Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Reflecting Property Of A Paraboloidal Mirror

"Mom, check out my headlight", said Tee, a sharp 7 yr old. "cool! how did you do that?", asked his mom. "Conics, just conics", replied Tee.

Explain the conic concept Tee is referring to.

**The strings**:

S_{7}P_{4}A_{41} (Motion - Linear).
**The math**:

Pj Problem of Interest is of type *motion* (linear). The ray model of light implies linear motion of light.

*Conics*, formally known as conic sections are curves that were originally derived from slicing a cone with a plane. The parabola, the ellipse and the hyperbola are very well known conics. The circle is also a conic section, however, its identity as a circle is dominant. Apollonius is credited with the first detailed analysis of conic sections.

Tee used the reflecting property of a parabolic mirror for his headlight. If a light source is at the focus of a parabolic mirror, the parabolic surface of the mirror will reflect all rays of light from the light source at its focus in directions parallel to the axis of the parabolic mirror. The result is a powerful beam of light concentrated in one direction.

This property is commonly used in automobile headlights which consists of a paraboloid (a paraboloid is formed by rotating a parabola about its axis) with a silvered surface so that it can reflect light and a light bulb at its focus. The light emanating from the bulb is reflected in the direction of the axis providing a concentrated beam of light in that direction (figure 21.2. where F is the focus). This property of the paraboloidal mirror is also utilised in searchlights and flashlights.

The reverse of the reflecting property of a paraboloidal mirror is also very useful. In other words, light rays parallel to the axis of a paraboloidal mirror will be reflected through the focus of the mirror. Hence there will be a high concentration of light at the focus. A telescope uses such concentration of light effectively. The axis of the telescope is directed toward the star. Since distance from star to telescope is very far, rays from the star into telecope are parallel to the axis for all practical purposes. Hence when they are incident on the surface of the paraboloid mirror of the telescope, they will be reflected to the focus of the mirror.

The reflecting property of paraboloidal mirror is also the principle used in paraboloidal reflectors which are used to concentrate radio waves emanating from a small source into a powerful beam and in paraboloidal antenna which is used to pick up faint radio signals in order to produce relatively strong signals at the focus.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings