Refraction of Light from Plane Surface, Critical Angle & Total Internal Reflection

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(C) We know

$\sin c = \frac{n_{2}}{n_{1}} \Rightarrow \frac{n_{1}}{n_{2}} = \frac{1}{\sin c}$

$\Rightarrow \frac{n_{1}}{n_{2}} = \frac{1}{\sin 45} = \frac{\sqrt{2}}{1}$

$n_{1} : n_{2} = \sqrt{2} : 1$

(2)

$i = θ_{c} \Rightarrow i = \sin^{- 1} (\frac{1}{μ})$

$\Rightarrow i = 45 °$

According to Snell’s law,

$1 \sin 45 ° = \sqrt{2} \sin r \Rightarrow \frac{1}{\sqrt{2}} = \sqrt{2} \sin r \Rightarrow \frac{1}{\sqrt{2}} = \sqrt{2} \sin r$

$\Rightarrow r = 30 °$

Now, $Δ x = t \sec 30 ° \sin 15 ° = 4 \sqrt{3} \times \frac{2}{\sqrt{3}} \times \frac{1}{4} = 2 cm$

(31)

$h_{app} = \frac{h_{1}}{μ_{1}} + \frac{h_{2}}{μ_{2}} = \frac{6}{8 / 5} + \frac{6}{3 / 2} = 4 + \frac{15}{4} = \frac{31}{4} cm$

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