A beam of light is incident from air on the surface of a liquid. If the angle of incidence is 38.0° and the angle of refraction is 26.5°, fi

Question

A beam of light is incident from air on the surface of a liquid. If the angle of incidence is 38.0° and the angle of refraction is 26.5°, find the critical angle for total internal reflection for the liquid when surrounded by air.

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Cherry 3 mins 2021-07-22T10:00:45+00:00 1 Answers 0 views 0

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    2021-07-22T10:02:43+00:00

    Answer:

    The critical angle for total internal reflection for the liquid when surrounded by air is 46.8 degrees.

    Explanation:

    Given that,

    Angle of incidence, i = 38°

    Angle of refraction, r = 26.5°

    Firstly, we will find the refractive index of the liquid. It can be calculated using Snell’s law as :

    n=\dfrac{\sin i}{\sin r}\\\\n=\dfrac{\sin (38)}{\sin (26.5)}\\\\n=1.37

    The relation between refractive index and critical angle for total internal reflection for the liquid is given by :

    \sin\theta_c=\dfrac{1}{n}\\\\\sin\theta_c=\dfrac{1}{1.37}\\\\\theta_c=46.8^{\circ}

    So, the critical angle for total internal reflection for the liquid when surrounded by air is 46.8 degrees.

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