Question

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

• A. $75cm$
• B. $25cm$
• C. $65cm$
• D. $150cm$

Answer 1

The correct option is A $75cm$

we have,

$\angle i=\angle r$

$\tan i=\tan r$

$\frac{r}{h}=\frac{R-0.2}{H}$

$\frac{0.2}{h}=\frac{1-0.2}{3}$

$\frac{0.2}{h}=\frac{0.8}{3}$

$h=\frac{0.2\times 3}{0.8}$

$\therefore h=0.75m=75cm$