Height of the lamp post

Geometry Level 5 John is walking by the edge of a road at night.

There is a lamp post besides the road, which is working. The nearest point on the road to the lamp post is $P$.

His shadow is produced due to the light from the lamp post.

When he walks from point $R$ to point $Q$, he notices that the length of his shadow at point $R$ was $\dfrac{3}{2}$ times the length of his shadow at point $Q$.

Next, when John walks from point $Q$ to point $P$, he further notices two things.

$1)$ $Q$ is halfway between $P$ and $R$.

$2)$ The length of his shadow when he was at point $Q$ and the distance between him and the pole at point $P$ are equal.

On the basis of the data collected by John, find the height of the lamp post (in meters), if his height is $1.8 \ m$.

$\textbf{Details And Assumptions}$

$\bullet$ $P$, $Q$ and $R$ are co-linear and are on the edge of the road.

$\bullet$ Ignore any light other than that coming from the lamp post in question.

$\bullet$ Source : Problems plus in IIT Mathematics by Asit Das Gupta.

$\bullet$ Image Credit : Red Edge

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