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Ptolemy's Optics One of the many works published by the Greek astronomer Ptolemy (A.D. ca. $100-170 )$ was Optics. In this book Ptolemy reports the results of refraction experiments he conductedby observing light passing from air into water. His results are asfollows: angle of incidence $=10.0^{\circ},$ angle of refraction $=8.00^{\circ}$ angle of incidence $=20.0^{\circ}$ , angle of refraction $=15.5^{\circ} .$ Find thepercentage error in the calculated index of refraction of water foreach of Ptolemy's measurements.

$6.2 \%$$3.8 \%$

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

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Yeah, given the results of refraction experiments that told me conducted, uh, when he observed the line passing from and to water. So we want to calculate the percentage error in the calculated index of refraction of water. Okay, for each of the measurements. Okay. So we know that the refractive indexes sign data I divided by sine data are okay, so just calculate for each, uh, role of data. And so for the first role, you get 1.248 and then for the second row, you calculate you get 1.280 okay? And we know that, uh, the mhm. Okay, so the effective index of water is 1.3 tree, and then we can calculate percentage era by using, uh, and water minus n divide by and water, then multiply by 100%. Okay, so if you do that for the first roll, the the error, the percentage error is 6.2% and then the second roll, the error percentage error is 3.8% mhm. So the answer for this question? Yes, in this, uh, box. And that's all

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