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The chart shows the speed at which light travels through different media.

\begin{tabular}{|l|c|}
\hline
\multicolumn{1}{|c|}{Medium} & Speed of Light (m/s) \\
\hline
Water & [tex]$2.25 \times 10^8$[/tex] \\
\hline
Air & [tex]$2.99 \times 10^8$[/tex] \\
\hline
Glass & [tex]$1.97 \times 10^8$[/tex] \\
\hline
Diamond & [tex]$1.24 \times 10^8$[/tex] \\
\hline
\end{tabular}

In which medium would light have the longest wavelength?

A. Water
B. Air
C. Glass
D. Diamond


Sagot :

To determine in which medium light would have the longest wavelength, we should consider the relationship between the speed of light in a medium and its wavelength. The wavelength [tex]\(\lambda\)[/tex] of light in a medium is given by the equation:

[tex]\[ \lambda = \frac{v}{f} \][/tex]

where:
- [tex]\(\lambda\)[/tex] is the wavelength,
- [tex]\(v\)[/tex] is the speed of light in the medium, and
- [tex]\(f\)[/tex] is the frequency of the light.

For a given frequency [tex]\(f\)[/tex], the wavelength [tex]\(\lambda\)[/tex] is directly proportional to the speed of light [tex]\(v\)[/tex] in that medium. Therefore, the medium with the highest speed of light will have the longest wavelength.

Let's compare the given speeds of light in different media:

- Speed of light in water: [tex]\(2.25 \times 10^8 \, \text{m/s}\)[/tex]
- Speed of light in air: [tex]\(2.99 \times 10^8 \, \text{m/s}\)[/tex]
- Speed of light in glass: [tex]\(1.97 \times 10^8 \, \text{m/s}\)[/tex]
- Speed of light in diamond: [tex]\(1.24 \times 10^8 \, \text{m/s}\)[/tex]

Among these, the speed of light is highest in air, which is [tex]\(2.99 \times 10^8 \, \text{m/s}\)[/tex].

Therefore, light would have the longest wavelength in air.
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