Convex Definition and 283 Threads

Hello! I'm stuck on this problem... A thin flat plate of partially reflecting glass is a distance (b) from a convex mirror. A point source of light (S) is placed a distance (a) in front of the plate so that its image in the partially reflecting plate coincides with its image in the mirror...

Homework Statement Given D a a closed convex in R4 which consists of points (1,x_2,x_3,x_4) which satisfies that that 0\leq x_2,0 \leq x_3 and that x_2^2 - x_3 \leq 0 The Attempt at a Solution Then to show that either the point a: = (1,-1,0,1) or b:=(1,0,0,-1) is part of the...

Rays from the sun subtend an angle theta (in radians) at the pole of a convex mirror (in radians) at the pole of a mirror of focal length f. If the diameter of the sun is D ,then diameter of the image of the sun formed by the mirror is: (a) f theta (b) 2 f theta (c) 6 f theta (d) none...

Homework Statement A combination of two thin convex lenses of equal focal lengths,is kept separated along the optic axes by a distance of 20 cm between them.The combination behaves as a lens system of infinite focal length.If an object is kept at 10 cm from the first lens,its image...

An object and a screen are fixed at a distance of 80cm apart and a convex lens forms a real image of the object on the screen. When the lens is moved along its axis a distance of 16cm, a real image of the object is again formed on the screen. Find the focal length of the lens and the...

Convex mirror. PLEASE HELP! Homework Statement An object 30 cm tall is placed 20 cm in front of a convex mirror. If the height of the image is +10 cm, find the focal length of the mirror. Homework Equations The Attempt at a Solution I know to use 1/f = -(Image distance from V)...

Homework Statement Why do fish appear bigger when you look at them through a fishbowl? Homework Equations The Attempt at a Solution because objects in water appear bigger than they actually are? this has to do with change in the medium from air n1 to water n2?

Homework Statement An object is placed 6 metres from a convex lens of focal length 30cm. A concave lens of focal length 5cm is then placed 20 cm from the concave lens, on the side distant from the object. Determine the position, magnification and nature of the final image formed (to solve...

Can someone tell me if my logic in answering the following questions is ok: 1. Suppose that f(x) and g(x) are convex on (a,b). Show that the functions h(x)=max[f(x), g(x)] is also convex on (a,b). -I said that since f and g are convex their second derivatives are not equal to zero in (a,b)...

A real object is placed at the zero end of a meterstick. A large concave mirror at the 100 cm end of the meterstuck forms an image of the object at the 82.4 cm position. A small convex mirror placed at the 20 cm pisition form a final image at the 6.3 cm point. What is the radius of curvature of...

let f:(a,b)-> a differentiable function, f is a convex function iff for every x in (a,b) the tangent line to f's graph in x is below f. i tried it this way: suppose f is a convex function, then for every 0<d<1 and every s,t in (a,b), f(dt+(1-d)s)<=df(t)+(1-d)f(s), now the tangent line in...

# Diameter of a Plano-convex lens is 6 cm and the thickness at the center is 3 mm. If the speed of light in the material of the lens is 2 x 10^8 m/sec, what is the focal length of the lens? I solved it in the following way: Let R be the radius of curvature of the convex surface. Given that AB...

# A convex lens of focal length 10 cm forms a real image of an object placed at a distance of 20 cm from it. Midway between the convex lens and the position of the image a thin concave lens is introduced. The image formed now is at a distance of 5 cm away from the earlier position. What is the...

I have to complete a problem about locating an image for a convex lens but I'm having trouble with it. I tried it out, but I can't complete it. Can someone help please? Locate the image for the convex lens below. Use any two rays to do so. Give the characteristics of the image. I'm having...

Sir, I am posting these questions for the 3rd time as you didn't respond. Please respond. 1)A convergent beam of light is incident on a convex mirror of radius of curvature 60 cm as shown in figure. What is the nature and position of the image formed by it? I solved it in the following way...

