Alayer 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?

Refractive index of unknown liquid = 1.56

Explanation:

Using Snell's law as:

Where,  

 is the angle of incidence  ( 65.0° )

is the angle of refraction  ( 53.0° )

is the refractive index of the refraction medium  (unknown liquid, n=?)

is the refractive index of the incidence medium (oil, n=1.38)

Hence,  

Solving for ,

Refractive index of unknown liquid = 1.56

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.