How Much Can a 6ft Man See of His Image in a Mirror?

[SAWiz]

A 6ft tall man stands in front of a mirror (2ft tall)
The mirror is 5ft away from the man and 4 ft above the ground.
How much of his image can he see?



A 6ft tall man stands in front of a mirror (2ft tall)
The mirror is 10 ft away from the man and 4 ft above the ground.
How much of his image can he see?

 

[AtticusFinch]

By the laws of geometric optics the angle of reflection is equal to the angle of incidence. Both are measured to the normal (an imaginary line perpendicular to the mirror).

The 6ft tall man looks at the bottom of a mirror 2 feet below his head. Therefore a light ray entering his eye needs to have an angle of reflection of arctan(2/5). If you draw this out it becomes clear that the image that appears in the bottom of the mirror is a point 4 ft below the man's head.

Do the same as above for the next part and prove to yourself that it doesn't matter how far the man stands away from the mirror. He still can only see 4 ft below his head. (You can demonstrate this using a bathroom mirror).