Question

A ray of light is incident on a glass sphere from water as shown. If ${\mu }_{\text{glass}=\frac{3}{2}}$ and ${\mu }_{\text{water}=\frac{4}{3}}$. The angle of incidence so that the ray which enters the sphere does not come out of the sphere is

• A. ${\text{tan}}^{-1}\left(\frac{8}{9}\right)$
• B. ${90}^{\circ }$
• C. ${\text{tan}}^{-1}\left(2\right)$
• D. ${\text{sin}}^{-1}\left(\frac{64}{81}\right)$

Answer 1

The correct option is B

${90}^{\circ }$

In $\Delta \text{AOB}$

$\text{AO = OB}$

${\mu }_{\text{w}}\text{sin}\theta ={\mu }_{\text{g}}\text{sin}c$ ...... (1)

and $\text{sin}c=\frac{{\mu }_{\text{w}}}{{\mu }_{\text{g}}}$ ....... (2)

$\therefore \text{sin}\theta =\frac{{\mu }_{\text{g}}}{{\mu }_{\text{w}}}\times \frac{{\mu }_{\text{w}}}{{\mu }_{\text{g}}}$

$\Rightarrow \theta ={90}^{\circ }$