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  • A glass prism of refractive index 1.5 is immersed in water <img alt="\left(\mu=\frac{4}{3}\right)" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28%5Cmu%3D%5Cfrac%7B4%7D%7B3%7D%5Crig

A glass prism of refractive index 1.5 is immersed in water \left(\mu=\frac{4}{3}\right) . A light beam incident normally on the face AB is totally reflected to reach the face BC if:

Option: 1

\quad \sin \theta \leq \frac{2}{3}


Option: 2

\cos \theta \geq \frac{8}{9}


Option: 3

\sin \theta>\frac{8}{9}


Option: 4

\quad \cos \theta \leq \frac{8}{9}


Answers (1)

best_answer

\text { Here, }{ }^a \mu_{\mathrm{g}}=1.5=\frac{3}{2},{ }^{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3} \\

{ }^{\mathrm{a}} \mu_{\mathrm{w}} \times{ }^{\mathrm{w}} \mu_{\mathrm{g}}={ }^{\mathrm{a}} \mu_{\mathrm{g}} \\

\therefore \quad{ }^{\mathrm{w}} \mu_{\mathrm{g}}=\frac{{ }^{\mathrm{a}} \mu_{\mathrm{g}}}{{ }^{\mathrm{a}} \mu_{\mathrm{w}}}=\frac{3 / 2}{4 / 3}=\frac{9}{8}

\mathrm{ \text { As } \sin C=\frac{1}{{ }^w \mu_g}=\frac{1}{9 / 8}=\frac{8}{9} \\ }

\mathrm{ C=\sin ^{-1}\left(\frac{8}{9}\right) }

For total internal reflection, \mathrm{ \theta>C }

\mathrm{ \theta>\sin ^{-1}\left(\frac{8}{9}\right) or \sin \theta>\frac{8}{9} }

Posted by

shivangi.bhatnagar

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