What is Concave: Definition and 200 Discussions

Homework Statement An object is mirrored in a concave mirror. Construct the image of the object using two rays from the object. (draw in the picture) Homework Equations None needed? The Attempt at a Solution So the upward arrow is the object, f is the focal point I assume. I am to draw two...

Homework Statement My question is similar to this one (https://www.physicsforums.com/threads/metric-function-composed-with-concave-function.566338/), I think. I have a concave function f: [0, \infty) \rightarrow [0, \infty) where f(0) = 0, f(x) > 0, x \neq 0 and I need to show that this...

Why is there excess pressure always on the concave side or surface of the meniscus? In my book it is also written that excess pressure balance the vertical resultant forces due to surface tension. How can a pressure balance a force? My teacher said that shape of meniscus does not depend on...

Homework Statement When a T.rex pursues a jeep in the movie Jurassic Park, we see a reflected image of the T.rex via a side-view mirror, on which is printed the (then darkly humorous) warning: “Objects in mirror are closer than they appear.” Is the mirror flat, convex, or concave? Homework...

Homework Statement A light bulb is placed 10.7 cm in front of a concave mirror. When the concave mirror is replaced by a plane mirror in the same location, the bulb's image moves 4.00 cm closer to the mirror. Calculate the focal length of the concave mirror. I am given: do: 10.7 and 4.00 is...

Homework Statement A diverging thin lens and a concave mirror have focal lengths of equal magnitude. An object is placed (3/2)f from the diverging lens and the mirror is placed a distance 3f on the other side of the lens. Using Gaussian optics, determine the final image of the system after two...

I read that concave mirrors are part of a sphere, and concave mirrors can also be expressed in a parabola equation, but a parabola equation is expressed as #4py=x^2# and a circle as #x^2+y^2=R^2#. So the two can't be the same right? Can someone please explain this? Thank you in advance :)

Homework Statement B) Using the mirror equation, find the image distance. Homework Equations 1/do + 1/di = 1/f The Attempt at a Solution [/B] B) do = 2cm f = 4cm 1/do + 1/di = 1/f 1/di = 1/f - 1/do 1/di = do/f(do) - f/f(do) 1/di = (do-f)/(f*do) di = (f*do)/(do-f) = (4cm * 2cm)/(2cm - 4cm)...

Homework Statement A point object at 15 cm from a concave mirror of radius of curvature 20 cm is made to oscillate along principal axis with amplitude 2 mm. Find the amplitude of its image. Homework Equations Mirror formula : 1/v + 1/u = 1/f Here u=-15 cm , f=-10...

Why is the focal point to the left of a concave lens called the second focal point? Isn't it just a matter of the name? So can't the focal point on the left of the lens be called F1 instead of F2?

Homework Statement Where do you put an object in front of a concave mirror of focal length 10cm to produce an image that is inverted and 2.5 times greater than the object? Homework Equations \frac{1}{f}=\frac{1}{P}+\frac{1}{Q} Where: Q=Image distance from mirror P=Object's...

What effect would a convex (concave) lens have on paraxial rays? For a convex lens, the rays would pass through and converge on the focus on the other side. For a concave lens, the rays would reflect back to the focus on the same side. Is this correct?

Homework Statement x Determine all intervals over which the function f(x)=∫√(1+t^2) dt is concave upward 1 Homework Equations I know concave...

I apologize if this is the wrong forum but I need access to mathematicians who know what's happening with polygonal math. I created an unproven algorithm (or heuristic) back in 1999/2000 for bounding shapes with polygons. It was interesting because it was fast, general for polygons of any...

I'm trying to focus a 3mm diameter laser beam (527nm) to a 0.3mm spot size. According to this online calculator I need a +500mm focal length lens and a -50mm FL lens separated by 450mm. However, in practice this did not produce a focused spot. I'm assuming this calculator has made some...

Homework Statement (a) I hold a flat mirror 22.4 cm in front of my face. There is a freckle on my face 1 mm in diameter. Find the angular size of the freckle on the image of my face as viewed by my eye. (b) Repeat for a concave mirror which has a focal length of 39 cm. (c) What is the...

