Question

A plane mirror of circular shape with radius $r=20 \, cm$ is fixed to the ceiling. A bulb is to be placed on the axis of the mirror. A circular area of the radius $R=1 \, m$ on the floor is to be illuminated after reflection of light from the mirror. The height of the room is $3 \, m$ . What is the maximum distance from the centre of the mirror and the bulb so that the required area is illuminated?

• A. $75 \, cm$
• B. $70 \, cm$
• C. $80 \, cm$
• D. $100 \, cm$

Answer 1

Answer: (A)

$\text{tan} \theta = \frac{\text{r}}{\text{h}} = \frac{\text{R}}{3 + \text{h}}$

​ $\frac{0 \text{.} 2 0}{\text{h}} = \frac{1}{3 + \text{h}} \Rightarrow 0 \text{.} 6 + 0 \text{.} 2 \text{h} = \text{h}$
$0 \text{.} 8 \text{h} = 0 \text{.} 6 \Rightarrow \text{h} = \frac{3}{4} \text{m}$
$h=75cm$