A few very short electricity & magnetism problems. Problem 1. Answer the followi

Question

A few very short electricity & magnetism problems.

Problem 1. Answer the following questions (each 10 points, total 60 points) (a) A photon has the energy of 1eV, what is the frequency of this photon? (b) A one-dimensional dielectric optical waveguide has a waveguide core made of a high refractive index material with refractive index of n2=1.5 and two claddings (top and bottom) made of a low refractive index material with refractive index n1=1.45, what is the numerical aperture of this optical waveguide? (c) Light is propagating in a lossy dielectric medium with a complex index of refraction n=1.45-0.0001j, where j is an imaginary number. What is the phase velocity of this light, and what is the travel range in this lossy medium. (d) A plane optical wave has an optical intensity of 1250 watts per square meter, what are the amplitudes of the electric field and the magnetic field of this plane wave in vacuum. (e) Light travel from water (n=1.33) to the air (n=1.0), what is the critical incident angle for total internal reflection? (f) Light travel from the water (n=1.33) to the air (n=1.00), what is the Brewster angle?

Explanation / Answer

a)

Energy = Planck Constant * Frequency

Now 1 eV = 1.6 * 10^-19 Joules

We know the Planck constant = 6.626 * 10^-34 J s

So, Frequency = 1.6 * 10^-19 / 6.626 * 10^-34 = 2.4147 * 10^14 Hertz.

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