Analyze the given statements about light and rainbows: I. Colour depends on frequency. II. In prism dispersion, yellow deviates more than green. III. Rainbows need heavy rain.

Let's analyze each statement:

I. The colour of light depends on its frequency.
The colour of visible light is determined by its wavelength or, equivalently, its frequency. Different frequencies correspond to different colours in the electromagnetic spectrum. For example, red light has a lower frequency than blue light. This statement is correct.

II. When white light is dispersed by a triangular prism, yellow is deviated more than green.
When white light passes through a prism, it disperses into its constituent colours because the refractive index of the prism material varies slightly with the wavelength of light. Shorter wavelengths (higher frequencies) are refracted more than longer wavelengths (lower frequencies). The order of colours from least deviated to most deviated is Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV). Since yellow has a longer wavelength than green, yellow light is deviated less than green light. This statement is incorrect.

III. Rainbows are formed when rains fall heavily.
Rainbows are formed by the dispersion, refraction, and internal reflection of sunlight by water droplets in the atmosphere. While rain is necessary to provide the water droplets, the intensity of the rainfall ("heavily") is not a strict requirement. Rainbows can form during light rain or even mist, as long as there are sufficient water droplets and sunlight. Therefore, stating that they are formed only when rain falls heavily is not entirely accurate. This statement is incorrect due to the qualifier "heavily".

Based on this analysis, only statement I is correct.

The final answer is $\boxed{\text{A) I only}}$.