Answer to Question #144646 in Optics for Promise Omiponle

Question

(Even if you can't access the image, you may still be able to solve) Suppose a man stands in front of a mirror as shown in the figure. His eyes are 1.85 m above the floor, and the top of his head is 0.15 m higher. https://usu34ny.theexpertta.com/images/bbpxdisb.ihe.png

(a) Find the height above the floor of the bottom of the smallest mirror in which he can see both the top of his head and his feet.
(b) Find the height above the floor of the top of the smallest mirror in which he can see both the top of his head and his feet.

Answer 1

a)

$$\theta_i=\theta_r\to\tan{\theta_i}=\tan{\theta_r}\\\frac{AB}{BC}=\frac{BD}{BC}\to AB=BC\\AD=AB+BD\\AD=2AB=2BD\\BD=0.5(1.85)=0.925\ m$$

b)

$$GD=GA+AD\\\theta_i'=\theta_r'\to\tan{\theta_i'}=\tan{\theta_r'}\\\frac{GA}{GE}=\frac{GF}{GE}\to GA=GF\\AF=0.15=GA+GF=2GA=2GF\\GA=0.5(0.15)=0.075\ m\\GD=0.075+1.85=1.925\ m$$