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A person swimming 0.80 m below the surface of the water in a swimming pool looks at the diving board that is directly overhead and sees the image of the board that is formed by refraction at the surface of the water. This image is a height of 5.20 m above the swimmer. What is the actual height of the diving board above the surface of the water?

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Physics 103

Chapter 34

Geometric Optics

Section 3

Refraction at a Spherical Surface

Reflection and Refraction of Light

Wave Optics

Rutgers, The State University of New Jersey

University of Washington

University of Winnipeg

Lectures

02:51

In physics, wave optics is the study of the behavior of light, or other electromagnetic waves, as they interact with matter. It is a branch of classical optics. While the term "optics" usually refers to the study of light propagation in free space, "wave optics" is used when it is important to take into account the effects of the material the light is traveling through. Wave optics is mostly concerned with the behavior of waves near the boundary between different media. When waves from a single source interact with each other their behavior can be difficult to predict. For example, two waves of the same frequency and wavelength can interfere, leading to a phenomenon known as interference fringes.

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

01:10

A person swimming $0.80 \m…

01:53

$\cdot$ To a person swimmi…

A person swimming $1.00 \m…

00:42

As an aid in understanding…

00:53

A person is swimming $1.0 …

03:37

You're standing in wa…

02:28

A 150-cm-tall diver is sta…

01:50

The path of a diver diving…

03:31

A skin diver is $2.0 \math…

02:17

$\cdot$ A skin diver is 2.…

03:15

A 1.8-m-tall diver is stan…

03:49

A 150 -cm-tall diver is st…

Thanks. Okay, so we're doing Chapter 34. Problem. 19 year. And so this problem says a person swimming 0.8 meters below the surface. And I have this drawing here, so it's strong. This is zero point E meters below the surface of water, and it says it's you're looking at the diving board that is directly overhead, and the person sees an image of the board that is formed by refraction at the surface of the water. This image is a height of 5.2 meters above the swimmer And what is the actual height of the diving board? So I just drew this as to scale er, just to show that there is an image formed on the other side of the surface. So we know the image is negative. Um, but I drew it as the image being closer, but we don't actually know that. So we're gonna have to use our equation to figure out we could use some geometry. But we can also just use our usual sign convention in our lindsay equations to figure this out. So don't take that as meaning. The image is necessarily going to be closer or not. we have not figured that out yet. So But let's go ahead and label where these distances. So this would be our object distance. And this over here s prime will be art image distance. So it tells us that s prime is 5.2 meters or negative 0.2 meters since it's on the same side as the object. Now, when we're talking about the surface of the water here, we can think that has a plane lens, so it has an infinity radius of curvature, which is gonna be important. So now we can plug this into our equation, hurt Lynn's on two different between two different mediums. And what we're left with here is we see that we see that the end of the oh, yeah, We should also mention that this top interfaces detail right in a and this is water down here and in a is one and waters 4/3. So our equation then becomes the A over the object distance. It's not equals, um, plus in water over the image distance. And this should equal in the distant or the difference in these and that should he over the radius of curvature right. Cool. So this is our equation. That's gonna let us figure out what we want. So we're wanting to figure out what this object distances the actual height of diving board above the water. So first, let's plug in our equals infinity, and we should see that the right side goes to zero, Which is good. Simplifies this for us. So now we should have been a over s equals negative in W over s prime. We can then solve this and we should see that s equals negative in A s prime over in. Maybe now we can just easily plug that in. This is negative for thirds. I'm sorry. 4/3 in W, but interviews on the bottom. Right, So we're gonna have to flip that. So this is negative. 3/4 times negative, 5.2. Awesome. And if we play that in in a I just left. That is one right. That's just one. If you plug it in your calculator, we should see the s is 3.9 meters. Cool. So what that means is the object is actually closer than the image. So when you're in the water looking straight up a diving board. The object is closer than it appears. It appears 5.2 meters away, but it's actually only 3.9 meters away from the surface.

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