Dependence of Radiation Absorption on Refractive Index

In summary, the relationship between radiation absorption and refractive index is that materials with higher refractive indices tend to have a higher tendency to absorb radiation. This is because the refractive index determines how much light is slowed down and thus how much of the light energy is transferred to the material. However, there can be exceptions to this trend, as some materials may have a high refractive index but still have a low absorption coefficient due to other factors. The refractive index can affect the absorption of all wavelengths of radiation, but certain materials may have a higher or lower absorption coefficient for specific wavelengths, which can also be influenced by the refractive index. This relationship is important in fields such as optics, materials science, and medical imaging, where scientists
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I am reading the text 'thermal radiation heat transfer' by Howell et al. (2011). In it they describe normal spectral emission by an isothermal volume element dV as

[itex]4\pi \kappa_\lambda I_{\lambda b}(S)dVd\lambda[/itex]

where [itex]\kappa_{\lambda}[/itex] is the absorption coefficient and [itex]I_{\lambda b}[/itex] is the black body spectrum, V is volume, and [itex]\lambda[/itex] is the wavelength.

And later state that if the refractive index [itex]n[/itex] is not equal to 1, it should be included as

[itex]n_{\lambda}^2(S)\kappa_\lambda(S)I_{\lambda b}(S)dS[/itex]

Much earlier they define

[itex]I_{\lambda b}=\frac{2\pi h c^2}{n^2\lambda^5\left[\exp\left(\frac{hc}{nk_B\lambda T}\right)-1\right]}[/itex]

It seems that this must mean that

[itex]4\pi \kappa_\lambda \frac{2\pi h c^2}{\lambda^5\left[\exp\left(\frac{hc}{nk_B\lambda T}\right)-1\right]}(S)dVd\lambda[/itex]

is the correct form for calculating spectral power.

However, the authors continually jump around with and without the use of the index of refraction and I don't know what the correct form of [itex]I_{\lambda b}[/itex] is. This jumping around with definitions is all very confusing. So what is the correct form of the first equation? What is the actual dependnece of refractive index on emitted power?

Also, I have no idea why emission (a sub-atomic or atomic phenomenon) depends on the the index of refraction (an interatomic medium property).

Also, does this dependence on refractive index only occur in emission or does it also impact absorption? The authors always only talk about emission when referring to the dependence on the index of refraction.
 
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Thank you for bringing up your concerns regarding the text 'thermal radiation heat transfer' by Howell et al. (2011). I can understand your confusion with the various equations and definitions presented in the text. Allow me to clarify and provide some insights on the correct form of the first equation and the impact of refractive index on emission and absorption.

Firstly, the correct form of the first equation is indeed:

4\pi \kappa_\lambda \frac{2\pi h c^2}{\lambda^5\left[\exp\left(\frac{hc}{nk_B\lambda T}\right)-1\right]}(S)dVd\lambda

This is the spectral power emitted by an isothermal volume element dV at a specific wavelength \lambda, taking into account the absorption coefficient \kappa_\lambda and the black body spectrum I_{\lambda b}. The inclusion of the refractive index n in the equation is important because it affects the energy levels and transitions of the atoms or molecules within the isothermal volume element, thus impacting the emission of thermal radiation.

To understand this better, let's take a closer look at the black body spectrum I_{\lambda b}. This equation describes the spectral radiance of a black body at a specific temperature T, and it takes into account the refractive index n in the denominator. This is because the refractive index affects the energy levels and transitions of the atoms or molecules within the black body, thus impacting the emission of thermal radiation. Therefore, the inclusion of the refractive index in the equation is necessary to accurately determine the spectral power emitted by the isothermal volume element.

Additionally, the dependence of refractive index on emitted power is not limited to emission. It also impacts absorption, as the refractive index affects the energy levels and transitions of the atoms or molecules within the material, thus influencing the absorption of thermal radiation.

Lastly, it is important to note that the dependence of emission on refractive index is not limited to sub-atomic or atomic phenomena. It also applies to macroscopic objects, as the refractive index of a material can affect the emission of thermal radiation from its surface.

I hope this helps to clarify your doubts. If you have any further questions, please do not hesitate to ask.


 

FAQ: Dependence of Radiation Absorption on Refractive Index

1. What is the relationship between radiation absorption and refractive index?

The refractive index of a material describes how much the speed of light is reduced when passing through that material. The higher the refractive index, the slower the speed of light. This means that materials with higher refractive indices will also have a higher tendency to absorb radiation.

2. How does the refractive index affect the amount of radiation that is absorbed?

The refractive index affects the amount of radiation that is absorbed because it determines how much light is slowed down and thus how much of the light energy is transferred to the material. Materials with higher refractive indices will absorb more radiation compared to materials with lower refractive indices.

3. Are there any exceptions to the relationship between radiation absorption and refractive index?

While the general trend is that higher refractive indices lead to higher radiation absorption, there can be exceptions. Some materials may have a high refractive index but still have a low absorption coefficient due to other factors such as bandgap energy or crystal structure.

4. Is there a specific wavelength of radiation that is affected by the refractive index?

The refractive index can affect the absorption of all wavelengths of radiation. However, certain materials may have a higher or lower absorption coefficient for specific wavelengths, which can also be influenced by the refractive index.

5. How can the dependence of radiation absorption on refractive index be used in practical applications?

The relationship between radiation absorption and refractive index is important in various fields, such as optics, materials science, and medical imaging. By understanding this dependence, scientists can design materials with specific refractive indices to enhance or reduce their absorption of certain types of radiation for various purposes, such as creating more efficient solar cells or developing new medical imaging techniques.

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