Question

A layer of oil (n = 1.46) floats on an unknown liquid. A ray of light originates in the oil and passes into the unknown liquid. The angle of incidence is 67.0°, and the angle of refraction is 50.0°. What is the index of refraction of the unknown liquid?

Answer 1

1.75

Step-by-step explanation:

refractive index of oil, n1 = 1.46

angle of incidence, i = 67°

angle of refraction, r = 50°

Let the refractive index of unknown liquid is n2.

According to Snell's law

Refractive index of medium 2 with respect to medium 1 = Sin i / Sin r

Here medium 1 is oil and medium 2 is unknown liquid.

`_(1)^(2)\textrm{n}=(n_2)/(n_1)=(Sin i)/(Sin r)`

`(n_2)/(1.46)=(Sin 67^(\circ))/(Sin 50^(\circ))`

`(n_2)/(1.46)=(0.92)/(0.766)`

n2 = 1.75

Thus, the refractive index of unknown liquid is 1.75