To determine the medium in which light would have the longest wavelength, we need to understand the relationship between the speed of light, wavelength, and frequency. The relationship is given by the equation:
[tex]\[ v = \lambda f \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of light in the medium.
- [tex]\( \lambda \)[/tex] is the wavelength of light in the medium.
- [tex]\( f \)[/tex] is the frequency of light, which remains constant across different media.
Since the frequency [tex]\( f \)[/tex] is constant, the wavelength [tex]\( \lambda \)[/tex] is directly proportional to the speed of light [tex]\( v \)[/tex]. This means that the medium with the highest speed of light will have the longest wavelength.
Given the speeds of light in different media:
- Water: [tex]\( 2.25 \times 10^5 \, \text{m/s} \)[/tex]
- Air: [tex]\( 2.99 \times 10^3 \, \text{m/s} \)[/tex]
- Glass: [tex]\( 1.97 \times 10^0 \, \text{m/s} \)[/tex]
- Diamond: [tex]\( 1.24 \times 10^0 \, \text{m/s} \)[/tex]
Comparing these values, the speed of light is highest in water. Therefore, light will have the longest wavelength in water.
So, light would have the longest wavelength in water.
