Question

A fluorescent lamp of length $1m$ is placed horizontally at a depth of $1.2m$ below ceiling. A plane mirror of length $0.6m$ is placed below the lamp parallel to and symmetric to the lamp at a distance $2.4m$ from it. The length of the reflected patch of length on the ceiling________.

Answer 1

Let $CD$ be the fluorescent lamp placed below the ceiling at a depth of $1.2m$.

Let $AB$ be the plane mirror placed below the lamp and $PQ$ be the reflected patch on the ceiling.

By symmetry of triangles, $MN=0.2m$

$PE=1m$ and $QF=1m$

Therefore, $PQ=1+1+1=3m.$