A girl of height 150 cm with her eye level at 140 cm stands in front of plane mirror of height 75 cm fixed to a wall. The lower edge of the mirror is at a height of 85 cm above her feet level. The height of her image the girl can see in the mirror is

Question

A girl of height 150 cm with her eye level at 140 cm stands in front of plane mirror of height 75 cm fixed to a wall. The lower edge of the mirror is at a height of 85 cm above her feet level. The height of her image the girl can see in the mirror is (A) 130 cm (B) 140 cm (C) 120 cm (D) 150 cm

Tardigrade Admin · Accepted Answer

Ray diagram of a girl standing in front of a plane mirror is given below,

Applying the property of triangle and from similar triangles

OP M_{1}

and

O I_{1} I_{2}

tan θ = \frac{P M _{1}}{OP} = \frac{I _{1} I _{2}}{O I _{1}}

Since,

P M_{1} = 140 - 85 = 55 c m

Let

OP = a

and

O I_{1} = 2 a

tan θ = \frac{55}{a} = \frac{x}{2 a}

\Rightarrow x = 55 \times 2 = 110 c m

So, the maximum height seen by the girl,

H = 110 + 10 = 120 c m

Since, the height above her eyes, has not effected the mirror height,
because it is just in front of the mirror.

Q. A girl of height 150cm with her eye level at 140cm stands in front of plane mirror of height 75cm fixed to a wall. The lower edge of the mirror is at a height of 85cm above her feet level. The height of her image the girl can see in the mirror is

130 cm

140 cm

120 cm

150 cm

Q. A girl of height $150 c m$ with her eye level at $140 c m$ stands in front of plane mirror of height $75 c m$ fixed to a wall. The lower edge of the mirror is at a height of $85 c m$ above her feet level. The height of her image the girl can see in the mirror is