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25 March, 00:18

You can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of 47.3° when submerged in ethanol, which has an index of refraction of 1.361? (b) What would the critical angle be for this substance in air?

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  1. 25 March, 04:20
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    a) 1.851

    b) 32.68°

    Explanation:

    The relation between critical angle and index of refraction is as follows

    Sin C = 1 / μ

    C is critical angle and μ is refractive index.

    Given C = 47.3

    Sin 47.3 = 1 / μ

    0.735 = 1 / μ

    μ = 1 /.735

    = 1.36

    This is with respect to ethanol.

    1.36 = refractive index of material / refractive index of ethanol

    refractive index of material = 1.36 x refractive index of ethanol

    = 1.36 x 1.361 = 1.851

    If critical angle for this substance be A

    Sin A = 1 / 1.851 =.54

    A = 32.68°.
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