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A pond with a total depth (ice + water) of 3.25 $\mathrm{m}$ is covered by a transparent layer of ice, with a thickness of 0.38 $\mathrm{m} .$ Find the timerequired for light to travel vertically from the surface of the ice tothe bottom of the pond.

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Physics 103

Chapter 26

Geometrical Optics

Wave Optics

Hope College

University of Winnipeg

McMaster University

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all right. So for this problem in the pond of total depths of 3.25 meters, that has a layer of ice on top of it of 0.38 meters. And that means that the water underneath that layer of ice must have a depth of 2.87 meters. And we're wondering if a ray of light comes vertically down through the water. How much time does it take to get from the surface of the ice, the top of the surface of the ice to the bottom of the pond and whether we're figure out was willing to take the time that it takes to get through the ice and at the time it takes to get through the water, those time will be different because the light is gonna have a different velocity of the ice Senators in the water. So we'll say the time it takes to get through the ice. This is gonna be the distance that has to travel 0.38 meters, divided by its velocity. How do we find the velocity of light within the ice? We're gonna use the lights index of refraction where the index of a fraction of ice is gonna be equal to the speed of light divided by the velocity of light within the ice. So you can solve this equation for the velocity of light from the ice. We're just gonna be equal to the speed of light if I buy the index of refraction. So if we plug this into our equation here once a 0.38 divided by the fraction of the speed of light, which is three times 10 to the eighth over the index of refraction ice is 1.31 If we do our math correctly here, this should give us an answer off 1.7 nanoseconds. Now, if you go through the same exact process to find the time it takes, the lights travel through the water. Where is the time it takes for the light travel from water. So we're gonna be equal to our displacement 2 27 meters divided by the velocity of late. It's in the water. The velocity of light within the water is gonna be equal to speed of light. Bye bye. The index of refraction of water. We're gonna do the same output outbreak manipulation as we did for the ice index of refraction. We're in a plug it into our equation here for safety, said W. It's gonna be equal to 2.7 divided by three times 10 to the eighth over 1.3 three now, because that is the index of refraction, of water and every door math correctly here. This should give us an answer of 12 point seven nanoseconds. Now, in order to find the total time that the light had to take in order to travel from the surface of the ice to the bottom of the pond, they said, we have to add the times that it took to travel through the ice and the water together. So what to say t survive Plus TCW, it's gonna be equal to 12.7 plus 1.7, which is going to give us an answer of 14.4 nanoseconds

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