A light wave travels from air into a medium of refractive index 1.54. If the wavelength of the light in air is \(5.9\times10^{-7}\)m, calculate its waveleng...
A light wave travels from air into a medium of refractive index 1.54. If the wavelength of the light in air is \(5.9\times10^{-7}\)m, calculate its wavelength in the medium
Answer Details
The relationship between the wavelength of light in two different media and their refractive indices is given by the formula:
\begin{equation*}
\frac{\lambda_1}{\lambda_2} = \frac{n_2}{n_1}
\end{equation*}
Where:
\begin{itemize}
\item \(\lambda_1\) is the wavelength of light in the first medium
\item \(\lambda_2\) is the wavelength of light in the second medium
\item \(n_1\) is the refractive index of the first medium
\item \(n_2\) is the refractive index of the second medium
\end{itemize}
In this case, the light wave travels from air (first medium) into a medium of refractive index 1.54 (second medium). Therefore, we can use the above formula to find the wavelength of the light in the second medium:
\begin{align*}
\frac{\lambda_1}{\lambda_2} &= \frac{n_2}{n_1} \\
\lambda_2 &= \frac{n_1}{n_2} \lambda_1 \\
&= \frac{1}{1.54} \times 5.9 \times 10^{-7} \mathrm{m} \\
&\approx 3.84 \times 10^{-7} \mathrm{m}
\end{align*}
Therefore, the wavelength of the light in the medium is approximately \(3.84\times10^{-7}\)m.
Answer: \boxed{2}. \(3.8\times10^{-7}\)m.