As we know when light is falling top of an object it casts the shadow at behind of the object
Here, we can see from $\bigtriangleup ABE$ and $\bigtriangleup CDE$
$ \angle B = \angle D $ & $\angle E = \angle E$
∴ By proportionality theorem,
$\dfrac{AB}{CD} = \dfrac{BE}{DE}$
Given, $ CD = 1.5 \: m \\ BD = 3 \: m \\ DE = 3 \: m \\ \therefore AB = \: ?$
∴ $\dfrac{AB}{1.5} = \dfrac{3 + 3}{3}$
$ AB = \dfrac{6}{3} \times 1.5$
$AB = 3 \: m$
∴ Height of the Lamp post is $3 \: m $ which is option B)