Question

it is 165 cm from your eyes to your toes. your standing 200 cm i front of a tall mirror. how far is it from your eyes to the image of your toes?

Answer 1

Concepts and reason The concept used to solve this problem is the image distance for a mirror problem. Initially, the horizontal distance from the eyes to toes' image in the mirror can be calculated by using the relation between the horizontal distance and the object distance. Then, the distance from the eyes to the image of the toes can be calculated by using the relation between the height and the horizontal distance.

Fundamentals

The expression for the horizontal distance is, \(d=2 x\)

Here, \(d\) is the horizontal distance and \(x\) is the distance of the object in front of the mirror. The expression for the distance from the eye to the image is, \(D=\sqrt{d^{2}+h^{2}}\)

Here, \(D\) is the distance from the eye to the toes and \(h_{\text {is the height of the toes. }}\)

The expression for the horizontal distance is, \(d=2 x\)

Substitute \(200 \mathrm{~cm}\) for \(x\)

\(d=2(200 \mathrm{~cm})\)

\(=400 \mathrm{~cm}\)

The value of the horizontal distance is calculated by using the value of the distance from the object in front of the mirror. The distance from the object in front of the mirror is the object distance.

The expression for the distance from the eyes to the toes is,

\(D=\sqrt{d^{2}+h^{2}}\)

Substitute \(400 \mathrm{~cm}\) for \(d\) and \(165 \mathrm{~cm}\) for \(h\),

\(D=\sqrt{(400 \mathrm{~cm})^{2}+(165 \mathrm{~cm})^{2}}\)

\(=432.7 \mathrm{~cm}\)

The distance from the eyes to the toes is \(\mathbf{4 3 2 . 7 \mathrm { cm }}\).

The distance from the eyes to the toes in the mirror is calculated in terms of height of the toes and the horizontal distance. The distance is actually the hypotenuse of a rectangular triangle.