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The speed of light in a media $M_{1}$ and $M_{2}$ are $1.5 \times 10^{8} m / s$ and $2 \times 10^{8} m / s$ respectively. A ray of light enters from medium $M_{1}$ to $M_{2}$ at an incident angle i. If the ray suffers total internal reflection the value of i is

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$i \geq \sin^{- 1} (\frac{4}{3})$

$i \geq \sin^{- 1} (\frac{3}{2})$

$i \leq \sin^{- 1} (\frac{3}{4})$

$i \geq \sin^{- 1} (\frac{3}{4})$

answer is D.

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Detailed Solution

$μ_{1} = \frac{C}{V_{1}} = \frac{3 \times 10^{8}}{1.5 \times 10^{8}} = 2 μ_{2} = \frac{C}{V_{2}} = \frac{3 \times 10^{8}}{2 \times 10^{8}} = \frac{3}{2}$

Sin c $= \frac{μ_{2}}{μ_{1}} = \frac{3}{4}$

For TIR $\sin i \geq \sin c ∴ i \geq \sin^{- 1} (\frac{3}{4})$

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