# Homework Help: Intensity of a reflected and transmitted light

1. Dec 15, 2013

### sapz

1. The problem statement, all variables and given/known data
Hello!

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

I have a light ray of intensity I0 comming (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 $I_0*R_{\perp} = I_0*(1-T_{\perp})$?

2. Relevant 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 (:

2. Dec 15, 2013

### Simon Bridge

3. Dec 16, 2013

### 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.

4. Dec 16, 2013

### 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)

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

Last edited: Dec 16, 2013
5. Dec 16, 2013

### sapz

Thank you ehild