Homework Statement Find the correct image produced by the concave lens. F is focal length. Homework Equations If an object is placed between F and 2F, the image will be inverted, real, larger and beyond 2F. The Attempt at a Solution I choose the answer A. Is it correct? *Please...

Please show that if f is a continuous concave downward function on [a,b],then the average of the function f is greater than f[(a+b)/2],thank you in advance.

Homework Statement A spherical ball of mass m and radius r rolls without slipping on a rough concave surface of large radius R .It makes small oscillations about the lowest point.Find the time period. Ans : 2∏\sqrt\frac{7(R-r)}{5g} Homework Equations The Attempt at a Solution...

Hey guys, So some friends and I are studying for a test and we came across this question. I've absolutely no idea what the answer is simply because every website I've found only shows parallel rays and a ray going through the centre of the lens. It's incredibly aggravating. Anyway here's the...

Can we see a real image with our naked eye without using a screen to capture image? Also, we all know that virtual image formation in a concave mirror will be always erect. Check out the image below. Spoon here acts as a concave mirror and the image is inverted. Why is it virtual then?

Hello I may well be all wrong about this but I am trying to understand from a microscopic point of view why Entropy is a concave function of internal energy. I found this in the following .pdf: http://physics.technion.ac.il/ckfinder/userfiles/files/avron/thermodynamics_potentials.pdf I...

When you look in spoon from a reasonable distance you see an inverted image of yourself in the mirror. How can you see a real image in the mirror when I thought you saw virtual images in a mirror and real images had to be caught on a screen.

Let g(x)=max_{i=1,...,m} f_{i}(x) where f_{i} are continuous concave functions and let X = \{x: a_{j}^T x \geq b_{j} for j=1,\cdots, k \} be a polytope; M(x) = \{i: f_{i}(x) = g (x) \} and J(x) = \{j: a_{j}^T x = b_{j} \}. We define a "special" point to be a point \hat{x} for...

Homework Statement f(x)=(2x)/((x^2)-25) find concave up and down Homework Equations The Attempt at a Solution I found the second derivative to b -4x((-2x^2)-24) ----------------- ((x^2)-25)^2 i found the only inflection point was x=0 (which was correct) I plugged in values on both the...

A ray of light is coming along the line $y=b$,($b>0$), from the positive direction of the x-axis and strikes a concave mirror whose intersection with the $x-y$ plane is the parabola $y^2 = 4ax$,($a>0$). Find the equation of the reflected ray and show that it passes through the focus of the parabola.

Homework Statement y= (x^2 -7) e^xThe Attempt at a Solution I'm trying to find inflection points by setting the second derivative=0 I found that the derivative is: ##2xe^{x}+x^{2}e^{x}-7e^{x}=0## ##e^{x}[2x+x^{2}-7]=0## Then, the 2nd derivative: ##e^{x}[(x-1)(x+5)]=0##, then the inflection...

Homework Statement On what intervals is the function f(x) = x^4 − 4x^3 both decreasing and concave up? x < 0, 2 < x < 3 x < 3 x < 0, x > 2 x > 0, x < -3 2 < x < 3 Homework Equations The Attempt at a Solution I tried to get the derivative of f(x) to make it greater than 0...

Hi all, I have a question. Suppose f : [ 0, l) \rightarrow ℝ is concave , increasing and continuous where l < ∞ and g : [ 0, l) \rightarrow ℝ is also concave, nondecreasing and continuous on the same interval. Can we claim that f and g intersect finitely many times in this interval (possibly...

Lens problem! Hi guys, When an object is placed in front of a convex lens ( not between Focus and optical centre ), the image formed on the other side should be inverted and real. My question is, with the mentioned placement of the object, will the image be laterally inverted? Further more...

My question is as follows: Does the focal length of a concave lens change when put into a medium such as water? Initially the focal length of the lens is 20 cm in air. Would it get larger or small in water?

So I know these equations 1/f = 1/p + 1/i m = -i/p f: focal length p: object distance from mirror i: image distance from mirror m: magnification Let's say that I have an object in front of a concave or convex mirror with the same |f|. p is much larger than the radius of curvature...

