1.) explain the three radiation laws. How are they used to draw 2d plot of radiated energy
versus wavelength for sun as energy source.what are the assumptions used
The three radiation laws you're referring to are the Stefan-Boltzmann law, Wien's displacement
law, and Planck's radiation law. These laws describe the spectral distribution of energy radiated
by a black body, which is an idealized object that absorbs and emits all frequencies of
electromagnetic radiation.
1. Stefan-Boltzman’s Law:
This law states that the intensity of radiation emitted by a radiating body is proportional to the
fourth power of the absolute temperature of that body
Radiation flux = ƐσT4
Where,
σ = Stefan-Boltzman’s constant = 5.67 x 10-5 ergs cm-2 sec-1K-4
Ɛ = Emissivity of a body (0 < s > 1.)
T = Absolute temperature of the surface in °K.
For example, radiation flux density from a body at 303°K is greater than at 273°K by 52 per cent
although the increase in absolute temperature is only 30°K.
The Stefan-Boltzmann law helps us understand how the total radiated energy from an object
changes with its temperature.
Wein’s Displacement Law:
According to this law, the wavelength of maximum intensity of emission of radiation from a black
body is inversely proportional to the absolute temperature of the radiating body. It is given by the
following equation:
Wavelength (λmax) of maximum intensity of emission (µ) = b/T
Where,
λmax is the wavelength at which maximum radiation is emitted. It decreases as the temperature
increases.
b is constant = 2897
T is the temperature of the surface in Kelvin
Hence, λmax (µ) = 2897 T-1
The temperature of the sun is 6000 °K for which the value of maximum wave length is 0.5µ, and
that of the earth the average temperature is 300 °K for which the value of maximum wavelength
is 10µ. Out of the total energy emitted by sun, 7 per cent is with wavelength less than 0.4µ, 44
per cent is with a wavelength ranging from 0.4 – 0.7µ and 49 per cent is having wavelength
greater than 0.7µ.
3. **Planck's Radiation Law**:
- Planck's law provides a more detailed spectral distribution of energy radiated by a black
body across a range of wavelengths.
- The equation is:
\[B(λ, T) = \frac{2hc^2}{λ^5} \cdot \frac{1}{e^{\frac{hc}{λkT}} - 1}\]
- Where:
- \(B(λ, T)\) is the spectral radiance of the black body at a given wavelength \(λ\) and
temperature \(T\).
- \(h\) is Planck's constant.
- \(c\) is the speed of light.
- \(k\) is Boltzmann's constant.
Now, to draw a 2D plot of radiated energy versus wavelength for the Sun as an energy source,
we make some assumptions:
1. **Black Body Assumption**: While the Sun is not a perfect black body, it behaves similarly to
one in many aspects. We assume it emits radiation as if it were a black body.
2. **Sun's Temperature**: The Sun's surface temperature is approximately 5,500 degrees
Celsius (about 5,773 Kelvin). This temperature is used in the Stefan-Boltzmann law, Wien's
displacement law, and Planck's radiation law calculations.
3. **Spectral Distribution**: To create the plot, you would use Planck's radiation law to calculate
the radiance (energy per unit area per unit wavelength) across a range of wavelengths. This will
give you a curve that peaks in the visible range.
4. **Stefan-Boltzmann Law**: You can also use the Stefan-Boltzmann law to find the total
radiated energy per unit area (emissive power) and compare it to the radiance at specific
wavelengths.
By utilizing these laws and assumptions, you can create a 2D plot that shows how the radiated
energy from the Sun varies with wavelength, with a peak in the visible spectrum due to its
temperature. This plot is known as a "black body spectrum" for the Sun and provides valuable
insights into the Sun's emission characteristics.
2.) once light photons interact to the earth object what phenomena take place at interaction
junction? explain using law of conservation of energy.
