Into the light!

As shown in the diagram above, there is a light source at a height of \(H\), and a man of height \(h\) walks toward it with constant velocity \(v\).

Photons hit the road (which is made of mirror) at point \(P\) and reflects into the man's eye (approximated by a point-like photoreceptor located exactly at the height \(H\) above the ground).

Due to the motion of the man, the location of \(P\) moves toward the light with velocity \(u\).

Find the ratio \(\dfrac{v}{u}\).

Details and Assumptions:

  • Take \(H:h = 3:1\).
  • Give your answer to 3 decimal places.
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