Question

A layer of oil (n = 1.38) floats on an unknown liquid. A ray of light originates in the oil and passes into the unknown liquid. The angle of incidence is 65.0°, and the angle of refraction is 53.0°. What is the index of refraction of the unknown liquid?

Answer 1

Answer:

Refractive index of unknown liquid = 1.56

Explanation:

Using Snell's law as:

$n_i\times {sin\theta_i}={n_r}\times{sin\theta_r}$

Where,  

${\theta_i}$  is the angle of incidence  ( 65.0° )

${\theta_r}$ is the angle of refraction  ( 53.0° )

${n_r}$ is the refractive index of the refraction medium  (unknown liquid, n=?)

${n_i}$ is the refractive index of the incidence medium (oil, n=1.38)

Hence,  

$1.38\times {sin65.0^0}={n_r}\times{sin53.0^0}$

Solving for ${n_r}$,

Refractive index of unknown liquid = 1.56