Yeah, its been several years since I've had any optics classes so I'm struggling to remember. I recall doing some matrix multiplication for compound lenses but I don't dare delve that deeply. I don't think it is impossible, just more effort.
What 'd' should be used for calculating the power when including the third lens? So I have the first two lenses easy enough. But I'm not sure if I take the P12 to be the distance of the second lens, the average of the distance from 1->3 and 1->2 or just the total distance. I suspect it is the...
Homework Statement
I have a compound thick lens problem that I need to find the sign of the refractive power.
Homework Equations
Thick lens equation and focal length equation.
The Attempt at a Solution
I believe all I need to do is calculate the focal length of the first two thick lenses and...
For example
##E=Cs^2\hat{s}##
##s=rsin(\theta)## and ##\hat{s}=sin(\theta)\hat{r}+cos(\theta)\hat{\theta}##
so ##E=(rsin(\theta))^2(sin(\theta)\hat{r}+cos(\theta)\hat{\theta})##
##\int E \cdot dA=E4\pi r^2=4\pi r^2(rsin(\theta))^2(sin(\theta)\hat{r}+cos(\theta)\hat{\theta})##
The next...
The problem is to find the flux through a sphere where the E field is given in cylindrical coordinates. I can't convert the field into spherical as the question specifically asks that I do it the other way. And, I must also finally graph the divergence on the sz plane.
Homework Statement
The trick to this problem is the E field is in cylindrical coordinates.
##E(\vec{r})=Cs^2\hat{s}##
Homework Equations
##\int E \cdot dA##
The Attempt at a Solution
I tried converting the E field into spherical coords and I can find the flux that way but it is a...
Homework Statement
I got a problem wrong on a quiz and I'm pretty positive on all the other questions as being correct but maybe this one..
How does the gravitational force at the event horizon (Schwarzschild radius) behave as the black hole mass increases?
Homework Equations...
Thanks for the comment. It's not often I get excited about what my physics tell me but being able to, even roughly, determine the components of such an event is pretty cool. Wish my EM class calculated things as interesting.
Thanks again!
Homework Statement
This is third and last part of a question whose first part was solved on here earlier. Given the spin angular momentum of the Earth and the Orbital (around Earth) angular momentum of the moon calculate the mass of an object that if it hit the Earth at it's radius (glancing...
I figured it out! Instead of setting c cos\theta=\betac I set it equal to ux and used the x transform. I started out with the right idea but needed to forget about the beta and think about the x axis. Thanks for the help.
Okay, I understand now. This is what I get for trying to take short cuts to get ≈results. I finally got the number I expected to get. Thanks for all the help!
I'm missing something because when I put values in here I'm not getting anything near 11 km/s. I took out the Earth's radius and it only got me an additional 2 m/s.
Using G=6.67(10)-11
m=6(10)24
r=rh-rearth=1.5(10)9-6.4(10)6=1.4936(10)9
equation then gives me 732m/s
Also, Voko, I...
Potential energy would be
PE=\frac{Gm_1m_2}{r}
KE=PE
\frac {m_2v^2}{2}=\frac{Gm_1m_2}{r}
\frac {v^2}{2}=\frac{Gm_1}{r}
v=\sqrt{\frac{2Gm_1}{r}}
Unless I"m using the wrong equation for PE this is exactly the same as I had before.
I have the equation has the instructor has it posted on his slide show. Regardless I forgot to actually multiply by that factor anyway. Using my instructor's equation:
Hill radius would be: 1.71707(10)9
Using the factor of three instead: 1.5(10)9
That one is just plug and play so I...
Homework Statement
Find the hill radius of Earth and calculate the velocity of an object falling from that radius (and from rest from the Earth's frame) at the point where it impacts the Earth.
Relate this velocity to the escape velocity of Earth.
Homework Equations
Hill radius:
r_h=R...
Okay, so there's no contraction for y so y'=y. For x':
x^\prime = \gamma (x-\beta tc)
So for the observer's frame the angle should be:
tan(\theta^\prime)=\frac{y^\prime}{x^\prime}
\gamma = \frac{1}{\sqrt{1-\beta}}
tan(\theta^\prime) = (\frac{y^\prime \sqrt{1-\beta}}{ (x-\beta...
I don't think they necessarily mean that the light is emitted towards the station. So I've placed the ship and station at the origin at the moment the light is emitted. The ship says it sent the beam out at some angle but clearly the station disagrees on the angle.
For the formula I have the...
Although I am far from being a great physics student (I come here often with questions) I do one thing that really helps me understand difficult problems that seems a no brainer in retrospect. When I'm at my whits end with a question I come to this forum and type out my issue as clearly and...
Homework Statement
A space station observes a high-speed rocket passing by at speed β c in the +x direction. The rocket suddenly emits a light ray from a powerful laser. According to the space station, the light ray was emitted at an angle of θ with respect to the +x-axis. However, the...
It's sad when someone else understands my equations better than I do. You were right. to begin with ##R≈r_{p \bullet}##
I wrote that correctly to begin with but then forgot exactly what I meant. I left it as little are but, yes they're equivalent. I expanded out everything using little r but...
I'll be asking tomorrow during office hours. I've just gone over 2.3.5 and it says for boundaries that are curved I need to use a "very small A" which I don't entirely understand. I'll work the problem tonight as the book has it and adjust it later I guess. Like you said, I would expect to have...
I am using Griffith's but the problem was adjusted by the teacher to be as I stated. I've performed this evaluation before but the limits were never as they are here. Well, the second and third are but the first is not.
Shoot, I think maybe the confusion comes from an accidental notation problem.
it is r_p not r_{p \bullet}
the latter makes it look like I'm referring to the distance of the planet to the black hole. Rather it should just be the orbital radius of the planet to it's host star. So it could...
Homework Statement
Standard E field problem where I'm to find the field at 3 positions of a hollow sphere that has a charge density k/r^2
r ≤ a
a ≤ r < b
b ≤ r
Homework Equations
∫Eda=Q/ε
The Attempt at a Solution
I guess the thing that is tripping me up are the limits. I know...
Homework Statement
(a) Consider a planet orbiting a star of mass M?, on a circular orbit with circular
velocity vp. What is the planet's orbital radius, in terms of vp and M?
(b) Now suppose that the star (carrying the planet along with it) enters a nearly radial
orbit around a black hole of...
Perfect, thank you! That put us a bit closer to the index (I figured this was the case) and gives me a way to make quick comparison's for future experiments. Really appreciate it.