When photons of light interact with an object on Earth, several phenomena can take place at the
interaction junction. These phenomena are explained by the law of conservation of energy,
which states that energy cannot be created or destroyed but can only change forms. Here's how
the law of conservation of energy applies to these interactions:
1. **Absorption**:
- When photons are absorbed by the object, they transfer their energy to the atoms or
molecules within the material.
- The law of conservation of energy tells us that the total energy of the system (photons +
object) remains constant. Therefore, the energy of the absorbed photons is converted into other
forms of energy within the object, such as thermal energy (heat) or electronic excitation.
- Mathematically, this can be expressed as: \(E_{\text{incoming photons}} = E_{\text{absorbed
energy}} + E_{\text{other forms}}\).
2. **Reflection**:
- In the case of reflection, photons bounce off the object's surface without being absorbed.
- The law of conservation of energy still applies, but in this case, the energy of the incident
photons is conserved by being reflected back into the environment.
- Mathematically, this is represented as: \(E_{\text{incoming photons}} = E_{\text{reflected
photons}} + E_{\text{transmitted photons}} + E_{\text{other forms}}\).
3. **Transmission**:
- When photons pass through a transparent or translucent object, they are not absorbed but
continue their journey through the material.
- The law of conservation of energy applies here as well, ensuring that the energy of the
incident photons is conserved as they emerge on the other side.
- Mathematically, it can be expressed as: \(E_{\text{incoming photons}} = E_{\text{transmitted
photons}} + E_{\text{other forms}}\).
4. **Scattering**:
- Scattering occurs when photons interact with the object's atoms or molecules and change
direction but are not absorbed.
- The law of conservation of energy is upheld in this process, as the energy of the incident
photons is redistributed among the scattered photons and other forms of energy within the
object.
- Mathematically, it is described as: \(E_{\text{incoming photons}} = E_{\text{scattered
photons}} + E_{\text{other forms}}\).
5. **Emission**:
- In some cases, objects can emit photons of light. This can happen when the object has
absorbed energy from another source (e.g., heating) and subsequently re-emits it as light.
- Again, the law of conservation of energy holds true, ensuring that the energy emitted as
photons equals the energy previously absorbed or gained by the object.
In all these interactions, the law of conservation of energy serves as a fundamental principle,
accounting for the conservation of energy in various forms during the interaction between light
photons and objects on Earth. This principle helps us understand how energy is transferred,
transformed, and distributed within the system.
3.) how scattering of light in the atmosphere depends on particle size and
wavelength ? explain in detail.
Scattering of light in the Earth's atmosphere depends on particle size and wavelength due to a
phenomenon known as Rayleigh scattering. Rayleigh scattering is responsible for the blue color
of the sky and plays a crucial role in the dispersion of sunlight in all directions. Here's a detailed
explanation of how Rayleigh scattering depends on particle size and wavelength:
**1. Particle Size Dependence**:
Rayleigh scattering is most strongly influenced by the size of the scattering particles. In this
context, scattering particles typically refer to gas molecules (e.g., nitrogen and oxygen) and
aerosols (tiny solid or liquid particles suspended in the air).
- **Small Particles**: Rayleigh scattering is most effective when the scattering particles are
much smaller than the wavelength of the incident light. Specifically, the scattering intensity (\(I\))
is inversely proportional to the fourth power of the wavelength (\(λ\)) and is proportional to the
inverse square of the particle size (\(r\)):
\[I \propto \frac{1}{λ^4} \cdot \frac{1}{r^2}\]
- This equation indicates that smaller particles are more effective at scattering shorter
wavelengths (blue and violet light) than longer wavelengths (red and yellow light).
- **Larger Particles**: For larger particles that are comparable in size to the wavelength of light,
the Rayleigh scattering effect diminishes. In this case, the scattering behavior begins to follow
different scattering laws, such as Mie scattering, which becomes more dominant as particle size
increases.
**2. Wavelength Dependence**:
- **Shorter Wavelengths**: Rayleigh scattering is inversely proportional to the fourth power of
the wavelength (\(λ^4\)), which means that shorter wavelengths are scattered more effectively.