Sir, 1) A man 2 meters tall stands 5 meters in front of a large vertical plane mirror. What is the angle subtended by his image in the mirror at his eye? I solved it in the following way: Let AB represent the man and CE represent the mirror mounted on the wall.Here I am assuming that the...

In my econ homework, I was asked to prove that: A set C is convex iff a C + b C = (a+b) C for all nonnegative scalars a and b. All that I'm given is that the definition of a convex set is, for x,y elements of a convex set C: (1-a) x + a y exists in C, for 0<a<1 My thoughts were to first...

Hello everyone, I seem to be getting all the mirrors right that where concave but now i have a convex one and it doesn't seem to be working when im' finding the image distance and magnification/properties. Here is the problem: Heres my work: both the i and the m where wrong, i also tried...

Hello, I am a little confused on how to prove these half planes are convex, and my book does not actually show an example. ---------- So here is a problem, my book briefly talks about it: Show that the plane 2x - 3y >= 6 is convex. So if we let A = (2,-3), and X = (x,y), then we can write...

Hi, Let C_1 and C_2 be nonempty convex sets and suppose C_1 \cap C_2 \neq \emptyset . I read a text that claims \textup{cl}(C_1 \cap C_2) \subset \textup{cl}(C_1) \cap \textup{cl}(C_2) since C_1 \cap C_2 \subset \textup{cl}(C_1) \cap \textup{cl}(C_2). I am able to prove the latter, but I...

If A and B are nonempty convex sets. And C = A + B. How to prove int(C) = int(A) + int(B)?

I have an object that is surrounded by air and sits a distance U=30 from a convex surface. The convex surface has a radius of R=5. The index of refraction of the refracting media is n=1.33. How do I determine the magnification of the object?

I would like to be sure in the following, not prove it, just have it confirmed... If a function f is convex, then it has 1.) only one maximum and no minimum 2.) only one minimum and no maximum infinity and -infinity are not included.

Hello! I've got some questions concerning convex sets. We've had a lecture about convex sets this week, and got a some basic problems to solve. I think I can't use the material in the lecture to solve the problem. I'm just not sure about whether I fully understand the concept and can use it...

A convex lens is placed on a flat glass plate and illuminated from above with monochromatic red light. When viewed from above, concentric bans of red and dark are observed. What does one observe at the exact center of the lens where the lens and the glass plate are in direct contact.

An object that is 31 cm in front of a convex mirror has an image located 20 cm behind the mirror. How far behind the mirror is the image located when the object is 19 cm in front of the mirror? For this problem, I know I have to use the mirror equation but I keep getting the wrong...

Convex mirrors are being used to monitor the aisles in a store. The mirrors have a radius of curvature of 4 m. What is the image distance if a customer is 20 m in front of the mirror? From using the mirror equation, i came up with an answer of 1.82m but when i submitted it for webassign, it...

Lez prob hi, An object is moving with velocity 0.01 m/s towards a convex lens of focal length 0.3m. Find the magnitude of rate of separation of image from the lens when the object is at a distance of 0.4 m from the lens. Also calculate the magnitude of the rate of change of the lateral...

I know that magnification of a single convex mirror is always positive (that is, greater than 0) based on f<0, but does the size of the magnification depend on the magnitude of the object distance?

If you have a convex mirror, and you point a light at it horizontally, does the light always reflect through the focal point? (the point halfway on the line connecting border and the center, parallel to the light's initial path) I remember learning this, but I think of a mirror in the shape...

The rear view on the passenger side of late model cars warn us theat objects may be closer than they appear. I think the mirror used is convex. But why is that type of mirror selected? thanks joe

Problem 8. A concave amkeup mirror is designed so that a person 28.7 cm in front of it sees an upright image ata distance of 51.1 cm behind the mirror. What is the radius of curvature of the mirror? Answer in cm. Note: What is the radius of curvature formula? Problem 19. A convex...

Hi, I know that when entering a convex lens, light rays bend towards the center due to refraction. But why do they keep bending towards the center once they exit the lens? Should'nt they now bend away from the lens because they are going from a denser to a rarer medium? Thanks SK