A Tank Holds a Layer of Oil, of Thickness $T _ { \mathrm { O } } = 1.65 \mathrm {~m}$

A tank holds a layer of oil, of thickness $T _ { \mathrm { O } } = 1.65 \mathrm {~m}$ , that floats on a layer of syrup of thickness $T _ { \mathrm { S } } =$ $0.830 \mathrm {~m}$ , 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 syrup?

A) $1.54$
B) $1.94$
C) $1.25$
D) $1.75$
E) $1.36$