Question

The speed of light in the vacuum is 3 x10^8 m/s. What will be its speed in a medium whose refractive index is 2?​

Answer 1

Analysis→

Here we're that's the speed of light (in vacuum) is $\rm{3\times10^8\frac{m}{s}}$ And we've to find the speed of light in the medium whose refractive index(n) is 2. And we know that:-

$\displaystyle\rm{Refractive\:Index_{Of\:medium}=\dfrac{Speed\:Of\:Light_{In\:Vacuum}}{Speed\:Of\:Light_{In\:Medium}}}$

$\rm{n=\dfrac{c}{v}}$

Given→

• Speed of light(in vacuum)= $\rm{3\times10^8\dfrac{m}{s}}$
• Refractive index=2

To Find→

The speed of light in vacuum.

Answer→

$\large{\underline{\boxed{\leadsto{\rm{n=\dfrac{c}{v}}}}}}$

$\implies\rm{n=\dfrac{c}{v}}$

$\implies\rm{2=\dfrac{3\times10^8\frac{m}{s}}{v}}$

$\implies\rm{v=\dfrac{3\times10^8\frac{m}{s}}{2}}$

$\implies\rm{v=\dfrac{ \cancel{3}\times10^8\frac{m}{s}}{\cancel{2}}}$

$\implies\rm{v=1.5\times10^8\frac{m}{s}}$

${\boxed{\boxed{\implies{\bf{v=1.5\times10^8\frac{m}{s}\checkmark}}}}}$

☞ Hence the speed of light in the medium whose refractive index is 2 is $\rm{1.5\times10^8\frac{m}{s}}$ which is the required answer.

Know More→

Refractive index of some mediums:-

$\boxed{\begin{tabular}{c | 1} Material Medium & Refractive Index(n) \\ \cline{1-2} Air & 1.0003 \\ Water & 1.33 \\ Ice & 1.31 \\ Alcohol & 1.36 \\ Kerosene & 1.44 \\ Fused Quartz & 1.46 \\ Crown Glass & 1.52 \\ Rock salt & 1.54 \\ Dense Flint Glass & 1.65 \\ Ruby & 1.71 \\ Diamond & 2.42 \end{tabular}}$

$\Large\maltese{\underline{\underline{\bf{Request\leadsto}}}}$

• View the answer on website to see the table.

HOPE IT HELPS.