A Tank Holds a Layer of Oil, of Thickness $T _ { O } = 1.43 \mathrm {~m}$

Multiple Choice

A tank holds a layer of oil, of thickness $T _ { O } = 1.43 \mathrm {~m}$ , that floats on a layer of syrup of thickness $T _ { \mathrm { S } } =$ $0.640 \mathrm {~m}$ , 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 $0.900 \mathrm {~m}$ from the axis. The ray continues and arrives at the oil-air interface, $2.00 \mathrm {~m}$ to the right of $P$ and at the critical angle. What is the index of refraction of the oil?

A) $1.64$
B) $1.66$
C) $1.68$
D) $1.60$
E) $1.62$