Question

Determine the critical angle for a pair of media having refractive indices 1.5 and 1.8?

Answer 1

Step 1: Assuming the quantities

Let, the critical angle be ${\mathrm{\theta }}_{\mathrm{C}}$

Step 2: Explanation of the given quantities

Refractive index of the first medium,${\mathrm{\mu }}_1=1.5$

Refractive index of the second medium,${\mathrm{\mu }}_2=1.8$

Step 3: Calculation for the critical angle

By using the relation

$$\begin{gathered} {\mathrm{\theta }}_{\mathrm{C}}={\sin }^{-1}\left(\frac{{\mathrm{\mu }}_1}{{\mathrm{\mu }}_2}\right) \\ {\mathrm{\theta }}_{\mathrm{C}}={\sin }^{-1}\left(\frac{1.5}{1.8}\right) \\ {\mathrm{\theta }}_{\mathrm{C}}={\sin }^{-1}\left(\frac{5}{6}\right) \\ {\mathrm{\theta }}_{\mathrm{C}}=56.{44}^{\circ } \end{gathered}$$

Thus, the critical angle for a pair of media having refractive indices 1.5 and 1.8 is $56.{44}^{\circ }$.