How tall must a plane mirror be to see your full reflection?

[Novus Dakota]

How tall must a plane mirror be to let you see your entire reflection? I know i have to find the angle and incedince but i don't know where to go from there. i am 5 11. thanks

 

[kevinalm]

Think of the mirror as aperature halfway between you and your eye, only the optical path is folded so your eye is 2 times the distance to the mirror away from your body.

 

[thepatientmental]

To calculate the height of a plane mirror for full reflection, we can use the law of reflection, which states that the angle of incidence is equal to the angle of reflection. In this case, the angle of incidence is the angle at which you are looking at the mirror, and the angle of reflection is the angle at which your reflection appears to be in the mirror.

Since we know that the angle of incidence and the angle of reflection are equal, we can use basic trigonometry to find the height of the mirror. Let's say that you are standing 5 feet away from the mirror and your height is 5 feet 11 inches (5.917 feet). Using the tangent function, we can set up the following equation:

tan θ = opposite/adjacent

Where θ is the angle of incidence, opposite is your height (5.917 feet), and adjacent is the distance from you to the mirror (5 feet). Solving for θ, we get:

θ = tan^-1(5.917/5) = 51.3 degrees

Since the angle of incidence and the angle of reflection are equal, the angle of reflection is also 51.3 degrees. Now, we can use the same equation to find the height of the mirror:

tan θ = opposite/adjacent

Where θ is the angle of reflection, opposite is the height of the mirror, and adjacent is the distance from the mirror to the floor (which we can assume is the same as the distance from you to the mirror, 5 feet). Solving for opposite, we get:

opposite = tan(51.3) x 5 = 6.45 feet

Therefore, the mirror must be at least 6.45 feet tall to allow you to see your entire reflection. Keep in mind that this is just an estimate and may vary depending on your exact height and distance from the mirror.