Question

A ray of light is incident at the glass–water interface at an angle $i$, it emerges finally parallel to the surface of water, then the value of ${\mu }_g$ would be

• A. $\left(\frac{4}{3}\right).sin\left(i\right)$
• B. $\frac{1}{sin\left(i\right)}$
• C. $\frac{4}{3}$
• D. $1$

Answer 1

The correct option is B $\frac{1}{sin\left(i\right)}$

$\text{Given :}{\mu }_w=\frac{4}{3}$

$\text{Since the ray finally emerges}$
$\text{parallel to the water surface.}$
$r\text{must be the critical angle}$.

$\therefore sin\left(r\right)=\frac{sin\left({90}^{\circ }\right)}{{\mu }_w}\Rightarrow sin\left(r\right)=\frac{1}{{\mu }_w}\Rightarrow sin\left(r\right)=\frac{3}{4}$

$\text{At the water-glass interface}$
${\mu }_g.sin\left(i\right)={\mu }_w.sin\left(r\right){\mu }_g=\frac{{\mu }_w\times sin\left(r\right)}{sin\left(i\right)}=\frac{\frac{4}{3}\times \frac{3}{4}}{sin\left(i\right)}=\frac{1}{sin\left(i\right)}$