Question

What is the speed of light and wavelength in a medium having refractive index $\mu =1.5$, if the wavelength of light in air is $780\text{nm}$ ?

• A. $2\times {10}^8\text{m/s}$ and $520\text{nm}$
• B. $1.5\times {10}^8\text{m/s}$ and $520\text{nm}$
• C. $2\times {10}^8\text{m/s}$ and $500\text{nm}$
• D. $1.5\times {10}^8\text{m/s}$ and $500\text{nm}$

Answer 1

The correct option is A $2\times {10}^8\text{m/s}$ and $520\text{nm}$

Given :
Refractive index, $\mu =1.5$
Wavelength of light in air,
${\lambda }_a=780\text{nm}$

Let $v$ be the speed of light in the medium.

And we know that,
$\mu =\frac{c}{v}=\frac{{\lambda }_a}{{\lambda }_m}$

$\Rightarrow v=\frac{c}{\mu }=\frac{3\times {10}^8}{1.5}=2\times {10}^8\text{m/s}$.

Also, $\mu =\frac{{\lambda }_a}{{\lambda }_m}$

$\Rightarrow {\lambda }_m=\frac{{\lambda }_a}{\mu }=\frac{780}{1.5}=520\text{nm}$

Hence, option $\left(a\right)$ is the correct answer.