A tank holds a layer of oil, 1.43 m thick, which floats on a layer of syrup that

Question

A tank holds a layer of oil, 1.43 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:
The picture is here: http://www.chegg.com/homework-help/questions-and-answers/tank-holds-layer-oil-158-m-thick-floats-layer-syrup-066-m-thick-liquids-clear-intermix-ray-q2444317

The correct answer is 1.64

Explanation / Answer

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 = 1.43m

So, tan(a)=1.1/1.43 = 0.77

Hence, a = 37.56 degrees

So, sin(a) = 0.61

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) = 1/0.61 = 1.64...

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.