Convex Definition and 283 Threads

Homework Statement An object is placed 32.7 cm from the reflecting surface of a convex mirror having a focal length of -10.8 cm. Determine the image distance. Homework Equations IDK The Attempt at a Solution Could someone please tell me what equation I should use? Thanks!

Homework Statement The virtual image produced by a convex mirror is one-quarter the size of the object. b) What is the focal length of this mirror? Homework Equations 1/di = 1/f - 1/do The Attempt at a Solution i found di to be -9.3 cm but when i solved for f i keep getting it...

Homework Statement A convex spherical mirror has a radius of curvature R = 20.0 cm and produces an upright image precisely one-quarter the size of an object. Calculate the separation distance between the object and its image? Homework Equations M = (image height)/(object height)...

Homework Statement Let f:\mathcal{O}\subset\mathbb{R}^n\rightarrow\mathbb{R}, \mathcal{O} is an open convex set. Assume that D^2f(x) is positive semi-definite \forall x\in\mathcal{O}. Such f are said to be convex functions.Homework Equations Prove that f((1-t)a+tb)\leq...

I want to know when a vehicle travels at a constant velocity along a convex and concave bridges, in what bridge the normal reaction of the vehicle is higher... I think it is on cancave bridge... am I right? because I got it by equations...

Hey, When dealing with convex mirrors I know that the image will always be virtual,upright and diminished. So when I am using descartes's formulae i know that for convex mirrors that the focal length is negative, but does my 1/di become negative? because virtual images have a negative height...

Homework Statement For each thin lens shown in the figure , calculate the location of the image of an object that is 18.5 {\rm cm} to the left of the lens. The lens material has a refractive index of 1.50, and the radii of curvature shown are only the magnitudes...

Homework Statement How do I show that if f\in C^2 \text{(}\mathbb{R}\text{)} is convex then the function yf(y^{-1}\textbf{x}) is convex on (x,y):y>0?Homework Equations I know the standard definitions and whatnot about convexity, but I tried chugging through the algebra and didn't have any...

Homework Statement Hello Two plano convex with f1=f2=30mm and R1=15.45mm and R2=-R1. The two plano convex have the same thickness too (3.16 mm) and their curves colide in the propagation axis. I believe you understand what i mean What is the focal length of the two plano convex system...

Homework Statement Show that the union of convex sets does not have to be convex. Homework Equations The Attempt at a Solution Is it enough to just show a counterexample? Or is that not considered a complete proof? My example is...S = {1} and T = {2}.

Homework Statement What is the image distance for an automobile 4.5 m in front of a convex miror with a 0.15 m focal length? I found this to be 0.155 m The question I'm having a problem with is: What is the magnification? Homework Equations magnification = - (image distance/object distance)...

1. Shiny lawn spheres placed on pedestals are convex mirrors. One such sphere has a diameter of 40 cm. A 12 cm robin sits in a tree 1.5 m from the sphere. a) Where is the image of the robin? b) How long is the robin's image? 2. 1/f = 1/do + 1/di 3. a. 1/f = 1/do + 1/di...

Convex mirror problem help?? Homework Statement a convex mirror has a focal length of 75cm. an object with a height of 2.0m is 6.0m from the mirror. a) what is the distance from the object's virtual image to the mirror? b) what is the height of the object's image? Homework Equations...

Homework Statement Prove that the virtual image in a convex mirror is always smaller than the real object. Homework Equations m = -\frac{d_{i}}{d_{O}} The Attempt at a Solution Not a homework problem. Something which is bothering me, and haven't been able to prove yet. Thanks!

Homework Statement An object is located 14 cm in front of a convex mirror, the image being 7 cm behind the mirror. A second object, twice as tall as the first one, is placed in front of the mirror, but at a different location. The image of this second object has the same height as the other...

Hi everyone, I've got this problem to solve: My problem is that I don't fully understand the question. I have found such definition of convex hull: So I do have to prove, that all the roots of W'(z) [let's denote them as z'_k] must be able to be written in such form: z'_k = \sum_{k=1}^n...

Homework Statement Given only the distance between the object and its image (p +q), how is it possible to find p, the distance of the object from the convex lens? Homework Equations 1/p + 1/q = 1/f in this case, p + q =40 also, the image is smaller than the original, so p > 2f The...

