A scientist is carrying out an experiment to determine the index of refraction for a partially reflective material. To do this, he aims a narrow beam of light at a sample of this material, which has a smooth surface. He then varies the angle of incidence. (The incident beam is traveling through air.)
The light that gets reflected by the sample is completely polarized when the angle of incidence is 46.5°.
(a) What index of refraction describes the material?
n =
(b) If some of the incident light (at θi = 46.5°) enters the material and travels below the surface, what is the angle of refraction (in degrees)?

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whitneytr12 whitneytr12 · Answer 1 · 2020-08-06T03:45:08+02:00

Answer:

a) 1.05

b) 43.6°

Explanation:

a) The index refraction that describes the material can be found using Brewster's law:

[tex] \theta_{1} = arctan(\frac{n_{2}}{n_{1}}) [/tex]

where:

n₁ is the refractive index of the initial medium through which the light propagates (air) = 1

n₂ is the index of the material=?

θ₁ = 46.5°

[tex] n_{2} = n_{1}tan(\theta_{1}) = tan(46.5) = 1.05 [/tex]

Hence, the material's index refraction is 1.05.

b) The angle of refraction can be found as follows:

[tex] n_{1}sin(\theta_{1}) = n_{2}sin(\theta_{2}) [/tex]

[tex]sin(\theta_{2}) = \frac{n_{1}sin(\theta_{1})}{n_{2}} = \frac{sin(46.5)}{1.05} = 0.69[/tex]

[tex] \theta_{2} = arcsin(0.69) = 43.6^{\circ} [/tex]

Therefore, the angle of refraction is 43.6°.

I hope it helps you!