Question

Optics 401-01 (Fall 2017) Examla Name Professor: Dr. T. X. Zhang 1. (10 pts) Briefly describe Pierre de Fermat and his significant work on optbcs 2. (40 pts) For a one-dimensional harmonic wave with amplitude of 3x 10 em, wavelength of 2 x 10 cm, speed of 6 x102m/s, and initial phase of 45 (G) Determine the wave frequency, wave number, and the wave angular frequency (ii) Express the wave function (ii) Find the phase at -4x10 "'s and x 2x10 cm

Answer 1

1)

Pierre De Fermat was a French mathematician born on 17th August 1601 in Beaumont-de-Lomagne, France to a wealthy merchant family. His early schooling was from the local Franciscan monastery. He took his higher education from the University of Toulouse. Fermat was a Lawyer by profession but is credited most for his accomplishments in the field of mathematics.

Fermat was one of the most prominent mathematicians of the first half of the seventeenth century and would have been more acclaimed if more was known about his personal life. Many top mathematicians claim to have been influenced by Fermat’s work including Isaac Newton and Andrew Wiles.

Work on optics

Fermat’s work in optics was an advance to the theory of light by Heron of Alexandria. He made some corrections to the theory such as his demonstration of refracted light that should be measured by optical distance which is always a minimum. He also gave the correct fact that light passes more slowly in a dense medium. It was this work by Fermat that influenced the famous mathematician Johann Bernoulli to forming the calculus of variations.