I had a quick question: Is the following proof of the theorem below correct? Theorem: If C is a convex subset of a Topological vector space X, and the origin 0 in X is contained in C, then the set tC is a subset of C for each 0<=t<=1. Proof: Since C is convex, then t*x + (1-t)*y...

Homework Statement I solved the problem, but upon further observation, I discovered that what I did didn't make sense. (these are rounded numbers, which shouldn't make a difference in my question) do = 13 cm (do is what I solved for in the problem, and according to the online system it was...

Hi all, I want to know whether it is correct that every convex polygon has an inner-circle (& hence an inner-radius). I think it is only possible for triangle and for regular polygon. Am I right? If there is any convex N-gon having sides a_1,a_2,...,a_N which has an incircle, then...

Homework Statement Let x* be an element of a convex set S. Show that x* is an extreme point of S if and only if the set S\{x*} is a convex set. Homework Equations (1-λ)x1 + λx2 exists in the convex set The Attempt at a Solution I'm not too sure what S\{x*}, I asssumed it was...

Homework Statement What is the number of edges of a convex polytope with n vertices all of whose faces are triangles. Homework Equations # of faces + #of vertecies = # of edges + 2 The Attempt at a Solution My reasoning is as follows: n/3 + n = # of edges + 2 4n/3 - 2 =...

Does anyone have a textbook on multivariable complex analysis, and do they define a holomorphically convex domain in terms of the union of an ascending series of compact subsets? If so, how exactly does the definition go? Was it D=\bigcup K_n where K_n is holomorphically convex and compact...

How do i prove this? Let S = {(X1, …., Xn) € R^n | Xi ≥0, X1 + … +Xn = 1}. Show that S is convex. Suppose f(Si) = {X1, X2,..., Xn} AND g(Si) = {X1 + X2+ ...+Xn} but If do that, then f(Si) and g(Si), both will increase. Now I'm not sure where to go from here. *PS: Both functions are...

How do i go about showing that if f(x)=\left\|x\left\| then f(x) is a convex function. I'm thinking in the direction of the triangle inequality but don't know how to go about it. Any clues? thanks

Homework Statement Let a function f : R => R be convex. Show that f is necessarily continuous. Hence, there can be no convex functions that are not also continuous. Homework Equations The Attempt at a Solution F is continuos if there exist \epsilon >0 and \delta>0 such that |x-y|<...

Homework Statement Assume f is a continuous real function defined in (a,b) such that f(\frac{x+y}{2})<=\frac{f(x)+f(y)}{2} for all x,y in(a,b) then f is convex. Homework Equations The Attempt at a Solution my attempt is to suppose there are 3 points p<r<q such that f(r)>g(r)...

In a conversing lens, if the object is not within the focal point, then the magnification is "-". But in the case where the object is placed in the focal point, then the magnification is "+"?

Homework Statement A converging lens (convex lens) creates an image that is 2 times the size of the object. The object is placed: Homework Equations -di/do = hi/ho 1/f = 1/di + 1/do The Attempt at a Solution I thought the answer was that the object is place two focal lengths...

Hello! I'm trying to find some information about my problem but it doesn't seem very easy. 1 - I have a convex polyhedron defined as the intersection of several half-planes. 2- Now I would like to obtain a triangularization of the polyhedron surface in the best way. Can anyone indicate me...

Can anyone explain to me the procedure that one would follow to you find the focal length of a concave lens using a convex lens? Thanks.

Hi all, if light was to go straight through a convex lens would it come out straight or inverted to a point? also if light was to go through the same lens but goes through going inwards how would the light be refracted?

Could anyone comment on the convexity of f(x,y) = (x^2) * exp(y) ... i.e. x square into e to the power y. I did try to find Hessian of the same and the value I get is : Hessian(x,y) = -2 * x^2 * exp(2y)... which looks <= 0 for all x and y. I assume this should imply f(x,y) is...

So I got a lab to plan and design an experiment to determine the focal length of a convex lens and involve the use of lens eq. and by means of plotting a graph...I have a basic rundown of what needs to be done and all but I am somewhat in a dilemma i don't have any access to any of the apparatus...

I'm really bad at physics and am quite lost on a homework assignment of mine. Any help that I can get would be fantastic, thanks. Homework Statement A concave mirror has a radius of curvature of 60 cm. Calculate the image position and magnification of an object placed in front of the...

