Chapter 23, Problem 76GP

To determine

we must find the index of refraction of given material and identify the material.

Answer to Problem 76GP

Solution:

Refractive index of given medium is 1∙578 and the material is flint-glass.

Explanation of Solution

Given in the question that a pulse of light is traveling in certain medium and takes 2∙63 ns to travel 0∙500 m in that medium.

Given:

Given that Distance travelled = 0∙500 m

Time taken to travel the distance = 2∙63 n s= $2\cdot 63\times {10}^{-9}s$

Formula used:

$\left(\text{1}\right)\text{ Speed = distance/ time}$

$\left(\text{2}\right)\text{Refractive index of any material = speed of light in vaccum/ speed of light in the medium}$

Calculation:

$\text{Speed of light in the medium = distance/time}$

$\begin{array}{l}\begin{array}{l}{V}_m{=}_{ }0\cdot 500m/2\cdot 63\times {10}^{-9}s\\ \Rightarrow V_m=0\cdot 190\times {10}^{9}m/s\end{array}\hfill \\ \Rightarrow V_m=1\cdot 9\times {10}^{8}m/s\hfill \end{array}$

Now refractive index of the medium = velocity of light in vacuum/velocity of light in medium

So refractive index of medium = $V_c/V_m$= $\left(3\times {10}^8/1\cdot 9\times {10}^8\right)=1\cdot 578$

So now we can check from the refractive index table that the material is Flint-glass.