A ray is incident at a small angle of incidence $i$ on one face of a prism with angle of prism $6^{\circ}$ and emerges from the second face. If the prism is dipped in transparent liquid of refractive index $1.2$ and angle of deviation is $2^{\circ}$ , then what is the refractive index of prism material?

1.20

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1.82

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1.60

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1.98

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Solution

The correct option is C $1.60$
The angle of deviation by thin prism is given by,

$δ = (^{1} μ_{2} - 1) A$

$\Rightarrow 2^{\circ} = (\frac{μ}{1.2} - 1) \times 6^{\circ}$

$\Rightarrow \frac{2}{6} = \frac{μ}{1.2} - 1$

$\Rightarrow \frac{μ}{1.2} = \frac{1}{3} + 1 = \frac{4}{3}$

$\Rightarrow μ = \frac{4 \times 1.2}{3} = 1.60$

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