In their paper published in the journal Applied Optics, Rafael González-Acuña, Héctor Chaparro-Romo, and Julio Gutiérrez-Vega outline the math involved in solving the puzzle, give some examples of possible applications, and describe the efficiency of the results when tested.
Over 2,000 years ago, Greek scientist Diocles recognized a problem with optical lenses—when looking through devices equipped with them, the edges appeared fuzzier than the center.
The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/sfor a time of 4.10 seconds.
Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Determine the displacement of Ben's car during this time period.
They report that their technique can produce lenses that are 99.9999999999 percent accurate.
The researchers suggest the formula can be used in applications including eyeglasses, contact lenses, telescopes, binoculars and microscopes. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission.The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6.The four kinematic equations are: In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion.(a) Geometry of the problem and notation used for the distances.The origin of the coordinate system is located at the center of the input surface z a 0, 0 0.If Ima's acceleration is -8.00 m/s, then determine the displacement of the car during the skidding process.(Note that the direction of the velocity and the acceleration vectors are denoted by a and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. The second step involves the identification and listing of known information in variable form. (Always pay careful attention to the and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form.In his writings, he proposed that the effect occurs because the lenses were spherical—light striking at an angle could not be focused because of differences in refraction.Isaac Newton was reportedly stumped in his efforts to solve the problem (which became known as spherical aberration), as was Gottfried Leibniz.I posted a problem here, each week from 2002 to 2004. Half of them are physics (the odd weeks), and half are math (the even weeks). After all, I call them "Problems of the Week," and not "Problems of the Hour"!Many of the physics problems can be found scattered throughout the textbook (the red book on this page) for the Physics 16 course here at Harvard.