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.
