A tank holds a layer of oil,of thickness T_o = 1.43 m,that floats on a layer of syrup of thickness T_s = 0.640 m,as shown in the figure.Both liquids are clear and do not mix together.A light ray,originating at the bottom of the tank at point P,crosses the oil-syrup interface at a point 0.900 m from the axis.The ray continues and arrives at the oil-air interface,2.00 m to the right of P and at the critical angle.What is the index of refraction of the oil? A)1.64 B)1.62 C)1.60 D)1.66 E)1.68

Question

Quizplus · Accepted Answer

Let's call the index of refraction of the syrup "n". Using Snell's Law, we can find the angle of incidence at the oil-syrup interface:

sin(theta1) = n*sin(theta2)

sin(theta1) = (1.00)*(sin(90 degrees - 41.81 degrees)) = 0.641
sin(theta2) = (n)*(sin(41.81 degrees)) = (0.900/1.43) = 0.629

Thus, n = 1.64.

A Tank Holds a Layer of Oil,of Thickness To =

A Tank Holds a Layer of Oil,of Thickness T_o =