Geometrical OpticsMedium
Question
One side of an equilateral prism is painted by a transparent material of refractive index $n_{2}$. The refractive index of prism is 1.6 . The minimum value of $n_{2}$ required for total internal reflection from painted face is $\_\_\_\_$ .
Options
A.$\frac{3\sqrt{3}}{1.6}$
B.$\sqrt{3}$
C.$\frac{3.2}{\sqrt{3}}$
D.$\frac{4\sqrt{3}}{5}$
Solution
Sol. [Key Concept: TIR at the painted face needs $sin\ C = n_{2}/n_{1}$; use the prism geometry for $n_{2}$.]
For surface QR
$${i = 60^{\circ} }{1.6sin60^{\circ} = \mu sin90^{\circ} }{\mu = 1.6 \times \frac{\sqrt{3}}{2} = \frac{4}{5} \times \sqrt{3} }$$
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