

Intensity of light is the energy flowing through a unit area which is perpendicular to the light beam, in unit time. It is the energy density multiplied by the speed of light.

http://en.wikipedia.org/wiki/Intensity_(physics)

Anything that can transmit energy can have an intensity associated with it. For an electromagnetic wave, if E is the complex amplitude of the electric field, then the time-averaged energy density of the wave is given by

$$\left \langle U \right \rangle= \frac{n^2 \epsilon_0}{2} |E|^2$$ ,

and the intensity is obtained by multiplying this expression by the velocity of the wave, c/n:

$$I = \frac{c n \epsilon_0}{2} |E|^2$$

where n is the refractive index, c is the speed of light in vacuum and \epsilon_0 is the vacuum permittivity.

The low-case letters t and r mean the amplitude transmission and reflection coefficients.

They are defined as the ratio of the complex amplitude of the electric field in the transmitted or in the reflected beam to the amplitude of the incident beam. Sometimes they use the amplitudes of the electric field for S polarization and the amplitudes of the magnetic field in case of P polarization.

ehild

 

[sapz]

Thank you ehild