Optical fibres work on the principle of `total internal reflection`. This is a process where light waves are completely reflected back into the medium they are travelling in, without any loss of light. This makes optical fibres efficient for data transmission as the light signals can travel long distances without weakening.

Option 2, `refraction`, is the bending of light as it passes from one medium to another. While refraction is involved in total internal reflection, it isn`t the key principle on which optical fibres work.

Option 3, `scattering`, is a process where light is sent in different directions as it passes through a medium. This would not be effective for optical fibres as it would cause loss of signal and data.

Option 4, `interference`, is when two or more waveforms superpose to form a resultant wave. Interference can cause signal degradation in optical fibres but it`s not the principle on which they operate.

So, the correct answer is Option 1, `total internal reflection`.