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

Options

A. 130 cm
B. 140 cm
C. 120 cm
D. 150 cm

Answer

C

Explanation

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

Applying the property of triangle and from similar triangles `OPM_(1) and OI_(1) I_(2)`,
`tan theta = (PM_(1))/(OP)=(I_(1)I_(2))/(OI_(1))`
since, `PM_(1) = 140 - 85 = 55 cm `
Let `OP = a and OI_(1) = 2a`
`tan theta = 55/a = x/(2a) rArr x = 55 xx 2 = 110 cm`
So, the maximum height seen by the girl, ` H = 110 + 10 = 120 cm`
Since, the height above her eyes, has not effected the mirror height, because it is just in front of the mirror. Hence, the correct option is (c).