# one of the faces of a prism of refracting angle 30? is silvered. a ray of light incident at an angle 45 degree on the other face returns along its previous path after reflection and refraction from the silvered face, the refractive index of the prism is _______

$GivenA={30}^{o}\phantom{\rule{0ex}{0ex}}{i}_{2}={0}^{o}\phantom{\rule{0ex}{0ex}}Becausetherefractedrayretractsitspath\phantom{\rule{0ex}{0ex}}{r}_{2}=0\phantom{\rule{0ex}{0ex}}{r}_{1}+{r}_{2}=A\phantom{\rule{0ex}{0ex}}{r}_{1}+0=A\phantom{\rule{0ex}{0ex}}{r}_{1}=A={30}^{o}\phantom{\rule{0ex}{0ex}}\mu =\frac{\mathrm{sin}{i}_{1}}{\mathrm{sin}{r}_{1}}=\frac{\mathrm{sin}45}{\mathrm{sin}30}=\frac{{\displaystyle \frac{1}{\sqrt{2}}}}{{\displaystyle \frac{1}{2}}}=1.414\phantom{\rule{0ex}{0ex}}$

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