Eugene Hecht
ISBN #9780133977226
5th Edition
831 Questions
Homework Questions
Optics is a comprehensive exploration of the science of light, tracing its evolution from ancient theories and pivotal experiments by figures like Alhazen, Newton, Huygens, and Einstein to modern advances in optical communications and imaging. The book systematically builds from fundamental wave motion and electromagnetic theory to the refined study of light’s propagation, reflection, and refraction. It delves into both geometrical and Fourier optics, highlighting the mathematical and physical principles that govern phenomena such as interference, diffraction, and polarization. By bridging classical optics with modern topics like coherence, lasers, holography, and nonlinear effects, the text offers a thorough foundation and practical insight for both students and researchers in the field.
Chapter 2
Wave Motion
Chapter 3
Electromagnetic Theory, Photons, and Light
Chapter 4
The Propagation of Light
Chapter 5
Geometrical Optics
Chapter 6
More on Geometrical Optics
Chapter 7
The Superposition of Waves
Chapter 8
Polarization
Chapter 9
Interference
Chapter 10
Diffraction
Chapter 11
Fourier Optics
Chapter 12
Basics of Coherence Theory
Chapter 13
Modern Optics: Lasers and Other Topics
Problem 1
Consider the plane electromagnetic wave in vacuum (in SI units) given by the expressions $E_{x}=0, E_{y}=2 \cos \left[2 \pi \times 10^{14}(t-x / c)+\right.$ $\pi / 2],$ and $E_{z}=0$ (a) What are the frequency, wavelength, direction of motion, amplitude, initial phase angle, and polarization of the wave? (b) Write an expression for the magnetic flux density.
Ajay Singhal Numerade Educator
Problem 2
Show that the function $$\psi(z, t)=(z+v t)^{2}$$ is a nontrivial solution of the differential wave equation. In what direction does it travel?
Supratim Pal Numerade Educator
Problem 3
Show that the function $$\psi(y, t)=(y-4 t)^{2}$$ is a solution of the differential wave equation. In what direction does it travel?
Problem 4
The shape of the interface pictured in Fig. P.5.1 is known as a Cartesian oval after René Descartes, who studied it in the 1600 s. It's the perfect configuration to carry any ray from $S$ to the interface to $P$. Prove that the defining equation is $\ell_{o} n_{1}+\ell_{i} n_{2}=$ constant Show that this is equivalent to $$n_{1}\left(x^{2}+y^{2}\right)^{1 / 2}+n_{2}\left[y^{2}+\left(s_{o}+s_{i}-x^{2}\right)\right]^{1 / 2}=\text { constant }$$ where $x$ and $y$ are the coordinates of point $A$.
Narayan Hari Numerade Educator
Problem 5
Determine the resultant of the superposition of the parallel waves $E_{1}=E_{01} \sin \left(\omega t+\varepsilon_{1}\right)$ and $E_{2}=E_{02} \sin \left(\omega t+\varepsilon_{2}\right)$ when $\omega=120 \pi$ $E_{01}=6, E_{02}=8, \varepsilon_{1}=0,$ and $\varepsilon_{2}=\pi / 2 .$ Plot each function and the resultant.
Khoobchandra Agrawal Numerade Educator
Problem 6
Work your way through an argument using dimensional analysis to establish the $\lambda^{-4}$ dependence of the percentage of light scattered in Rayleigh Scattering. Let $E_{0 i}$ and $E_{0 s}$ be the incident and scattered amplitudes, the latter at a distance $r$ from the scatterer. Assume $E_{0 s} \propto E_{0 i}$ and $E_{0 s} \propto 1 / r .$ Furthermore, plausibly assume that the scattered amplitude is proportional to the volume, $V$, of the scatterer; within limits this is reasonable. Determine the units of the constant of proportionality.
Vipender Rao Numerade Educator
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