1. **Problem statement:** A girl stands 1.5 m from a wall with her eyes 1.6 m above the ground. A light source is on the wall 3 m horizontally from the girl and 2 m above the ground. We want to find the height on the wall to place a mirror so the girl can see the light reflected from it. 2. **Key principle:** The angle of incidence equals the angle of reflection. The mirror must be placed at a point on the wall where the light ray from the source reflects to the girl's eyes. 3. **Set coordinates:** Let the wall be the vertical line at $x=0$. The girl is at $x=1.5$ m, $y=1.6$ m. The light source is at $x=3$ m, $y=2$ m. 4. **Find the mirror height $h$ at $x=0$:** The mirror lies on the wall at $(0,h)$. 5. **Calculate slopes:** - Slope of light ray from source to mirror: $$m_1 = \frac{h - 2}{0 - 3} = \frac{h - 2}{-3} = -\frac{h - 2}{3}$$ - Slope of reflected ray from mirror to girl: $$m_2 = \frac{1.6 - h}{1.5 - 0} = \frac{1.6 - h}{1.5}$$ 6. **Reflection condition:** The mirror's surface is vertical, so the angle between incident and reflected rays with the normal (horizontal) must be equal. For a vertical mirror, the slopes satisfy: $$m_2 = -m_1$$ 7. **Set equation:** $$\frac{1.6 - h}{1.5} = -\left(-\frac{h - 2}{3}\right) = \frac{h - 2}{3}$$ 8. **Solve for $h$:** $$3(1.6 - h) = 1.5(h - 2)$$ $$4.8 - 3h = 1.5h - 3$$ $$4.8 + 3 = 1.5h + 3h$$ $$7.8 = 4.5h$$ $$h = \frac{7.8}{4.5} = 1.7333...$$ 9. **Answer:** The mirror should be placed approximately at $1.73$ m above the ground. **Final answer:** C 1.73 m above the ground