$解:由题意得,AB//A'B'//OS$
$∵AB//OS$
$∴△ABC∽△SOC$
$∴\frac {AB}{SO}=\frac {BC}{OC}$
$∵A'B'//SO$
$∴△A'B'C'∽△SOC'$
$∴\frac {A'B'}{SO}=\frac {B'C'}{OC'}$
$∵AB=A'B'$
$∴\frac {BC}{OC}=\frac {B'C'}{OC'}$
$设OC=(x+1)m,OC'=(x+5.8)m$
$∴\frac 1{x+1}=\frac {1.8}{x+5.8},解得x=5$
$∴OB=5m,OC=6m$
$∵\frac {AB}{SO}=\frac {BC}{OC}$
$∴\frac {1.5}h=\frac 16,解得h=9$
$答:路灯的高度为9米。$