Question

Question 18 10 pts A concave mirror in an amusement park has a radius of curvature of 5 m. A child stands in front of the mirror so that she appears 5 times taller than her actual height. If the image is upright, how far is she standing from the mirror? Please round your answer to one decimal place. Equations: m 1 = 1/3 + 7

Answer 1

Solution:

The raius of the curvature of the concave mirror,

r = 5 m

It is given that the child image is inverted and is 5 times taller than the actual

Therefore, we have magnification as follows

$m=\frac{-i}{p}$

$5=\frac{-i}{p}$

We have the concave mirror equation

- (2) f P

where

$f=\mathrm{focal\; length}=\frac{r}{2}=\frac{5}{2}=2.5\; \mathrm{m}$

From (1) and (2)

$\frac{1}{2.5}=\frac{1}{p}+\frac{1}{(-5p)}$

$\frac{1}{2.5}=\frac{1}{p}-\frac{1}{5p}$

$\frac{1}{2.5}=\frac{4p}{5p^{2}}$

$\frac{1}{2.5}=\frac{4}{5p}$

$p=\frac{4\times 2.5}{5}$

$p=2\; \mathrm{m}$

So, the child's is standing at a distance $p=2\; \mathrm{m}$ from the concave mirror.