Of course, if you consider two observers, one in frame S and the other in frame S' (moving at .99c relative to S), BOTH observers see the photon move at speed c... But the observer in S will see the person in S' move at nearly the same speed. That is, in S' the distance between the person and...
For (b), you just need to find when the complex exponentials have argument equal to a multiple of 2*pi, and then they will equal 1. It's very simple from where you got.
Actually, I believed that I am right in this case. We can define the vector components of a vector A as Ai=(A, ei) where the parentheses indicate an inner product and ei are the basis vectors. Translating the coordinates leaves us with the same ei, but any transformation that can be represented...
So the vector gets "dragged along" with the coordinate translation? I thought we think of the vector as sitting where it is, and when we try to express it in a new set of coordinates we are trying to find how it would be expressed in a different frame (much like a relativistic transformation)...
Wires are conductors, so within them yes- the line integral of the electric field is 0. But within the emf, this is not true, so the field is not conservative there.
I would add a slight word of caution: that formula is a condition for constructive interference, but you shouldn't really think of applying it in the strict normal sense. What it is saying is, "does a whole number of wavelengths fit in the difference?" And if the answer is yes, then you have...
Ah! So you're merely misunderstanding what that picture actually means. The wave is NOT a single ray, but rather a plane wave. That same picture is happening at each and every point in space along the same plane that is perpendicular to the direction of travel. Imagine those arrows translate all...
I think the non-monochromatisicity doesn't really bother me, since even a laser produces light at different wavelengths normally. The grating would help us separate these!
It was the fact that there is diffraction at all for an incoherent source that bothered me, not the smearing of colors...
I'm not sure I understand. The pattern is proportional to the Fourier Transform (squared) of the aperture function. But it doesn't make sense to take the Fourier Transform without having the phase information of the beam at the aperture. And if the phase is incoherent at the aperture, we can't...
An incandescent lightbulb produces incoherent light. But on Wikipedia, for instance, there is a picture of it producing a rainbow diffraction pattern on the diffraction grating page. But since the bulb is putting out incoherent light, it should be intensities rather than fields that add...
Flux through a closed surface is 0 by the divergence theorem... But only for the case of an inverse square field. In that case, the divergence of the field is 0 unless you have a point charge (a source or a sink) within the surface. So that relation is specific to electrostatics, gravity, and...