The regulation of plant growth is the role of different plant hormones and regulators of plant growth, predominantly the hormones Auxins, which are located at the tip of the coleoptile. Depending on the environment the plant is growing in, and the amount of Auxins the plant contains, plant growth is determined.
So there is a compound in the tip of the coleoptile that is responsible for the plant growing vertically in the dark or the plant growing towards the light directionally. To answer your question, we need to look at the different circumstances the plant is growing in. What's important here is that it has been shown that agar is permeable to chemical compounds produced in the coleoptile tip, but the mica is not.
The intact coleoptile has the intact amount of growth hormones in the coleoptile tip, so it will grow tall and straight in the dark, and tall and bent with directional light treatment.
The cut coleoptile (tip removed) doesn't have growth hormones that are located in the tip (the tip has been removed), so it will grow short and straight regardless of its environment.
The cut coleoptile with mica insert, which is not permeable to the compounds in the tip of coleoptile, would grow short and straight in both a dark environment and with directional tight treatment.
The cut coleoptile with agar insert would grow tall and straight in the dark, and tall and bent with directional light treatment, since agar is permeable to the compounds found in the tip of the coleoptile which ensure the growth of the plant.
