Question

A person is standing a distance D = 5.8 m in front of a flat, vertical mirror. The distance from the ground to his eyes is H = 1.6 m. An object is placed on the ground a distance d = D/2 = 2.9 m in front of the mirror. At what height h should the bottom of the mirror be so that the person can see the bottom of the object?

Answer 1

To see the bottom of the object in the mirror, the bottom of the mirror should be at a height of half the height of the person.

Step-by-step explanation:

To see the bottom of the object in the mirror, the person should be able to see an image of the bottom of the object reflected in the mirror.

Using the law of reflection, we can determine the height h at which the bottom of the mirror should be. The angle of incidence for the light from the bottom of the object is equal to the angle of reflection, so the height of the mirror should be equal to the height of the person's eyes, H, plus the height of the bottom of the object, h. We can calculate h using similar triangles:

h/H = d/D

where d is the distance from the object to the mirror and D is the distance from the person to the mirror. Substituting the given values, we have:

h = (d/D) * H

Substituting d = D/2, we get:

h = (D/2D) * H = H/2

Therefore, the bottom of the mirror should be at a height of half the height of the person.

Answer 2

it is at height of y = 0.533 m from ground

Step-by-step explanation:

As per law of reflection we know that angle of incidence = angle of reflection

so here we have

`tan\theta_i = tan\theta_r`

here we know that

`tan\theta_i = (y)/(d)`

also we have

`tan\theta_r = (H - y)/(D)`

now we have

`(H - y)/(D) = (y)/(d)`

here we have

`(1.6 - y)/(5.8) = (y)/(2.9)`

`3y = 1.6`

`y = 0.533 m`