Image Definition and 1000 Threads

Homework Statement Let ##n>1\in\, \mathbb{N}##. A map ##A:\mathbb{R}_{n}[x]\to\mathbb{R}_{n}[x]## is given with the rule ##(Ap)(x)=(x^n+1)p(1)+p^{'''}(x)## a)Proof that this map is linear b)Find some basis of the kernel b)Find the dimension of the image Homework Equations ##\mathbb{R}_{n}[x]##...

I'm trying to understand image and pre image better but I am having a hard time finding good examples. So here is one I did come across, let's say ##f:\mathbb{R} →\mathbb{R}## defined by ##f(x)=x^{2}##. Suppose also that ##D = [-1,2]## where ##D\subset \mathbb{R}##. If I'm looking for...

I get terribly confused to consider which rays for determining image formation via concave and convex lens? Many times examples take 3 rays into consideration - 1) A ray passing through Focus 2) A ray passing Optical Center (center of curvature) and 3)A ray parallel to principal focus. But the...

When we see things, we typically see one image which appears to have depth (if we have two functional eyes of course). I understand this is because the images from each eye are matched, and the slightly different perspective caused by the horizontal displacement of the eyes is used to generate...

Homework Statement A fish watcher at point P watches a fish through a glass wall of a fish tank. The watcher is level with the fish; the index of refraction of the glass is 8/5, and that of the water is 4/3. The distances are d1=8.0 cm, d2=3.0 cm, and d3=6.8 cm (a) To the fish, how far away...

Homework Statement Hi everybody! Being given three identical thin lenses with the same focal length, I have to determine ##a## (distance object-screen), ##d_a## (distance lens 1-lens2) and ##d_b## (distance lens 2-lens 3) so that a sharp image of the object appears on the screen regardless of...

Homework Statement The question is attached. Homework Equations The Attempt at a Solution I understand that the question would return to a typical conductor problem when ε2 >> ε1 so for the quadrant one, I placed image charges of q_1 at (d1 , 0 , -d2), -q1 at (-d1 , 0 , -d2) and another q1 at...

I have a large image that I made (a river running to the Washington coast on the Olympic Penninsula) by montaging together 32 pictures I took on my T3i in photoshop. It is 24,362 × 8,801 pixels. It looks like this (a smallified version): The photoshop file was greater than 2 gigabites...

Homework Statement For an object distance z = 200 mm, an object space index n = 1.5, and a front focal length ff = −80 mm, what is the effective focal length f and the magnification m? Is the image upright or inverted? Homework Equations Lots and lots of gaussian and Newtonian imaging...

Homework Statement . With this problem, how should I set image charges so as to satisfy the same boundary condition? And if possible, could you let me know how can that image charge configuration be deduced? Thanks for reading. Homework EquationsThe Attempt at a Solution Well, I first put...

I just came upon this sensor, in a new(?) camera by Sigma. It seems to be a clever idea. As anyone here got any special knowledge of the device or the technology? It solves a number of problems but, no doubt, introduces some new ones. Incredibly high res! I will stick with Pentax until I become...

https://en.m.wikipedia.org/wiki/File:Moon_egret.jpg Can we use better telescopes of this type (ground based gamma rays telescopes) to image the surface and subsurface of a planet with a lot of resolution?

I am working on a problem that goes like this: Show that $Ker (F) \cap I am (F) = \{0\}$ if $F: W \rightarrow W$ is linear and if $F^4 = F.$ I have the solution but there is one step which I need help: (the delineation is mine) (1) Suppose that there exists $x$, such that $x \in Ker(F) \cap...

I have an LCD display I'd like to use in a collimated HUD display, however it seems that I can't get the light (image) from it to collimate properly. I'm trying to use a lens with the focal distance of 4.5 cm. When I place the display 4.5 cm away from the lens' center I expected to achieve the...

Homework Statement An object is at a very large distance from a concave mirror of focal length 40cm. Find the distance from the image to the mirror. Is the image real or virtual? Homework Equations 1/u + 1/v = 1/f The Attempt at a Solution [/B] 1/u + 1/v = 1/40 The image has to be real...

