Question

Calculate the index of refraction for a medium in which the speed of light is $\mathbf{2}\mathbf{.}\mathbf{012}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\mathbf{m}\mathbf{/}\mathbf{s}$, and identify the most likely substance based on Table 25.1.

Short answer

The material is most probably polystyrene, and the index of refraction is 1.491.

Step-by-step solution

Concept Introduction

The ratio of the speed of light in a vacuum to the same quantity in the second medium of larger density is used to determine the Refractive Index (Index of Refraction). In descriptive prose and mathematical formulae, the refractive index variable is most usually represented by the letter n or n'.

Calculating the index of refraction

The relationship $n=\frac{c}{v}$modifies the speed of light in materials by altering its coefficient of refraction. We need to solve this equation for and determine the most comparable material by utilizing the values in the table 25.I.

$$\begin{gathered} n=\frac{c}{v} \\ =\frac{3.00\times {10}^{8}m/s}{2.012\times {10}^{8}m/s} \\ =1.491 \end{gathered}$$

This substance is most likely polystyrene, according to the table, and index of refraction is 1.491.