Final answer:
The apical meristem, or growth tip, of the radish plant controls phototropism through the detection of light and production of auxin, which accumulates on the shaded side of the stem and promotes bending towards light.
Step-by-step explanation:
The part of the radish plant that controls phototropism is the apical meristem, or the growing tip of the plant. This was first described by Charles Darwin and his son Francis, who found that the tip of the plant perceives light, although the bending response occurs at a different part, indicating that a signal travels from the tip to the base. Peter Boysen-Jensen later expanded upon this by demonstrating that a chemical signal, specifically the plant growth hormone called auxin (indole acetic acid, IAA), was responsible for initiating the bending response. He did this by conducting experiments where he cut off the plant tip and covered the cut section with gelatin or impermeable mica flakes to see if the seedling would still bend towards light.
Phototropins are blue-light receptors that also play a crucial role in phototropism by causing the accumulation of auxin on the shaded side of the stem, where it promotes cell elongation. This differential growth causes the plant to bend towards the light. Therefore, it's the interaction between phototropins and auxin, initiated at the plant's apical meristem, that directs the phototropic response.