Why is the parabola the most bent, concave, effective mirror? What are some properties of a third order mirror (absolute value of x^3)? There is no uniform focal point. Shouldn't shining a light beam along a normal to the x-axis reflect off of the function multiple times? Then take this to the...

1. Homework Statement f(x)=(2x^3+2x^2-5x-2) / 2(x^(2)-1) f''(x)=(-12x^5-24x^3+36x)/(4x^8-16x^6+24x^4-16x^2+4) Find the intervals where f is concave up. 2. The attempt at a solution (I am having trouble interpreting the results at the end or if I've made a mistake somewhere): Attempt at...

Given two (dependent) random variables X and Y with joint PDF p(x,y) =p(x|y)p(y) =p(y|x)p(x), let H[X] be real-valued concave function of p(x), and H[X|Y] the expectation of H of p(x|y) with respect to p(y). Examples of possible functions H include the entropy of X, or its variance. The...

Homework Statement Suppose the radius of curvature of a concave mirror is 5.0 cm a) Find the object distance that gives an upright image with a magnification of +1.51. Homework Equations 1/Do + 1/Di= 1/f m=-di/do=hi/ho The Attempt at a Solution First i convered all cm...

Let $$f:\mathbb{R}_{+}^2 \rightarrow \mathbb{R}$$ be $$f(x_1,x_2)=x_1^a x_2^b$$ for $$a>0$$ and $$b>0$$ Find restrictions on a>0 and b>0 that ensure that f(x_1,x_2) is concave. I tried solving this by finding the principal minors of the Hessian of this function and making first principal...

Homework Statement A small object is located 32.0cm in front of a concave mirror with a radius of curvature of 40.9cm. Where will the image be formed? Homework Equations tan(θ)=-h/di f=1/2R? The Attempt at a Solution Haven't been able to solve for theta. I'm not sure what...

Homework Statement How do you tell if a spherical refracting surface is convex or concave before drawing a ray diagram? (given the indices of refraction, center of curvature, s, and s') Homework Equations i read this: "A convex surface is one that bulges out in the middle toward the...

Are they the same thing? I know biconcave has R1=negative and R2= positive. edit: Thanks for any help.

I do not expect there to be one answer to this question... it is something which can probably be done several ways. However, I am trying to build a tool for my workshop and would love some insight into the necessary math to make it work. I've pasted a very rough sketch of some of the basic...

Hi, I have been reading about metric spaces and came across an elementary property that I am having difficulty proving. A quick search on these forums and google has also failed. Given a metric space with distance function d, and an increasing, concave function f:\mathbb{R} \rightarrow...

Homework Statement A biconvex symmetrical lens is cut in two halves and placed as shown in figure. if a point object is placed in the left how many images will be formed options - (a) Two images (b) Three images Homework Equations The Attempt at a Solution As I...

A pin AB, 1cm long, is placed at an angle to the principal axis in front of a concave mirror, of focal length 5cm. Point B lies on the principal axis at a distance of 4 cm. Point A is such that the angle ABP is 60°, where P, the pole, is the point where the principal axis intersects the mirror...

A concave lens always forms a virtual image (for a real object), will it always form a real image for a virtual object? (that is, when rays converge on it) If yes, why? If no, why?

Homework Statement Let f be a function from (1,0) to (1,0). Suppose that f is discontinuous. Show that f is not concave. Homework Equations The Attempt at a SolutionLet f:(0,1)-->(0,1). Suppose f is discontinous. Show that it is not concave.I've been working on this problem for over an hour...

Physically/conceptually, I understand why the unit normal vector will always point toward the side of concavity on a curve. It's because the unit normal's direction is the derivative of the unit tangent, and the unit tangent's change in direction is always toward the concave side. But how is...

"real" image from concave mirror Ok so in we are currently doing mirrors and reflections in physics and from what I learned there are 2 types of images: real and virtual. I know that a virtual image is what you see INSIDE the mirror; but what does a real image looks like? I can't find anything...

Homework Statement A science museum has created a huge concave mirror with a focal length of 5 m, and mounted it so that it covers the entire wall at one end of a long hallway. If you stand on a center line painted down the middle of the hallway, you're on the mirror's principal axis. You...