Final answer:
To solve for the height of the top and bottom of the mirror required for a man to see his full reflection, apply the Law of Reflection, considering the man's eye level and the additional height of his head. The bottom of the mirror should align with his eye level, and the top should be halfway the height of his head above his eyes. The mirror's height from the floor will be the sum of the man's eye level height and half of the remaining head height.
Step-by-step explanation:
The question pertains to the Law of Reflection, which is a principle in physics that describes how light reflects off surfaces. To solve problem number 34, we can apply this law to determine the size of the mirror needed for a person to see their entire body. Given the man's eye level is 1.65 m and the top of his head is 0.13 m higher, using geometric relations and the Law of Reflection, we can determine the minimal height of the mirror.
Assuming the man is standing close enough to the mirror, the bottom of the mirror must be at or below the level of the man's eyes to see his feet in the reflection. Considering angles of incidence and reflection, the top of the mirror must be at least halfway the distance between his eyes and the top of his head. So, the bottom of the smallest mirror should be at a height of 1.65 m from the floor, and the top would be 1.65 m + 0.13 m / 2 = 1.715 m from the floor.
To find this distance, we calculate the top and bottom of the mirror as follows: Top of the mirror = height of eyes + (height of head / 2) = 1.65 m + (0.13 m / 2) = 1.715 m. The bottom of the mirror = height of eyes = 1.65 m. Therefore, the height of the mirror from the floor is 1.715 m - 1.65 m = 0.065 m or 6.5 cm, which relates to the man's total height by a factor of the head's height above the eyes, divided by two.