Question

What percentage of the speed of light in vacuum is the speed of light in a diamond? Incorrect: Your answer is incorrect. answer in:_____%

Answer 1

Explanation

Step 1

find the speed of ligth in the diamond:

to do that we can use the formula

$refractive\text{ index\lparen}\mu)=\frac{c(\text{ speed of light in vaccum\rparen}}{s(\text{ speed of light in the material\rparen}}$

we know that :

$\begin{gathered} refractive\text{ index of diamond\lparen}\mu)=2.42 \\ speed\text{ of llight in the vaccum=c=300000 }\frac{km}{s} \end{gathered}$

so, replace and solve for speed of light in the diamond

$\begin{gathered} refractive\text{ index\lparen}\mu)=\frac{c(\text{ speed of light in vaccum\rparen}}{s(\text{ speed of light in the material\rparen}} \\ 2.42=\frac{3*10^5\frac{km}{s}}{s} \\ s=\frac{3\times10^5\frac{km}{s}}{2.42} \\ s=123966.9\text{ }\frac{km}{s} \\ \end{gathered}$

finally, to find the percentage apply this formula

$\begin{gathered} \text{ \% }=\frac{speed\text{ of light in diamond}}{spped\text{ of ligth invaccum}}*100\text{ \%} \\ replace \\ \text{ \%=}\frac{123966.9\frac{km}{s}}{3*10^5\frac{km}{s}}*100\text{ \%} \\ \text{ \%=0.413*100\%} \\ \text{ \%=41.3 \%} \\ rounded\text{ 41\%} \end{gathered}$

so, the answer is

41 %

I hope this helps you