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The place you get your hair cut has two nearly parallel mirrors 7.00 apart. As you sit between these mirrors in the chair, your head is 2.50 from the mirror in front of you. Looking toward this mirror, you first see your face and then, farther away, the back of your head. Side note: The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem. Neglect the thickness of your head. 1.How far away does the back of your head appear to be? (from you)

Respuesta :

Answer:

[tex]a''_b=18\ m[/tex]

Explanation:

Given:

  • distance between the parallel mirrors, [tex]l=7\ m[/tex]
  • distance of the head from the front mirror, [tex]a=2.5\ m[/tex]

By the laws of reflection we know that the image of an object appears at the same distance from the surface of a plane mirror as that of the object from the surface of the mirror.

Now the distance of the head from the rear mirror:

[tex]b=7-2.5[/tex]

[tex]b=4.5\ m[/tex]

Now the distance of image of the back of head in the rear mirror from the object head:

[tex]b'=2\times 4.5[/tex]

[tex]b'=9\ m[/tex]

Now this image is reflected into the front mirror from the image of the back of the heat in the rear mirror.

So, this is the second reflection of the actual object, which will form at a distance of:

[tex]a''_b=2\times 9[/tex]

[tex]a''_b=18\ m[/tex]

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