A block of glass with flat sides is surrounded by air. A ray of light traveling in the glass (refractive index na) is incident on the flat interface with air at the top surface of the block of glass. You observe that no light is refracted into the air if the incident ray in the glass has an angle of incidence (measured relative to the normal to the surface of the glass) greater than 38.1°. What is the refractive index of the glass?

n₂ = 1.62

Explanation:

The refraction of light between two materials is described by the expression

            n₁ sin θ₁ = n₂ sin θ₂

Where index 1 is of the incident material and index 2 the material is refracted.

If the material where it is refracted has a higher refractive index, there is an angle for which the refracted ray is parallel to the interface between the two materials, this phenomenon is called internal total reflection n

          n₁ sin θ₁ = n₂ sin  90

In this case the ray enters the material and does not leave it

Since lightning comes from air n₁ = 1

           n₂ = n₁ / sin θ₂

           n₂ = 1 / sin 38.1

            n₂ = 1 / 0.617

            n₂ = 1.62

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