Question

A plane mirror of circular shape with radius r=20cm is fixed to the ceilin.a bulb is to be placed on the axis of 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 maximum distance from the centre of the mirror and the bulb so that the required area is illuminated?

Answer 1

By law of reflection we can say

angle of incidence from the on mirror = angle of reflection from mirror to floor

now let say mirror is at "h" distance below the mirror

so

angle i = angle r

$tan i = tan r$

$\frac{r}{h} = \frac{R - 0.20}{H}$

$\frac{0.20}{h} = \frac{1 - 0.20}{3}$

$\frac{0.20}{h} = \frac{0.80}{3}$

$h = \frac{3}{4} = 0.75 m$

so position of bulb will be 0.75 m below the mirror