Question

Suppose you are 94 cm from a plane mirror.

Part A

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 4.1 mm ? Express your answer to two significant figures and include the appropriate units.

Answer 1

Neglating the angle between nose and eye we have,

$tan\theta = \frac{r}{d}$

$r= d tan \theta$

$r= 94\times tan\theta$

Now calculating for the tangent will get,

As you are half way between your image and you, we have to consider tanget as,

$tan\theta = \frac{0.41}{4\times 94}$

$tan\theta = 1.09\times 10^{-3}$

$\therefore r =102.46 \times 10^{-3}cm$

Area is given by

$A=\pi r^2$

$A=3.14\times {(102.46\times 10^{-5})}^2$

$A=3.30\mu m$