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The observer in FIGURE $26-65$ is positioned so that the far edge of the bottom of the empty glass (not to scale) is just visible. Whenthe glass is filled to the top with water, the center of the bottom ofthe glass is just visible to the observer. Find the height, $H,$ of theglass, given that its width is $W=5.7 \mathrm{cm} .$

3.3 $\mathrm{cm}$

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

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this question you have given this situation, um, you know, you know, empty glass that the observer is able to see three spot when the glass is empty. And then when the glasses fill with water a same viewing angle, the observer is able to see mm. The center off the bottom of the class. Okay, so we want to find the height off the glass, given that w is 5.7 cm. Okay. Okay. So to do this problem using stands law because, uh, clearly the light rate is reflected. Okay. When? When? When The When the glasses through it. Water. Okay, so So first we need to find So this is our date and go up incidents, and then this is our angle of refraction. Okay, So and snow slaw stays, uh, in air. Scientist one is going through and water. Okay. So I will put end of you scientists to okay. And then we know that the refractive index off heiress one, okay. And then society, the one is equal to n w. Data to. Okay, so from the diagram, um, so the fish, this is data one, This is data one. Okay, So science data one it is equal to on the opposite give up by the hype artiness. So using, uh, Category zero, this is what you get. Square off each square plus w square. So scientific ones w square off each square plus w square and then sign data to using the same idea. Uh, we have I'll be over to Good bye bye. Each square plus B over two square. Then so we can put, uh, we can put this into the above equation. Um, and the view w two h squared plus b over to square. Uh huh. Okay, so the w cancels, and then we are able to, uh uh huh. We can do so. Each square plus w two square is equal to, uh, nw square four, uh, each square plus w square. Okay, so you want to find each so, uh, h square minus? Um, we have NW square or four. Each square minus. Each square is equal to, um n w square over four minus a quarter. Okay. Times w square. He so? And we have, uh, NW square minus four. Each square. Is it? Go through, uh, in W square, minus one. Have you skway case of each is on W square, minus one by NW square minus four. Okay, square roots. Wait, Uh, maybe some algebra era. Oh, yeah. So this is okay. This will be each square minus, uh, and abuse square over for each square. Okay, so you should be flip. Okay. For minus and abuse square for minus and you square. Okay, So you put the refractive index of water 1.33 Uh huh. And so each is equal to 3.3 PM Me. Okay, so this is the answer for this question, and that's all.

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