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Light is refracted as it travels from a point A in medium 1 to a point $\mathrm{B}$ in medium $2 .$ If the index of refraction is 1.33 in medium1 and 1.51 in medium $2,$ how much time does it take for light to gofrom $\mathrm{A}$ to $\mathrm{B},$ assuming it travels 331 $\mathrm{cm}$ in medium 1 and 151 $\mathrm{cm}$ inmedium 2 ?

22.3 $\mathrm{ns}$

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

Rutgers, The State University of New Jersey

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University of Winnipeg

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all right. So this problem we have a ray of light is traveling through two mediums. It travels 3.31 years through the first medium that has an index of a fraction of 1.33 and then it travels 1.51 meters through the second medium, which has an index of refraction of 1.51 And the question that we're trying to answer is how much time does it take to travel through these two mediums and across these two distances? So, 1st 1 to say that the time it takes to travel through the first medium, it's gonna be equal to the distance. It travels to the first medium divided by the velocity of light within the first medium. We know the distance in the first medium is 3.31 meters. We don't know the velocity of light from first meeting how we can find it. We can say that the index of refraction of light within the first medium is simply equal in speed of light, divided by the velocity of light within the first medium. So the velocity of light within the first media must be equal to the speed of light divided by the index of refraction. Now we know the speed of light. We know the index of refraction so you can plug us into our equation. Would say this is equal to see over. And one would say finally, that TV one is gonna be equal to 3.31 divided by the speed of light which is three times 10 to the eighth all over the of refraction and one which is 1.33 If you plug all this correctly into our calculator, we should get an answer of 14 points. Seven nanoseconds now do the same thing for T to I would say that time it takes for the light travels. Second medium to be equal to the distance has to travel divided by the velocity is traveling at. So the distance a has travel is 1.51 divided by we do the same manipulation with the index of refraction. It's in the second medium. In order to find that it's equal to see over and to be equal to 51 fired by three times 10 to the eighth over and to which is 1.5. Now, if we do this correctly in our calculator, we should get an answer of 7.69 seconds. And to find the total time we simply adding two times together, we say t one plus t two. It's gonna be Teoh a total of 22.3 nanoseconds. That's the answer.

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