A transparent solid cylindrical rod has a refractive index

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A transparent solid cylindrical rod has a refractive

index u and is surrounded by air. A light ray isincident at mid point of one end of rod as shown.If 0 is angle of incident then u for grazing a lightalong the walls is(sin theta =1/√31) 2/√3(2) 13) 1\√3(4) √3​

Answered by admin @


Answer:

Refractive index of the material is given as

\mu = \frac{2}{\sqrt3}

Explanation:

If light is grazing along the walls then we have

\mu sin\theta_c = 1 sin 90

now we have

sin\theta_c = \frac{1}{\mu}

now at the entering face of the cylinder

1 sin\theta = \mu sin(90 - \theta_c)

sin\theta = \mu cos\theta_c

sin\theta = \mu\sqrt{1 - (\frac{1}{\mu})^2}

sin\theta = \sqrt{\mu^2 - 1}

as we know that

sin\theta = \frac{1}{\sqrt3}

so we have

\frac{1}{\sqrt3} = \sqrt{\mu^2 - 1}

\frac{1}{3} + 1 = \mu^2

\mu = \frac{2}{\sqrt3}

#Learn

Topic : Total internal reflection

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