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 illuminate

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?

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Answer:

A

Solution:

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

$\frac{0.20}{h} = \frac{1}{3 + h} \Rightarrow 0.6 + 0.2 h = h$

$0.8 h = 0.6 \Rightarrow h = \frac{3}{4} m$

$h = 75 cm$

TestHub · Accepted Answer

tan θ = r h = R 3 + h ​ 0 . 2 0 h = 1 3 + h ⇒ 0 . 6 + 0 . 2 h = h 0 . 8 h = 0 . 6 ⇒ h = 3 4 m h = 75 cm

Physics - Geometrical Optics Question with Solution | TestHub

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