Question

A tank holds a 2.38-m thick layer of oil that floats on a 1.24-m thick layer of brine. Both liquids are clear and do not intermix. Point O is at the bottom of the tank, on a vertical axis. The indices of refraction of the oil and the brine are 1.27 and 1.81, respectively. A ray originating at O reaches the brine-oil interface at the critical angle. What is the distance of this point from the axis?

Answer 1

Answer:

1.22m

Explanation:

Since

sinθ  =  refraction-of-the-oil/refraction-of-the-brine =1.27/1.81 = 0.702

θ = $sin^-^1$(0.702)

Hence

Critical angle = θ = 44.58°

tan(θ) = d/1.24

tan(44.58°) = d/1.24

Hence, 0.98 = d/1.24

The distance d = 0.98 x 1.24 = 1.22m