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$\bullet \mathrm{A}$ zoo aquarium has transparent walls, so that spectators on both sides of it can watch the fish. The aquarium is 5.50 $\mathrm{m}$ across, and the spectators on both sides of it are standing 1.20 $\mathrm{m}$ from the wall. How far away do spectators on one side of theaquarium appear to those on the other side? (Ignore any refraction in the walls of the aquarium.)

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6.53 mThe apparent distance traveled inside the medium will always be less than the distance traveled in air.

Physics 102 Electricity and Magnetism

Physics 103

Chapter 24

Geometric Optics

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

University of Washington

Simon Fraser University

Lectures

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.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

01:45

The back wall of a home aq…

04:22

You're visiting an aq…

03:51

A fish swims 20 cm fro…

02:01

04:09

A large aquarium has porth…

07:16

03:52

A goldfish is swimming at …

01:54

01:46

A fish in a flat-sided aqu…

01:56

04:21

To a fish in an aquarium, …

03:12

An outdoor circular fish p…

A scuba diver stands at th…

Okay, so for this problem, we want to consider that, uh, we have this aquarium and it has a certain length and then their viewers on both sides. And then we want to figure out what the perceived distances between the viewers. And so, um, basically what we want to do is we want to figure out how a sub questions. One answer is how long the tank appears to either viewer. And then we can add that to the distance between a few hours. Yeah. Pause vis. Having some trouble with my tablet. Okay, great. My tablets working. So let's answer the question of finding the apparent depth by considering, um, let's say you could think of it as considering on object. See here and you're here and you want to figure out where the object appears. Relative, um, where Yeah, we're the image of this object at the other end would appear to get the effective length of the tank. So the hoops So the image position is at 5.5 meters, so ass is equal to 5.5 and the index of refraction where the object is's 1.33 because it's in water the dark down here. And, um, if the one we want to find us prime, where the index of refraction is air, so that's and B equals one, and then the equation we would use to do this is theater Asian that most generally describes having a, um, curve surface leading an index of refract on object with some difference in an index of refraction. Um I mean, yeah, I wish there was a nice name for this equation, but it's 24.11 or if there is one, I wish I knew it. Um, but yeah, I'm just pulling up the book now so I can copy up. They don't have it memorized. So it's 24.11 um, so it's on a over US plus and be divided by s prime. So and then it's gonna be n b minus and a over our But then the if this is a flat plane than the you could think of the curvature radius is being infinite. So that sets the right hand side to zero. So that becomes the case. And then we want to solve for us prime. If we bring this over and cross multiply then we get the bus prime equals S and B over and a So, um, we want to take 5.5 and divide it by 1.33 and we obtain that. That's equal to find Dr. So that's 4.51 I think there's three sync fix on the 5.5. Okay, that looks kind of funny. You go ahead and fix that. So that's five planes 514.51 And then we want to add that to this distance where the length doesn't change its size. These two are each 1.2. So I would say that they see each other 4.51 so I'll just call that deice. The distance between them is 4.51 plus two times one point to see if I could get out of my head. So it's 2.4, so that would make the total distance between them a 6.91 meters. Oh,

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