Recent content by Jon.G

I know localisation microscopy 'beats' the limit on resolution by activating individual sources and rendering a final image, but what are the limits that prevent the resolution of the images of these individual fluorophores? Is it just the number of photons collected? Cheers

Hello, I have been looking into NV in diamond and how it can be used for nanoscale magnetometry, and was wondering if anyone could help explain how it works or link to a paper that does. Is it just a spin 1 state (splits to 3 levels) that undergoes NMR or is there something else happening? I'm...

Ooh ok thanks. So I went through it with n=2,3 and 4 and [A, F(B)] = [A, B]F'(B) was shown for each of them. For the sum is it simply that when n is any value, fn is a constant so that (for example) [A,f2B2] = [A, f2B]B + f2B[A, B] f2 a constant and can be taken outside of [] as it effect both...

Homework Statement A and B commute with their commutator, C=[A,B] Show that [A, F(B)] = [A, B]F'(B) F(B) = ∑n=0∞fnBn Homework Equations [A,B] = AB - BA [A,BC] = [A,B]C + B[A,C]The Attempt at a Solution So all I can think to do is: [A,Bn] = [A,BBn-1] = [A,B]Bn-1 + B[A,Bn-1]...

That just made me realize DX The expression 1/(1+(z-1)) is the same as 1/(1-(-(z-1))) and the general rule is: 1/(1-x) = Σxn That double minus is where the -1 factor came from. I think I understand it, now sure if I explained why I understand it well enough (so many brackets). Just missed out on...

Homework Statement So I'm checking my solutions to past question and there's one bit that throws me. 1/(1+(z-1)) = Σ(-1)n(z-1)n (for 0<|z-1|<1) I don't know where the (-1)n factor came from. Is it just something that always happens that I didn't know about / forgot about, or is there some...

Homework Statement Estimate the diffraction angle. The spectrometer is made from rolling up a 30cm long piece of cardboard into a tube. Duct tape is placed over one end, and a thin slit is made. The other end has a diffraction grating held in place. I look through the diffraction grating and...

Homework Statement For large intensities, what is the maximum ratio of atoms in N1 compared with N3? I suppose this is just a bit of maths I'm struggling with, seems simple I just can't get it for whatever reason D: Working through previous question, I got to: N3= (Ip/Is) / ((Ip/Is) +1 ) N1...

Homework Statement A beam of light is reflected from the surface of some unknown liquid, and the light is examined with a linear sheet polarizer. It is found that when the central axis of the polariser (that is, the perpendicular to the plane of the sheet) is tilted down from the vertical at an...

oh wow I actually can't believe I didn't see that. I am familiar with Euler's Formula and don't know why I didn't think of it in this situation. When I'm home I'll try using that and then post how I get on. Thanks for your time

Homework Statement Determine the largest set on which the function is analytic. f(z) = (z2-2)e-xe-iy Homework Equations z=x+iy f(x+iy) = U(x,y) + iV(x,y) Ux=Vy Uy=-Vx The Attempt at a Solution I think I'm right in saying that f(z) is analytic if the CR equations (provided above) are...

I've been reading up about vacuum tubes and (more specifically) the Audion, and how they were used for instruments/amplifiers. This isn't anything I'm learning about on my degree, just things I'm reading up on myself so forgive me if I'm a little slow to grasp some parts. I understand how the...

Wow, thanks a lot! Some very interesting points there. I knew about "muting" the strings at the different intervals but never really make the connection :P

You're right, I didn't think of that :) I read this and quickly recorded the same note a few times but plucking at different points and it definitely has a noticeable effect on the relative intensities of the spectrum. If I remember correctly, plucking at L/n should remove every nth harmonic (in...

This is not a homework question per se, but rather something I have come across during a homework project. Using Audacity, I recorded a few different instruments playing the same notes (investigating timbre). I noticed that (using a steel string acoustic guitar) the first harmonic at 131 Hz...