2 (18 points). A tank holds a layer of oil, of thickness To = 1.65 m, that float

Question

2 (18 points). A tank holds a layer of oil, of thickness To = 1.65 m, that floats on a layer of syrup of thickness Ts 0.830 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 syrup? air 200 m oil 0.90 m syrup T,I

Explanation / Answer

angle of incidence at oil-air inreface, i = tan^-1(1.1/0.9)

= 50.7 degrees

so, refractive index of oil, n_oil = 1/sin(50.7)

= 1.29

angle of incidence at syrup-oil interface, i = tan^-1(0.9/0.83)

= 47.3 degrees

angle of refraction, r = 50.7 degrees

now use Snell's law

sin(i)/sin(r) = n_oil/n_syrup

==> n_syrup = n_oil*sin(r)/sin(i)

= 1.29*sin(50.7)/sin(47.3)

= 1.36 <<<<<<<<<------------------Answer

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