the maximum distance that can be travelled without dispersion increases with ___________ in wavelength.

The maximum distance that can be travelled without dispersion increases with an increase in wavelength.

Here's a step-by-step explanation:

1. Dispersion in optics refers to the phenomenon where light of different wavelengths travels at different speeds when passing through a medium, causing the light to spread out or "disperse".

2. The speed at which light of a particular wavelength travels through a medium is determined by the medium's refractive index for that wavelength. The refractive index is a measure of how much the light is slowed down compared to its speed in a vacuum.

3. The refractive index of most materials changes with the wavelength of the light, a phenomenon known as dispersion. This means that light of different wavelengths will travel at different speeds through the material, causing the light to spread out or "disperse".

4. Longer wavelengths of light are generally less affected by dispersion than shorter wavelengths. This means that light of a longer wavelength can travel a greater distance through a medium before it begins to disperse.

5. Therefore, the maximum distance that can be travelled without dispersion increases with an increase in wavelength.