during-a-daytime-football-game-you-notice-that-a-players-reflective-helmet-forms-an-image-of-the-sun

Question

During a daytime football game you notice that a player's reflective helmet forms an image of the Sun 4.8 $\mathrm{cm}$ behind the surface of
the helmet. What is the radius of curvature of the helmet, assuming it to be roughly spherical?

Nick Auwerda · Accepted Answer

question 30 says. During the daytime football game, you noticed that a player&#x27;s reflective helmet forms an image of the sun 4.8 centimeters behind the surface of the helmet. What is the radius of curvature of the helmet, Assuming it to be roughly spherical? Um, this is an interesting problem because the sun is so far away that we assume that it is intimately far away. So our object distance is infinity. And so I have one over infinity plus one over negative 4.8. Now, the reason that image distances negative is because it&#x27;s on the other side of them. Here is the light s O negative. 4.8 equals one over the focal length. No one over infinity is essentially zero. And so that tells me the focal length is actually negative 4.8 centimeters. And so I remember the radius of curvature. The focal length is equal to half negative. Half the reserve coverage here for a con vaccine here. And so I have negative 4.8 equals negative half are and so are is actually 9.6 centimeters

Kyle Godbey · Answer

problem. Eight is a sneakily ass one. If you recall that the radius of curvature is simply two times the focal length. And in this problem, since the rays from the sun or parallel, the image is gonna be at the focal point, which is like I said, half the radius so you can plug in the focal point that is mentioned in the problem. Eighteen, twenty centimeters and you see the radius of curvature is thirty seven point six centimeters.

Christopher Provencher · Answer

okay, In this problem, we have a solar cooker, which is really just a con cave mirror. We have rays from the sun hitting the mirror, deflecting and focusing on a focal point. And we rest to find what the radius of curvature for this mirror must be if we know its focal point. So the focal point given to us is 18.8 centimeters. Must have drawn a little picture. Here&#x27;s our mirror, some con cave mirror. We have rays of light that we seem to be parallel coming at the mirror. And once these race hit the mirror, they deflect and focus on some focal point. This focal point is given to us F 18.8 centimeters. And so we have to find greatest curvature of this spherical reflector. And the relationship is very simple for a spherical sort of, uh, reflector concave mirror. It&#x27;s the case that the radius of curvature are is simply two times the focal length. So the result from Greece curvature is simply 37.6 centimeters. That&#x27;s just a very simple relationship for any con cave mirror. The radius curvature of that mirror is equal to twice the focal life. So if you know the focal length multiplied by two, you got the answer and that&#x27;s it.

Zachary Warner · Answer

So we&#x27;re given to situations When an individual is looking into a hubcap for one situation, he&#x27;s looking at the hubcap and he sees his face 30 centimeters in back of it, so Q one would be equal to 30 centimeters. And then in the second, when he sees his image 10 centimetres in the back of the hubcap. So cute too, is equal to 10 centimetres. Okay, so now, using that, it wants us to find for part a the distance the individuals faces away from the hubcap and for part B wants us to find the magnitude of the radius of the hubcap. Okay, So to do that, we&#x27;re going to consider the fact that when the, uh when the hubcap is convex in the first part, it&#x27;ll have a specific relationship to the radius and the one that kong Uh, when the, uh, hubcap is Khan Cave in the second part, it will have another relationship to the radius as well as the image distance. So for the first part for the con cave part, uh, won over Negative kyu won because he says the images in the back of the hubcap plus one over the distance to the object or the person&#x27;s face is equal to two divided by the radius. So that&#x27;s for the first part, where the con convex part now for the Con Cave Park won over minus Q two again minus because he sees the image in the back of the hubcap plus one over the distance to the individual&#x27;s face. P. It&#x27;s the same in both cases is equal to two over our. So now we have two equations in two unknowns. Um, excuse me. So for the for the first part for the convex since it&#x27;s convex, the radius is negative. Here, we can consider that to be a negative radius. Okay, so we can add these two equations together. So what we end up with is one over negative kyu won plus won over P plus won over negative que tube plus one over P is equal to zero. Right, because it&#x27;s, uh, two overnegative are plus two over are so that&#x27;s equal to zero. Or, in other words, trying to isolate P to overpay is equal to is equal to one over kyu won, plus won over que tu or another word. Solving for P P is equal to two times Kyu won times Cute too divided by Q one plus que tu oh so plugging in the values for Q. Wanting que Tu into this equation, we find that the distance the person&#x27;s faces away from the hubcap is 15 centimeters looking box that in as our solution for part A. So let&#x27;s go ahead and indicate this is part of a now part B wants us to find the magnification. So to find the magnification, we can simply plug in the value for pee into either the equation for the con Cave or the convex. So it&#x27;s either into this equation, which I&#x27;m marking by a Red Star or into this equation. So I&#x27;m gonna go ahead and pick the 1st 1 the one on the left. There, let&#x27;s get a new page going. So we have be, um so, for B, we have, uh, two over negative Are is equal to won over P No. Once we got look a little nicer, won over p minus one over kyu won, and we now know P so we can go ahead and sell for our We find that the race of curvature are is equal to two times Kyu won Times P divided by Q one minus p so P is 15 centimeters. Q one is 30 centimeters. Plugging those values into this equation, we find that the radius of curvature is equal to 60 centimetres. When we can box that it is the solution for part B.

Katie Mcalpine · Answer

So in this question, we&#x27;re told that a solar cooker uses a conch aid mirror Point of the sun and we know that focuses 18 son Immune Aires. So we can say off is 18 c. M. And we want to know what the radius of curvature is. And for that, you can use the, um, simple formula F is equal to our over to, so our is to, uh so are is equal to 36 centimeters.

Mayukh Banik · Answer

we have magnification equals. I have the image of the height of the object with equals diameter of the image of a diameter of the object with equals negative You over b So we have a diameter of the image equals diameter of the object times over Be the negative sign requests negative, you know, and you is given by out, over to and we have be down below substituting these values. You got these you times the radius with 17 far D you don&#x27;t need dying&#x27;s are these definitely don&#x27;t divided by to be and he&#x27;s C 85 1000. You don&#x27;t go from here. The evens diameter comes out to be negative. Ziegel for cedar, for by 2 m it was 44 and five to centimeter with negative sign. So there&#x27;s a large one image. We large one image with diameter being 4.52 said

Problem

A convex mirror on the passenger side of a car pr…

Problem 30 Easy Difficulty

During a daytime football game you notice that a player's reflective helmet forms an image of the Sun 4.8 $\mathrm{cm}$ behind the surface of
the helmet. What is the radius of curvature of the helmet, assuming it to be roughly spherical?

Answer

9.6 $\mathrm{cm}$

Related Courses

Physics

Related Topics

Discussion

Top Physics 103 Educators

Christina K.

Liev B.

Aspen F.

Jared E.

Physics 103 Courses

Wave Optics - Intro

Multiple Aperture Interference - Overview

Recommended Videos

Watch More Solved Questions in Chapter 26

Video Transcript

James S. Walker

Physics

Christina K.

Liev B.

Aspen F.

Jared E.

Wave Optics - Intro

Multiple Aperture Interference - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

9.6 $\mathrm{cm}$

Physics

Christina K.

Liev B.

Aspen F.

Jared E.

Wave Optics - Intro

Multiple Aperture Interference - Overview

James S. WalkerPhysics

Christina K.

Liev B.

Aspen F.

Jared E.

James S. Walker

Physics