Question

A person's eye is at a height of 1.5m. He stands in front of a 0.3m length plane mirror bottom of which is 0.8m above ground. Find the length of his image he will be able to see in this mirror.

• A. 0.3m
• B. 0.6m
• C. 0.8m
• D. 1.5m

Answer 1

Answer: (B)

0.6m

Answer 2

The length of the image seen in a plane mirror is twice the vertical extent of the mirror visible to the observer's eyes. Given: Height of the person's eye from the ground, $h_e = 1.5$ m Length of the plane mirror, $L_m = 0.3$ m Height of the bottom of the mirror from the ground, $h_{bm} = 0.8$ m

The height of the top of the mirror from the ground is $h_{tm} = h_{bm} + L_m = 0.8 + 0.3 = 1.1$ m.

Since the eye level ($h_e = 1.5$ m) is above the top of the mirror ($h_{tm} = 1.1$ m), the observer can see the entire mirror. The vertical extent of the mirror visible to the observer is the full length of the mirror, which is $L_m = 0.3$ m.

The length of the image seen in a plane mirror is twice the vertical extent of the mirror visible to the observer. Length of image seen = $2 \times (\text{Visible mirror length})$ Length of image seen = $2 \times 0.3$ m = $0.6$ m.

This length is independent of the observer's height, as long as their eyes are positioned to see the relevant parts of the mirror.