f.5PHY一問

Draw the ray diagram as follows:
First draw the image of the man, which is at the same distance behind the mirror as the object (man) in front (say, d metres), with the same size as the object (1.8 m in height)
From the eyes of the man, construct two rays, one passess through the top of the mirror and end at the top of the man's image. The other passes through the bottom of the mirror and end at the feet of the man's image.
Now, you can see that the man'e eyes, the mirror and the image form two similar triangles, with heights (of triangles) equal to d and 2d respectively (the height of triangle is measured from the eye to the mirror and image).
Hence, d/2d = h/1.8
where h is the height of mirror
i.e. h = 1.8/2 m = 0.9 m
Since in the ray diagram, the rays pass through the top and bottom of the mirror, the height of 0.9 m so calculated is the mimium height.

人高度 1.8m

眼 1.74m

咁鏡要 1.74m + [(1.8m - 1.74m) / 2] <-- law of reflection

= 1.74m + 0.06m / 2

= 1.77m

2009-02-14 21:49:23 補充：
計漏野 @@

咁鏡要 [1.74m / 2] + [(1.8m - 1.74m) / 2] <-- law of reflection

= 0.87m + 0.03m

= 0.9m