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?

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Mergus Mergus · Answer 1 · 2019-08-27T06:56:16+02:00

Answer:

Refractive index of unknown liquid = 1.56

Explanation:

Using Snell's law as:

[tex]n_i\times {sin\theta_i}={n_r}\times{sin\theta_r}[/tex]

Where,

[tex]{\theta_i}[/tex] is the angle of incidence ( 65.0° )

[tex]{\theta_r}[/tex] is the angle of refraction ( 53.0° )

[tex]{n_r}[/tex] is the refractive index of the refraction medium (unknown liquid, n=?)

[tex]{n_i}[/tex] is the refractive index of the incidence medium (oil, n=1.38)

Hence,

[tex]1.38\times {sin65.0^0}={n_r}\times{sin53.0^0}[/tex]

Solving for [tex]{n_r}[/tex],

Refractive index of unknown liquid = 1.56