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?

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

Tardigrade Admin · Accepted Answer

texttan θ = ( textr/ texth) = ( textR/3 + texth) <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-cln2s0isd5qcn8ft.jpg" /> â (0 text. 2 0/ texth) = (1/3 + texth) ⇒ 0 text. 6 + 0 text. 2 texth = texth 0 text. 8 texth = 0 text. 6 ⇒ texth = (3/4) textm h=75cm

$75 c m$

$70 c m$

$80 c m$

$100 c m$

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

$\frac{0 . 20}{h} = \frac{1}{3 + h} \Rightarrow 0.6 + 0.2 h = h$
$0.8 h = 0.6 \Rightarrow h = \frac{3}{4} m$
$h = 75 c m$

75cm

70cm

80cm

100cm

tanθ=hr​=3+hR​ ​ h0.20​=3+h1​⇒0.6+0.2h=h 0.8h=0.6⇒h=43​m h=75cm

$75 c m$

$70 c m$

$80 c m$

$100 c m$

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

$\frac{0 . 20}{h} = \frac{1}{3 + h} \Rightarrow 0.6 + 0.2 h = h$
$0.8 h = 0.6 \Rightarrow h = \frac{3}{4} m$
$h = 75 c m$