A boy stands 3m from a plane mirror. His eyes are 1.5 above the floor.If he now moves to stand 6m from the mirror, can he still see his feet?
我唔係好明點解個答案係yes, 最好用圖解釋,唔該! ^_^
- 魏王將張遼Lv 71 十年前最愛解答
Again, with reference to the diagram below:
Suppose the boy stands straight and the mirror is also vertical, then lines L1 and L2 are perpendicular to his body.
Looking into the 2 pairs of right-angled triangles (one blue pair and one red pair), and together with the law of reflection, we can prove that the blue pair of triangles are congurent (reason: ASA) and so do the pair of red triangles.
Hence we can conclude that L1 meets the boy's body at the point between his top and his eyes and L2 meets the boy's body at the point between his eyes and his feet.
So to speak, L1 is 1.45m above the ground and L2 is 0.70m above the ground. Therefore the minumum required length of the mirror for the boy to be able to see his body's whole image is (1.45-0.70) = 0.75m which is half of his height.
In fact, for anyone to be able to his/her whole body's image, the mirror length should be half of his/her height.
And as D (the distance between the boy and the mirror) varies, the two pairs of right-angle triangles are still congurent and therefore the height of L1 and L2 above the ground are still the same, thus not affecting the minumum length of the mirror.
∴ If the boy moves towards or away from the mirror, he still can see his whole image.資料來源： My physics knowledge