A tank holds a layer of oil, 1.58 m thick, which floats on a layer of syrup that

Question

A tank holds a layer of oil, 1.58 m thick, which floats on a layer of syrup that is 0.66 m thick. Both liquids are clear and do not intermix. A ray, which originates at the bottom of the tank on a vertical axis, crosses the oil-syrup interface at a point 0.90 m from the axis. The ray continues and arrives at the oil-air interface, 2.00 m from the axis and at the critical angle. In the figure, the index of refraction of the syrup is closest to:

A) 1.37 B) 1.24 C) 1.17 D) 1.52 E) 1.66

*The correct answer to this question is B.) 1.24, but every time I post it people get the wrong answer. Please do the problem correctly and help explain why the answer is 1.24. Thanks!*

Explanation / Answer

using snell's law we have n1*sin(theta1) = n2*sin(theta2)-----------------------------(1) for the syrup oil layer interface. and n2*sin(theta2) = 1*sin(90)-------------------------------(2) => n2 = 1/sin(theta2). => n2 = 1.75 now from (1) we have n1 = 1/sin(theta1) => n1 = 1.24007

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