Converging Definition and 178 Threads

Back in the fractal craze, I wrote a simple application to generate the Mandelbrot set, and after way too many wasted hours, I noticed that the generating function frequently converged to sets of repeating values rather than single values. For example, for a 5 value convergent, the terms of the...

Homework Statement Determine whether each of the sequences converges or diverges. If it converges, find its limit. Explain with sufficient details each claim. Homework Equations (k) a_n=\sqrt{n^2+1}-n The Squeeze Theorem (If b_n<a_n<c_n, and both \displaystyle\lim_{x\rightarrow\infty}a_n...

Homework Statement Two converging lenses with focal lengths of 40 cm and 20 cm are 10 cm apart. A 2.0-cm-tall object is 60 cm in front of the 40-cm-focal-length converging lens. a. Use ray tracing to find the position and height of the image. do this accurately with a ruler. Determine the...

Homework Statement A converging lens and a diverging lens, separated by a distance of 30 cm, are used in combination. The converging lens has a focal length of 15 cm. The diverging lens is of unknown focal length. An object is placed 19 cm in front of the converging lens; the final image is...

A coin is located 20.0 cm to the left of a converging lens (f=16.0 cm). A second identical lens is placed to the right of the first lens, such that the image formed by the combination has the same size and orientation as the original coin. Find the separation between the lenses. So, f=...

Hello, does anyone know how a converging lens forms the Fourier transform of an aperture when the obs. screen is at distance=f? If each point emits a spherical wave, the lens should make it then parallel and the FT should be the interference resulting from that. However, if we decompose...

Homework Statement Let t1=sqrt(2) Let t_(n+1)=sqrt(2+sqrt(t_n)) (it's a recursively defined series) What does it converge to? Homework Equations The Attempt at a Solution I calculated it out for some values andI get 1.8312 (approx), but I don't want to express it in...

Homework Statement heres the equation that will converge conditionally: http://img440.imageshack.us/img440/9945/untitled3jg.jpg changes to An = n/(1 + nLNn) Homework Equations alternating series equation. converges conditionally. d/dn An = (1-n)/(1+nLNn)^2 The Attempt at a...

we used a converging lens and a screen with white paper in front of a window to form an image of a distant tree outside. This was about 15cm. When we used an optics bench and a candle to figure out the focus, it was 16.3cm... What would be a reason for the difference in the number?

hi i posted the same sort of question a few times before but this time it's a little different we did an experiment with a converging lens and a candle to find an image. When the candle was placed at the focal point, which was 16.3cm, an image appeared at 136cm. I know in theory, no image...

How far away from a converging lens must an object be ( in terms of focal length, f ) so that the difference between the image distance and the focal lengh is 1% of the focal length? I tried to translate the words into an equation based on the thin lens equation but i don't know if it is...

In order to find the integral of 1/(x*ln(x)) dx, I tried using the substitution method where u = 1/x and dv = 1/ln(x) dx . Then du = ln(x) dx. However this is where I got stuck. What would v equal? Or is their another way I should be approaching this integral in order to find if it...

"Suppose a_1\geq a_2\geq ... \geq a_n > 0 for all n such that \sum a_n converges. Show that na_n tends to zero." The best I can do is prove that a subsequence na_n converges to a number between the sum of the series and 0.

If subsonic flow is accelerated in a converging duct to mach 1 and then the duct is further converged, choked flow will occur. Will flow at the exit of the duct be compressed as the volume flow rate is decreasing but the mass flow rate has to remain the same.

I have a simple question that I can't seem to answer... why is it that when an object is at the focal point of a converging lense, the image is at infinity? How can you show this through ray diagrams?

A bright object is placed on one sid eof a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. The distance d_T = d_i + d_0 between the object and the screen is kept fixed, but the lens can be moved. Show that if d_t > 4f , there will be two...

I got a problem where it gives us a diagram with a lens, a source and a image. We have to draw the three principal rays. But after drawing the rays, how can I tell if it is a diverging or converging len? And how can I explain it verbally? Thanks a lot!

If a general statement like an->a where (an) is a sequence of non negative real numbers, how would we prove the sqare root an->the square root of a. When a=0, this can easily be done. But I don't see how this is possible from the given information for the case where a>0. Thanks for any help...

The following series can be shown to converge, but exactly what does it converge to? Euler was supposed to have proven it to sum to pi^2/6, but how? 1 + 1/4 + 1/9 + 1/16 + ... + 1/(r^2) as r -> infinity The following is a small maths puzzle that was asked in another forum, but which I...

What am I missing here? A person looks at a gem using a converging lens with a focal length of 15.0 cm. The lens forms a virtual image 26.0 cm from the lens. Determine the magnification. (1/p)+(1/q) = (1/f) p=? q=26 cm f=15 cm (1/15)-(1/26)= Ans^-1 = 35.5 cm (p) Magnification=...

A converging lens (convex) and a concave mirror, both of focal length 5.0 cm, are arranged with their axes in line. The lens and the mirror are 10.0 cm apart and a candle is placed 3 cm infront of the mirror. By using a ray diagram or some other metho, find the location of all the images...

1) Aconverging lens with a focal length of 7 cm forms an image of a 4 mm tall real object that is to the left of the lens. The image 1.10 cm tall and erect. Where is the object located? Where is the image located? 2) A converging lens with a focal length of 12 cm forms a virtual image 5 mm...

problem 24. A person looks at a gem using a concverging lense with a focal length of 13.7 cm. The lense forms a virtual image 35.5 cm from the lense. a) Find the magnifaction. This is what I have done so far: f=13.7 , q= -35.5 1/p+1/q=1/f 1/f-1/q=1/p...

How do you prove that the lim n->infinity (n-1/n)=1? I know that the definition of convergence for a sequence xn is for all E>0, there exists an N is an element of the set of a natural numbers and there exists a n>=N, such that lxn-Ll<E. Is it sufficient to just show that 1 is the least...

Trouble with a converging sequence... Having a numpty moment here with a proof, so any help would be great! Thanks! If (xn) is a convergent sequence with a non-zero limit, prove that there exists a positive integer N such that mod(xn)>amod(limxn) where n tends to infinity for the lim part...

I am having trouble with my homework. I know the answer but I can't figure out how to get there. The question is "An image of a flower is produced on a screen by a lens 1.60m from the screen. The image of the flower has a linear magnification of -2.5. What is the focal point of the lens?" I...

Hello, I am reading over the topic of converging and diverging lenses, and I had a question relating to phenomena of image formation as seen through these. Based on the ray diagrams that are typically used (freshman physics) how does one conclude whehter or not an image is inverted or...

For a lens of focal length f, what value of the distance between the object and the lens[D0] would give an image with a magnification of one? Is it possible to obtain a non-inverted image with a converging spherical lens? Explain please? Any response would be greatly appreciated, and I...