Homework Statement I have a few fundamental questions in optics about the focus and blurry images. Each textbook says that according to this picture the object image is the same. 1) If we move the screen to point further then the image will be blurry. What causes it to be blurry? 2) Why do...

Hi guys, I have a dicom image from a QC spect acquisition. reading the file in with dicom.read_file and pulling pixel data using numpy.pixel_array gives array of shape [2, 1024, 1024] The 2 represents two images, one from each detector head on the spect scanner and the 1024x1024 are the...

What are the possible causes of the horizontal noise stripes in this image: http://dsp.stackexchange.com/questions/20061/removing-periodic-noise-from-image-using-fourier-transform I'm currently studying on these kinds of noise, and how to eliminate them. Can these be caused by diffraction...

Homework Statement This is not really a homework or coursework question, but might be of interest to readers of this forum. It concerns what I have viewed on two separate occasions which baffles me. The setup was different it the two instances, but there are similar elements in both. In both...

Homework Statement The book ("Real World Physics") says A virtual image in a plane mirror is on the perpendicular from the object to the mirror Homework Equations I know that the normal line is perpendicular to the surface of the mirror And I know that the angle of the incidence and reflection...

Mirror/camera/TV etc. don't have a complex visual cortex system/perception like our eyes. Human eyes use rod,cone,neuron and above all perception of brain to make image. How come these devices create the same clear images/scenes at their surfaces by themselves without having the advance...

Hi everyone, Does someone know from which textbook the question below was taken from? The only given data the i found is q1=π*sin(πx/2). Thanks:)

I was wondering if it is possible to image the motion of individual air molecules? What I am picturing is using a laser to illuminate a volume of air, and using scattered light to measure the velocity of individual air molecules through the doppler shift of the scattered light. It seems that...

Homework Statement Homework Equations \frac{1}{p}+\frac{1}{q}=\frac{1}{f} The Attempt at a Solution I already had this typed in word so here is a screen shot: I don't understand why the negative is omitted in the "correct answer" "B." In solving this problem I wanted to proceed in...

Homework Statement I got the correct answers for A and B, I just need help with C and D. A. Find indicated currents. I1= I2 = 3 A ... IL = 6 A B. Find total power delivered by each source. PE = 12 V (3A) C. Find the total power delivered by each source and compare it to the power delivered...

Hi everyone, I have a question (or three) regarding Purcell's discussion of image charges, in pg 137-139 of the third edition of his EM book. He goes over the classic image charge example: a plane held at zero potential, and a charge Q a distance h above it. I'm fine with everything he...

Homework Statement An object 1.25 cm tall is placed 100 cm in front of a convex lens with a focal length of magnitude 50 cm. A concave lens with a focal length of magnitude 20 cm is placed 90 cm beyond the first lens. Where is the final image located? Homework Equations (1/s)+(1/s')=1/f s=...

Hey! :o Let $f:B\rightarrow C$ and $g:C\rightarrow D$. I want to show that Im(gf)=Im(g), when f is onto. I have done the following: Let $x\in \text{Im}g$. Then $\exists y\in C$ such that $g(y)=x$. Since $f$ is onto, we have that $\exists b\in B$ such that $f(b)=y$. Then...

I have no idea what I am doing wrong. I have already found multiple places on the internet which give clear examples of how to do this, yet I am still struggling. Please help me out, or at least point me somewhere. My code is below. I am trying to interpolate pixels of a full color image. The...

Hello everyone, I have been doing researches on this, but those topics I found are a bit different from what I am doing, I am trying to determine the actual size of an object in image/video (CCTV video tracks), my thinking is, if this object is moving, the size appears on the screen changes...

A plane mirror forms a virtual image of a real object placed in front of it and a real image of a virtual object placed in front of it. I can't picture the second case. Please show me a ray diagram showing real image formation by a plane mirror or just explain the case of real image formation by...

Really been spending time in Photoshop practicing astro image editing ... purchased a set of astro-imaging actions called Astronomy Tools Actions Set http://www.prodigitalsoftware.com/Astronomy_Tools_For_Full_… ... this is an actions addition for Photoshop I have been following a video ...

Hi. I'm trying to proof the image formation property of a concave spherical mirror. I know you can do this easily with a particular choice of rays (namely one that hits the vertex and one that passes through the center of the sphere) but I would like to show that a generic ray yields the same...

