A person 1.6 m tall is standing at the centre between two walls three metre high. What is the minimum size of a plane mirror fixed on the wall in front of him, if he is to see the full height of the wall behind him?

Question

A person 1.6 m tall is standing at the centre between two walls three metre high. What is the minimum size of a plane mirror fixed on the wall in front of him, if he is to see the full height of the wall behind him? (A) 0.8 m (B) 1 m (C) 1.5 m (D) 2.3 m

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/e35bd282ba1004e8dccb15aa197a317d-.png" /> tan θ=(h1/d)=(1.6-h1/d / 2) ...(i) tan α=(h2/d)=(1.4-h2/d / 2) ...(ii) h1=(3.2/3) and h2=(2.8/3) 3-h1-h2=1 m

Q. A person $1.6 m$ tall is standing at the centre between two walls three metre high. What is the minimum size of a plane mirror fixed on the wall in front of him, if he is to see the full height of the wall behind him?

0.8 m

1 m

1.5 m

2.3 m

$tan θ = \frac{h _{1}}{d} = \frac{1.6 - h _{1}}{d /2} ... (i)$
$tan α = \frac{h _{2}}{d} = \frac{1.4 - h _{2}}{d /2} ... (ii)$
$h_{1} = \frac{3.2}{3}$ and $h_{2} = \frac{2.8}{3}$
$3 - h_{1} - h_{2} = 1 m$

Q. A person 1.6m tall is standing at the centre between two walls three metre high. What is the minimum size of a plane mirror fixed on the wall in front of him, if he is to see the full height of the wall behind him?

0.8 m

1 m

1.5 m

2.3 m

tanθ=dh1​​=d/21.6−h1​​...(i) tanα=dh2​​=d/21.4−h2​​...(ii) h1​=33.2​ and h2​=32.8​ 3−h1​−h2​=1m

Q. A person $1.6 m$ tall is standing at the centre between two walls three metre high. What is the minimum size of a plane mirror fixed on the wall in front of him, if he is to see the full height of the wall behind him?

$tan θ = \frac{h _{1}}{d} = \frac{1.6 - h _{1}}{d /2} ... (i)$
$tan α = \frac{h _{2}}{d} = \frac{1.4 - h _{2}}{d /2} ... (ii)$
$h_{1} = \frac{3.2}{3}$ and $h_{2} = \frac{2.8}{3}$
$3 - h_{1} - h_{2} = 1 m$