Suppose a man stands in front of a mirror as shown below. His eyes are 1.38 m above the floor and the top of his head is 0.284 m higher. Find the height above the floor of the top of the smallest mirror in which he can see both the top of his head and his feet.
answer to 3 decimal places.
Answer :_
some points
law of reflection
diagram must be like this
For the Top of the mirror :-
From the figure , it is obvious that the top of the mirror is equal to GD, which is equal to
GD=GA+AD
Similarly as before we can find the distance GA , where thew triangle AGE and FGE shares the same adjecent side , and have the same angle as before due to law of reflection where the incident angle is equal to the reflected angle , and hence
And , from the givens we know that
AF=0.284
=GA+GF
=2GA
=2GF
thus,
thus, height of the top mirror which is equal to GD is
GD=GA+AD
= 0.142+1.38
= answer
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