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

Step-by-step 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 }(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=(3*10^5(km)/(s))/(s) \\ s=(3*10^5(km)/(s))/(2.42) \\ s=123966.9\text{ }(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{ \%=}(123966.9(km)/(s))/(3*10^5(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