Show the following properties of convex hull: (a) Co(CoA) = Co(A) (b) Co(AUB) \supseteqCo(A) U Co(B) (c) If A\subseteqB then Co(AUB)=Co(B) (d) If A\subseteqB then Co(A)\subseteqCo(B) The definition of a convex hull is a set of points A is the minimum convex set containing A. (c) is quite...

Homework Statement Let U be a non-empty, convex, open subset of R^2. Prove that U is homeomorphic to R^2. Hint: First prove that the intersection of a line in R^2 with U (if non-empty) is homeomorphic to an open interval in R^1. Then use radial projections.Homework Equations We just have the...

[SOLVED] Seperation of a Point and Convex Set Homework Statement Let C be a closed convex set and let r be a point not in C. It is a fact that there is a point p in C with |r - p| l<= |r - q| for all q in C. Let L be the perpendicular bisector of the line segment from r to p. Show that no...

Hello, I am interested in the average behaviour of the log of a function. I know the average of the function over the range of interest: F = \frac{1}{(b-a)} \int_a^b f(x) dx. I also know that f(x) is convex and bounded from below by 1. I want to know the average \frac{1}{(b-a)}...

[SOLVED] Little bit of convex analysis on a Hilbert space Homework Statement Let H be a Hilbert space over R and f:H-->R a function that is bounded below, convex and lower semi continuous (i.e., f(x) \leq \liminf_{y\rightarrow x}f(y) for all x in H). (a) For all x in H and lambda>0, show that...

Problem 1: A thin hollow glass sphere has a radius of 1 m. A coin is placed at the bottom of the glass sphere. 2.09 metre cube of a liquid of refractive index 1.5 is poured into the glass shpere. A person is viewing the object vertically. What is the apparent depth of the coin? Im not sure...

Homework Statement How do I find the relationship of magnification to the graph of "Object Distance vs. Image Distance" or the graph of "Inverse Object Distance vs. Inverse Image Distance" for data points collected from a light box and a convex lens? Basically for the lab I used a light...

This problem was suggested by Gokul43201, based on this year's Putnam A2. Suppose that K is a convex set in \mathbb{R}^2 which is contained in the region bounded by the graphs of the hyperbolas xy=1, xy=-1 (so the set is in the inner + shaped region which contains the origin also). What is...

Homework Statement Let O be an internal point of a convex quaddrilateral PQRS whose area is A. Prove that, if 2A = OP^2 + OQ^2 + OR^2 + OS^2, then PQRS is a square with O as its centre Homework Equations The Attempt at a Solution I have no idea where to start, except that I...

[SOLVED] Real analysis - show convex functions are left &amp; right differentiable Homework Statement Let f:R-->R be convex. Show f admits in every point a left derivative and a right derivative. Homework Equations A function f:R-->R is convex if x1 < x < x2 implies f(x)\leq...

Looking for an algebraic proof that a convex quadrilateral has intersecting diagonals So I'm trying to find an algebraic proof that the diagonals of a convex quadrilateral intersect because I'm working on a proof of a generalization of this idea into higher dimensions and I really have no idea...

A spherical mirror is polished on both sides. When used as a convex mirror, the magnification is +1/4. What is the magnification when used as a concave mirror, the object remaining the same distance from the mirror? I started with: mconvex = 1/4 mconcave = ? doconvex = doconcave...

First, I wonder whether I can put the post here... Given X=[0,1]^2 a(x)={y in X:||y-x||>=1/4} b(x)is the convex hull of a(x). Identify the set of fixed points. My answer is 3/4>=x>=1/4, 3/4>=y>=1/4, but I am not sure... What if we have a(x)={y in X:||y-x||>=1/2}? (My answer is...

X=[0,1]^2 a(x)={y in X:||y-x||>=1/4} b(x)is the convex hull of a(x). Identify the set of fixed points. My answer is 3/4>=x>=1/4, 3/4>=y>=1/4, but I am not sure... Thanks.

Let R be a convex region symmetrical about the origin with area greater than 4. Show that R must contain a lattice point different from the origin. This is the 2-D case of Minkowski's theorem, right ? How about the n-dimensional version ? The n-dimensional version is : Given a convex...