Question

A tank holds a layer of oil, 1.95 m thick, which floats on a layer of syrup that is 0.64 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 Figure 23.3a, the index of refraction of the oil is closest to:

Answer 1

This is a really simple question. A lot of unwanted data are given.

Take the tangent of the angle of incidence (a) at the oil-air interface.

We know the opposite side length for that angle is (2-0.9) = 1.1m

The adjacent side = 1.95m

So, tan(a)=1.1/1.95 = 0.56

Hence, a = 29.25 degrees

So, sin(a) = 0.489

Since a is the critical angle for oil-air interface, sin(a) will be the ratio of refractive indices of the materials

sin(a) = n(air) / n(oil)

Since n(air) = 1,

n(oil) = 1/sin(a) = 1/0.489 = 2.04