Teaser 2896: Light angles

From The Sunday Times, 25th March 2018 [link]

The hotel’s night clerk was always glancing at the novelty 12-hour clock facing her. Its hands’ rotation axis was exactly midway across and between three-quarters and four-fifths of the way up the four-metre high rectangular wall. Light rays directed out along the continuous-motion minute and hour hands made pencil beams across the wall. Twice during her 12-hour shift she saw the beams hit the top corners of the wall simultaneously, and twice she saw the beams hit the bottom corners simultaneously.

How wide was the wall to the nearest metre?