On a hypotenuse of a right prism $(30 ° - 60 ° - 90 °)$ of refractive index $1.50$ , a drop of liquid is placed as shown in figure. Light is allowed to fall normally on the short face of the prism. In order that the ray light may get totally reflected, the maximum value of refractive index is:

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1.25

1.30

1.47

1.20

answer is A.

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Detailed Solution

$\begin{array}{l} C_{max} = 60^{\circ} \\ ∴_{r} μ_{d} = \frac{1}{\sin 60^{\circ}} or \frac{μ_{g}}{μ_{ℓ}} = \frac{2}{\sqrt{3}} \\ ∴ μ_{ℓ} = \frac{\sqrt{3}}{2} μ_{g} = \frac{\sqrt{3}}{2} \times 1.5 = 1.3 \end{array}$

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