Related Experiment Video
Updated: Jun 6, 2026
09:43
Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
Published on: August 13, 2019
Local optical parameters of spherical polydispersions: simple approximations
Applied Optics
|November 10, 2010
Summary
New analytical solutions accurately estimate optical properties of large spherical particles using geometric optics. Edge effects improve accuracy, showing good agreement with Mie theory for cloud applications.
Area of Science:
- Optics and Photonics
- Atmospheric Science
Background:
- Accurate optical characteristics of polydispersions are crucial for atmospheric and material science.
- Existing methods may lack efficiency or accuracy for large particles.
Purpose of the Study:
- Derive new analytical solutions for local optical characteristics of spherical polydispersions.
- Improve accuracy of geometric optics approximation for larger particles.
Main Methods:
- Utilized the geometric optics (GO) approximation.
- Incorporated edge effects to enhance GO accuracy.
- Compared results with Mie theory calculations.
Main Results:
- Developed novel analytical formulas for extinction and absorption coefficients.
- Derived formulas for asymmetry parameters of phase functions.
- Demonstrated satisfactory accuracy compared to Mie theory.
Conclusions:
- The new analytical solutions provide accurate estimations for optical properties of large spherical particles.
- The derived formulas offer a simpler approach for calculating cloud optical characteristics.
Related Concept Videos
01:26Gauss's Law: Spherical Symmetry
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
01:23Spherical Coordinates
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
01:10Polymers: Molecular Weight Distribution
For any given polymer, the weight average molecular weight (Mw) is higher than, if not equal to, the number average molecular weight (Mn). The only situation in which the weight average molecular weight and the number average molecular weight are equal is when a polymer consists only of chains with equal molecular weight. However, this never happens in a synthetic polymer, since it is difficult to control the polymerization process up to a molecular level with accuracy to a hundred percent.
02:24Properties of Enantiomers and Optical Activity
It is essential to understand the difference between chiral and achiral interactions and the implications thereof in optical activity and their applications. Just as our feet, which are chiral, interact uniquely with chiral objects, such as a pair of shoes, but identically with achiral socks, enantiomers of a molecule exhibit different properties only when they interact with other chiral media. An example of a significant implication from this facet is the phenomenon known as optical activity,...
01:25Ostwald’s Dilution Law
Consider a binary electrolyte AB with a concentration ‘c’ that reversibly dissociates into its constituent ions. The degree of this dissociation is represented by ⍺. This means that the equilibrium concentration of each ionic species can be expressed as ⍺c. As well as this, the fraction of the electrolyte that remains undissociated at equilibrium is given by (1−⍺). The corresponding equilibrium concentration for this undissociated portion is then calculated as (1−⍺)c. For such solutions,...
01:26Spherical and Cylindrical Capacitor
A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...