A girl 180cm tall stands facing a mirror mounted on a wall 150cm away. She can just see her feet at the bottom edge of the mirror and her eyes are 10cm below the top of her head. the bottom edge of the mirror should be _above the floor . Also, the minimum length of the mirror should be _ if she can see the top of her head.
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F3 physics reflection
2010-10-24 6:05 am
回答 (1)
2010-10-24 7:29 am
✔ 最佳答案
In dealing with problems on reflection by plane mirrror, it is always useful to draw the image and then complete a ray diagram.The image of the girl is 150 cm behind the mirror, and is also 180 cm tall. In order to see the feet, a light ray coming from the feet of the image, passing through the bottom edge of the mirror, will enter the eyes of the girl.
Let h be the height at which the bottom edge of the mirror is above the floor. Then by similar triaangle, it is not difficult to obtain the following relation,
h/150 = (180-10)/(150+150)
i.e. h = 85 cm
The bottom edge of the mirror is therefore 85 cm above the floor.
Now, draw a light ray from the head of the image, passing through the top edge of the mirror, and entering into the eyes of the girl.
Let H be the length of the mirror. Then by similar triangles,
H/150 = 180/(150+150)
i.e. H = 180/2 cm = 90 cm
The length of the mirror is 90 cm
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