To determine in which medium light would have the longest wavelength, let's consider the relationship between the speed of light in a medium and wavelength. The speed of light [tex]\( c \)[/tex], frequency [tex]\( f \)[/tex], and wavelength [tex]\( \lambda \)[/tex] are related by the equation:
[tex]\[ c = f \cdot \lambda \][/tex]
When light travels through different media, its speed changes, but the frequency [tex]\( f \)[/tex] remains constant. Thus, the wavelength [tex]\( \lambda \)[/tex] is directly proportional to the speed of light [tex]\( c \)[/tex] in that medium:
[tex]\[ \lambda \propto c \][/tex]
This means that the medium with the highest speed of light will also have the longest wavelength.
Given the speeds of light in different media from the chart:
- Water: [tex]\(2.25 \times 10^8 \, m/s\)[/tex]
- Air: [tex]\(2.99 \times 10^8 \, m/s\)[/tex]
- Glass: [tex]\(1.97 \times 10^8 \, m/s\)[/tex]
- Diamond: [tex]\(1.24 \times 10^8 \, m/s\)[/tex]
We can observe that the speed of light is highest in air, at [tex]\(2.99 \times 10^8 \, m/s\)[/tex].
Therefore, the medium in which light would have the longest wavelength is air.
