Recent content by nathangrand

Is it that I need to use the optical path length..ie refractive index x physical length in my calculations? That will make it work I think but can someone explain why...

Imagine a dielectric made of of alternating layers of widths A and B and refractive indices (a*) and (b*). Find the effective refractive index, N So in general: c/n = wavelength x frequency = phase speed My thinking was find the total time taken for the wave to propagate through the...

Show the following, where U is a vector, and r is the position vector: \nabla(U.r) = U in polar coordinates Many Thanks

\nabla^2(Z)=0 Z= 0 for x=0, y=0 Z= x(1-x) for y=0 Z=0 for y=infinity Range 0<x<1 and y>0 (suppose strictly speaking should be x=1 and x=0 too) So all I want to do is solve this Use separation of variables: X''/X = a^2 = -Y''/Y Gives X = Aexp(ax) + Bexp(-ax) and Y=Ccos(ay) +...

Thanks - I'll give both methods a go and see how I get on!

A coal box, in the shape of a cuboid, is to be placed flush against a wall so that only its top, front and two ends are visible. How should the height h and the depth d be chosen so a to minimise the visible surface area A under the constraint that the box must be able to contain atleast a...

I know the expressions are there, I just can't fiddle around with the differetiation

how?

Infrared radiation, of wavelength λair = 1um in air, travels through a dispersive medium with refractive index n = 1.4505 and with dn/dλair = -0.01 per um at this wavelength. Calculate the speed at which the radiation carries information. So know that c/n = λf radiation carries...

anyone?

An open-ended quarter-wavelength, air-spaced, parallel-wire transmission line is found to be in resonance with an oscillator when its length is 0.25 m. When a capacitance of 1 pF is connected across the open end, it is found that the length of the line must be reduced to 0.125 m to obtain...

I agree! But how?

Cars pass at randoms times at an average rate of one a minute. The chance of a car stopping to give you a lift is one percent. What is the probability you will have got a lift within one hour? This has pretty much stumped me. I know λ=60 as expecting 60 cars an hour for the poisson...

A sign error isn't my problem - it's the magnitude I get wrong...

+ve into ground, -ve charge field up?