Question

a) calculate the speed of light in the glassb) the angle of incidence, θ.c) the refractive index of the liquid.

Answer 1

a) Given that refractive index of glass is 1.5,

We know that speed of light in medium of refractive index n is given by,

$v=\frac{c}{n}$

In this case,

$v=\frac{3\times10^8}{1.5}=2\times10^8\text{ m/s}$

b) Using Snell's law at the air-glass interface,

$\begin{gathered} n_{air}sin\theta=n_{glass}sin15\degree \\ \Rightarrow sin\theta=1.5\times0.2588 \\ \Rightarrow sin\theta=0.3882 \\ \Rightarrow\theta=22.84\degree\approx23\degree \end{gathered}$

c) Again applying Snell's law at the glass-liquid interface,

$\begin{gathered} n_{glass}sin60\degree=n_{liquid}sin90\degree \\ \Rightarrow1.5\times0.866=n_{liquid} \\ \Rightarrow n_{liquid}=1.299\approx1.3 \end{gathered}$