Recent content by ttzhou

Hi Simon, As mentioned in my post - the first focal length is defined as the distance from the first (or front) focal point to the first principal point, which is defined as the intersection of the first principle plane and the axis. The second focal length is defined analagously. I've...

Homework Statement In Sears' Optics, chapter 4, Sears claims that the first and second focal lengths (distance from first and second focal points to the first and second principal points, respectively) are equal, and he seems to imply that this is true in general, without proof. I am a...

Think I got it; algebra wasn't too bad. Much appreciated!

I have. This is going to be ugly, isn't it?

We've only gotten up to the Lorentz Transforms for velocities, but I'd imagine this could be extended. However, I'm letting V_a and V_b represent the speed of the spaceships relative to a common fixed reference frame, i.e. the frame where the length is "proper". Shouldn't then we just use the...

George, just wanted to this opportunity to thank you for the help - you probably get that a lot but nonetheless, felt I should say it. On the last topic, I already tried solving it that way, (clearly the speed of the faster ship subtract the speed of the slower ship is the relative speed, so...

I am currently staring at 4(1- \beta_b^2) = (1 - \beta_a^2) , which I got by dividing the Lorentz factor of each spaceship and setting them equal to 2 (the ratio of the measured lengths) If this is correct, how can I get relative velocity from this... I suppose this is what you refer to as...

oh ok I see what you mean. Thanks... Am I still correct in assuming we only need to deal with length here? Something that still feels unclear to me is the notion of length contraction in direction of motion. If the spaceship is moving toward the object, how would they perceive length...

The assumption I made, which I find very, very sketchy, is that L/L_0 = 1/2 (since length contracts in the moving frame), which I then am able to use to solve for \beta Relativity just isn't my thing... my instructor glazed over it very quickly without any details, but I need a lot of details...

Homework Statement Two momentarily coincident observers approach a small and distant object. One measures the object to be twice as large as the other's measurement. Find their relative velocity. Homework Equations Lorentz Transforms L/L_0 = \sqrt(1 - \beta^2) The Attempt at...

or micromass for that matter, he was the architect

msg me if you want some hints

Thanks very much, your hint was very concise and well chosen. All the best.

I think I have a proof involving finite descent; I eventually show that any ideal I is either equal to the ideal generated by some power of p (with 1 in the denominator), or we reach the point where the ideal generated by p is contained in I. Since I was able to show any proper ideal must be...

Thank you for the hint! Will see where it takes me.