Blue and violet light have shorter wavelengths and are thus scattered more strongly than red
and yellow light. This is why the sky appears blue during the day; blue and violet light from the
Sun is scattered in all directions by gas molecules in the atmosphere.
- **Longer Wavelengths**: Longer wavelengths, such as red and yellow light, are scattered less
by Rayleigh scattering. As a result, they tend to pass through the atmosphere with less
scattering and are more likely to reach an observer's eyes, especially during sunrise and sunset.
This is why the sky often appears reddish or orange during these times.
In summary, Rayleigh scattering in the Earth's atmosphere depends on both particle size and
wavelength. Smaller particles scatter shorter wavelengths (blue and violet) more effectively,
leading to the blue color of the sky during the day. Larger particles and longer wavelengths (red
and yellow) are scattered less, allowing them to dominate the colors observed during sunrise
and sunset. Understanding these principles of scattering is essential for explaining the color of
the sky and various optical phenomena in the atmosphere.
4.) Why particle nature of light is considered for remote sensing ? explain in the context of
different phenomena happen due to the particle nature of light
The particle nature of light, as described by photons, is considered in remote sensing for several
reasons. While light is traditionally understood as having both wave-like and particle-like
properties (wave-particle duality), the particle nature of light is particularly relevant in the context
of remote sensing. Here's why:
1. **Interaction with Matter**:
- Photons, as discrete packets of energy, interact with matter in a quantized manner. This
means that the energy exchange between light and matter occurs in discrete steps, which is
especially important when considering how electromagnetic radiation interacts with the Earth's
surface and the atmosphere.
- When photons encounter particles or molecules in the atmosphere or on the Earth's surface,
they can be scattered, absorbed, or transmitted. The quantized nature of photons allows us to
understand and model these interactions precisely.
2. **Scattering Phenomena**:
- The particle nature of light is essential for understanding scattering phenomena in remote
sensing. For example:
- **Rayleigh Scattering**: This type of scattering, which dominates in the lower atmosphere,
occurs when photons interact with gas molecules or particles much smaller than the wavelength
of light. The quantized nature of photons explains why shorter wavelengths (e.g., blue and
violet) are scattered more, leading to the blue color of the sky.
- **Mie Scattering**: Mie scattering occurs when particles are comparable in size to the
wavelength of light. Understanding the particle nature of light helps explain the scattering
patterns produced by larger aerosols or cloud droplets, which can affect remote sensing
observations.
3. **Absorption Spectroscopy**:
- Remote sensing often relies on absorption spectroscopy, where specific wavelengths of light
are absorbed by certain molecules or materials. The particle nature of light allows us to
precisely define these absorption lines, which are critical for identifying and quantifying the
presence of substances in the atmosphere or on the Earth's surface.
- For example, remote sensing instruments can detect the absorption lines of greenhouse
gases like carbon dioxide (CO2) and water vapor (H2O) in the atmosphere, aiding in climate
studies and weather forecasting.
4. **Quantum Efficiency**:
- Remote sensing instruments, such as detectors and sensors, are designed to measure the
number of photons received at various wavelengths. Understanding the particle nature of light
helps determine the quantum efficiency of these instruments, which quantifies their ability to
convert incident photons into measurable electrical signals.
- Accurate knowledge of quantum efficiency is essential for calibrating and interpreting remote
sensing data.
5. **Photometric Quantities**:
- Photometric quantities, such as radiance, irradiance, and radiant flux, are used in remote
sensing to describe the amount of light energy at different wavelengths. The particle nature of
light is fundamental in calculating these quantities and understanding their relationship with
observed data.
In summary, the particle nature of light is crucial in remote sensing because it helps explain
various phenomena related to the interaction of light with the Earth's surface and the
atmosphere. It provides the basis for understanding how photons are scattered, absorbed, and
transmitted, which in turn allows us to develop accurate remote sensing techniques and
interpret the data collected from remote sensing instruments.
5.)