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One method of determining the refractive index of a transparent solid is to measure the critical angle when the solid is in air. If #θ_c# is found to be 40.7°, what is the index of refraction of the solid?

Answer 1

The citical angle #theta_c# of a medium denser than air is the angle of incident of a ray in that medium refracted in air for which the angle of refraction becomes #90^@#

So refractive index #mu# of the medium w.r to air will be

#mu=sin("Angle in rarer medium")/(sin("Angle in the deser medium"# #=(sin90/sintheta_c) =(1/sin40.7^@)~~1.53#

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Answer 2

Axel Acevedo

Use the formula ( n = \frac{1}{\sin(\theta_c)} ) to find the refractive index.

( n = \frac{1}{\sin(40.7^\circ)} )

( n \approx 1.53 )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.