Answer to Question #111969 in Optics for Emily

Question

A convex mirror in an amusement park has a radius of curvature of 3.00 m. A man stands in front of the mirror so that his image is half as tall as his actual height. At what distance must the man focus his eyes in order to see his image?

Answer 1

As per the data given in the question,

Radius of curvature of the convex convex mirror (R)= 3m

Let the position of the image from the convex mirror is v and the position of the object from the mirror is v,

m is the magnification of the mirror, hi is the height of the image and ho is the height of the object.

it is given that

$\dfrac{h_i}{h_o}=m=\dfrac{1}{2}=\dfrac{v}{u}$

Now, applying the mirror formula,

$\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$

We know that, focal length (f)=$R/2=\dfrac{300cm}{2}=150cm$

now substituting the values,

$\dfrac{1}{-2u}+\dfrac{1}{-u}=\dfrac{1}{-150}$

$\Rightarrow \dfrac{-3}{2u}=\dfrac{1}{-150}$

$u=225 cm$

so $v=2\times 225=400cm$

So man should focus at 400 cm then he will be able to see the clear image.