Intensity of a reflected and transmitted light

In summary, the power transmission coefficient (or transmittance) is the ratio of the transmitted and incident light intensities: T=I(transmitted)/I(incident). The power reflection coefficient or reflectance is R=I(reflected)/I(incident). The intensity of light is the energy flowing through a unit area which is perpendicular to the light beam, in unit time. Anything that can transmit energy can have an intensity associated with it.
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sapz
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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 comming (S-polarized) to a glass surface at a certain angle, like in the picture:
illus2up.png


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

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

Homework Equations



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

[itex]T_{\perp} = \frac{n_tCos\theta_t}{n_iCos\theta_i}t_{\perp}^2[/itex]

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 (:
 
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  • #3
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
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

[tex] \left \langle U \right \rangle= \frac{n^2 \epsilon_0}{2} |E|^2[/tex] ,

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

[tex] I = \frac{c n \epsilon_0}{2} |E|^2[/tex]

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
 
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  • #5
Thank you ehild
 

1. What is the intensity of a reflected light?

The intensity of a reflected light is the amount of light energy that is bounced off a surface in a particular direction. It is measured in terms of the power of the light per unit area, also known as irradiance.

2. How is the intensity of a reflected light affected by the angle of incidence?

The intensity of a reflected light is affected by the angle of incidence, with the maximum intensity occurring when the angle of incidence is 0 degrees (perpendicular to the surface) and decreasing as the angle of incidence increases. This is due to the change in the amount of light energy that is reflected and transmitted at different angles.

3. What factors affect the intensity of a transmitted light?

The intensity of a transmitted light is affected by several factors, including the material properties of the medium through which the light is passing, the thickness of the medium, and the wavelength of the light. These factors can cause the intensity of the transmitted light to vary and can also result in the absorption of some of the light energy.

4. How is the intensity of a transmitted light related to the intensity of the incident light?

The intensity of a transmitted light is related to the intensity of the incident light through the material's transmittance, which is a measure of how much light is able to pass through the material. The transmittance is affected by the material's properties, thickness, and wavelength, as well as the angle of incidence.

5. How can the intensity of reflected and transmitted light be measured?

The intensity of reflected and transmitted light can be measured using a variety of instruments, such as photometers, spectrophotometers, and radiometers. These instruments use different methods to measure the amount of light energy and can provide accurate measurements of the intensity of light at different angles and wavelengths.

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