Answer :
Answer:
Horizontal distance to floor = 0.7246 m or 72.46 cm
Explanation:
The reflection of the nearest part of the floor will be seen at the bottom part of the mirror.
Let's start by imagining there is beam starting from the person's eyes hitting the bottom part of the mirror. It will be reflected at the same angle as it arrived. To find this angle we will use the following lengths:
Vertical Distance of eyes - Vertical distance of bottom edge of mirror
= 1.62 - 0.4 = 1.22 m
This will be used with the distance from the wall (2.21 m) to find the angle of incidence of the beam.
This is:
Tan(theta) = Perpendicular/Base
Tan(theta) = 1.22 / 2.21 = 0.552036
Taking the inverse of tan to find theta we get: Theta = 28.9°
This is the angle of incidence, and the angle of the reflected ray will thus be 90° - 28.9° = 61.1°
Since the height of the mirror and angle of reflection of the beam are known, we can calculate the horizontal distance of the floor:
Tan (61.1°) = Horizontal distance to floor / height of mirror
Tan (61.1°) = Horizontal distance to floor / 0.4
Horizontal distance to floor = 0.7246 m or 72.46 cm
The horizontal distance to the base of the wall is 0.724 m or 72.4 cm.
How do you calculate the horizontal distance?
Given that the person's eyes are 1.62 m above the floor. The person stands in front of a vertical plane mirror whose bottom edge is 40 cm above the floor.
Hence the reflection of the floor will be seen in the mirror.
Let consider that the person is seeing at the bottom of the mirror. The length of the perpendicular is given below.
Perpendicular Length = Vertical Distance of eyes - Vertical distance of the bottom edge of the mirror
Perpendicular Length = 1.62 - 0.4 = 1.22 m
The angle of reflection is calculated by given below.
The Angle of Reflection = Perpendicular Distance / Distance between the person and mirror
[tex]tan \theta = \dfrac {1.22}{2.21}[/tex]
[tex]tan \theta = 0.5520[/tex]
[tex]\theta = 28.9^\circ[/tex]
Thus the angle of reflection is 28.9 degrees.
The angle of incidence is calculated as given below.
Angle of Incidence = 90 degrees - angle of reflection
Angle of Incidence = [tex]90 ^\circ - 28.9 ^\circ[/tex]
Angle of Incidence = [tex]61.1^\circ[/tex]
This angle of incidence is used to calculate the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor.
Angle of incidence = Horizontal distance to floor / height of mirror
[tex]tan 61.1^\circ = \dfrac {x}{0.40}[/tex]
[tex]1.81 \times 0.4 = x[/tex]
[tex]x = 0.724 \;\rm m[/tex]
Hence the horizontal distance to the base of the wall is 0.724 m or 72.4 cm.
To know more about the distance, follow the link given below.
https://brainly.com/question/10681300.