Using a convex lens, can an image be formed at the focal point and if so where would the object have to be from the convex lens?

Hi everyone. The next link shows how the Andromeda should look like (from the Earth's surface) if its stars were much more brighter than they are (or if we could have a super-vision). http://www.iflscience.com/space/what-andromeda-would-look-night-if-it-were-brighter It seems so amazing as I...

Homework Statement A punctual source of light is in the focal point of a diverging lens. in which distance from the lens is the image. Draw the road of rays. Homework Equations The objects at focal point don't have an image. The Attempt at a Solution http://s32.postimg.org/ociblmif9/image.png...

Hi there, I have a question that I think has an answer but I cannot find it in the literature in any convincing way: I am using two models, WKB based and TMM based to calculate the transmission probability of electrons through a (initially rectangular) thin potential of the order of 1-2nm...

I have drawn a diagram of the incident and reflected rays of an object by the concave mirror. Red color shows the incident rays, black color shows the normals drawn from the center of curvature, while green color shows the reflected rays. Shouldn't all the reflected rays meet at one point. Any...

Homework Statement Compute the following parameters of the final image formed by the lens system shown in the figure below a) position b) size c) nature (Real, Virtual, Upright, Inverted, Etc.) Homework EquationsThe Attempt at a Solution i am kind of lost at where to begin...

Homework Statement A symmetric, double-convex, thin lens made of glass with n = 1.52 has a focal length in air of 40 cm. The lens is sealed into the opening in the left-hand of a tank filled with water (n = 4/3). At the right-hand end of the tank is a plane mirror 90 cm from the lens. Find the...

Please could someone explain why Earth looks to bright when it is so far away? Also, why can't we see any other objects (other planets and stars) in the image? Thank you.

Homework Statement Show that if ##f: A \rightarrow B## and ##E,F \subseteq A##, then ##f(E \cup F) = f(E) \cup f(F)##, and ##f(E \cap F) \subseteq f(E) \cap f(F)##. Homework Equations ##f(E) := \{f(x)~|~ x \in E \}##. The Attempt at a Solution Okay, showing ##f(E \cup F) \subseteq f(E) \cup...

1. A real inverted image I of an object O is formed by a certain lens (not shown); the object—image separation is d = 40.0 cm, measured along the central axis of the lens. The image is just half the size of the object, a. What kind of lens must be used to produce this image? b. How far from the...

Complete reflector novice here. Just got a reflector (using refractor before). I had no problems doing astrophotography with my refractor however with the reflector I get double images. Why is this so? Is this a collmination problem? It's not the camera because there's double images when I...

Hello, This question is from 1990 Turkey National Physics Olympics. I tried my best to translate it clearly. 1. Homework Statement https://s23.postimg.org/cotn29afv/Hollow+Spherical+Glass.jpg The sphere of radius 2R has an empty sphere inside with radius R. In order for the image of an object...

Homework Statement φ is a homomorphism of groups. φ: ℝ^x -> ℝ^x, where φ(α) = α^4, for all α ∈ ℝ^x. Note that ℝ^x is a group under multiplication. Describe ker(φ) and Im(φ). Homework EquationsThe Attempt at a Solution This is another one of those problems that has me scratching my head due...

Homework Statement I need to prove that if ##f: \mathbb{R} \rightarrow \mathbb{R}## then the following two statements are NOT equivalent: 1) For every ##E \subset \mathbb{R}## that is Lebesgue-measurable, ##f^{-1}(E)## is Lebesgue-measurable. 2) For every ##E \subset \mathbb{R}## that is...

Apparently, when viewed from a distance, the motions of a person approaching the event horizon of a black hole will appear to first slow down and then come to a complete stop as they pass through the horizon. Then, as I'm led to believe by what I've seen and read, that final 'frozen' image of...

Is there any way to design a lens or system of lenses where I see the same part of the image, irrespective of direction or angle of view. The light rays can be assumed to be collimated as viewing will be from a distance. Actually- I am looking at focusing on a point or specific area of the...

In Hydrogen atom, in center Proton and Electron revolving it. My question, is that enclosed in a cell, actually what we see in electron microscope. Regards Nilesh