Question

A person is six feet tall .How tall must a vertical mirror be if he is able to see his entire length?

explain answer mathematical !
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Answer 1

sᴏʟᴜᴛɪᴏɴ

let a person height be h = 6 feet

now assume a mirror of height h' which is hanged vertically in front of mirror in a such a way he is able to see his entire length.

mirror is X distance from person .

since it's a plane mirror then the image is formed X distance behind the mirror of same height h.

now

see attachment

In triangle AEF

$\tan( \alpha ) = \frac{ef}{ae}$

=( h'/2)/X ..... (1)

in triangle ADC

$\tan( \alpha ) = \frac{dc}{ad}$

=( h/2)/2x. ..... (2)

equating equation. ( 1) and (2)

(h'/2)/x = (h/2)/2x

h'/2x = h/4x

h '/h = 2x/4x

h' = h/2

⏩ h' = 3 feet [ h = 6 feet ]

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Answer 2

Answer:

3ft

If the top end of the mirror will be placed at the level of person eye then the image will be formed by following the law of reflection. Since

Angle of incidence = Angle of reflection

The part of the body in front of the mirror will be seen clearly by the eye. Moreover, a double length will also get reflected from the end of the mirror.

Thus if  the total length of the body is L then we need the length of the mirror to be L/2 to see the complete image. So if the person's height is 6 feet, we need a minimum 3 feet mirror which is placed at the level of eye to see the complete image of the person.

Explanation:

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