Question

A moth at about eye level is$\mathbf{10}\mathbf{ }\mathbf{\text{cm}}$in front of a plane mirror; a man is behind the moth,$\mathbf{30}\mathbf{ }\mathbf{\text{cm}}$from the mirror. What is the distance between man’s eyes and the apparent position of the moth’s image in the mirror?

Short answer

The distance between the eyes and the apparent position of the moth’s image in the mirror is, $i=40 \text{cm}$.

Step-by-step solution

Step 1: Identification of the given data

The object distance is,$10\text{cm}$.

A man is $30\text{cm}$in front of mirror.

Determining the concept

Use the property of the plane mirror to find the image distance. Then, calculate the distance between the eyes and the apparent position of the moth’s image in the mirror. For flat mirrors, the image distance and the object distance are equal (typically denoted by the symbol ${\mathit{d}}_{\mathbf{0}}$) (often represented by the symbol ${\mathit{d}}_{\mathbf{i}}$).In other words, the image is positioned the same distance from the mirror as the object is from the mirror.

Formula are as follows:

For plane mirrors,

The image distance is equal to the object distance.

role="math" localid="1662978167811" $\mathbf{\text{Imagedistance=Objectdistance}}$

(a) Determining the distance between the eyes and the apparent position of the moth’s image in the mirror.

In the plane mirror, the image is formed at a distance same as the object distance.

Thus,

$\text{Imagedistance}=\text{Objectdistance}=10\text{cm}$

Hence, the distance between man’s eyes and the apparent position of the moth’s image in the mirror is,

$\begin{array}{rcl}i& =& 30 \text{cm}+10 \text{cm}\\ & =& 40 \text{cm}\end{array}$

Therefore, the distance between the eyes and the apparent position of the moth’s image in the mirroris,$i=40 \text{cm}$.

The image distance from the mirror by using the property of the plane mirror can be calculated.