Chapter 23, Problem 7P

Suppose you are 94 cm from a plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 4.5 mm?

To determine

What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose?

Answer to Problem 7P

Solution:

$3.97\times {10}^{-6}{\text{m}}^{\text{2}}$

Explanation of Solution

Given info:

Suppose you are $v=94\text{cm}$ from a plane mirror.

Diameter of pupil $d_p{\text{=}}_{}\text{4}\text{.5 mm}$

Formula used:

$d_{mirror}/v=d_p/(v+u)$

Here, v and u are image and object distance.

Area of on the mirror,

$a_{mirror}=1\pi {(d_{mirror})}^2/4$

Calculation:

$\begin{array}{l}{d}_{mirror}/v=d_p/(v+u)\\ d_{mirror}/94\text{cm=4}\text{.5mm/(94cm+94cm)}\\ d_{mirror}=2.25\text{mm}\end{array}$

Therefore, the area on the mirror,

$\begin{array}{l}{a}_{mirror}=1\pi {(}^{d_{mirror}}/4\\ =3.14\times {(}^{2.25}/4\\ =3.14\times {(}^{2.25}/4\\ =3.97\times {10}^{-6}{\text{m}}^{\text{2}}\end{array}$