S3 Physical - light reflection

Leung

2015-01-17 11:40 pm

A room with length 13m and width 8 m. A pinhole video camera is installed at the corner R. The camera is filming the door XY through the mirror AB hung on the opposite wall. The width of the door is 3m. The distance between point X on the door and point Q is 1m.

1. Draw two rays to show hot the camera at the corner R can film the door XY ?

2. What is the minimum length of the plane mirror AB so that the pinhole camera can film the whole door XY ?

Location of image : https://www.sendspace.com/file/vt2bjb

Tks

回答 (1)

天同

2015-01-18 2:35 am

✔ 最佳答案

1. See diagram below:

圖片參考：https://s.yimg.com/rk/HA00458726/o/606561831.jpg

2. Refer to the diagram (the diagram is not to scale):

圖片參考：https://s.yimg.com/rk/HA00458726/o/1544652693.jpg

X'Y' is the image of mirror XY.
Let h be the minimum length of mirror AB
Consider triangle RAS, AS = (13 - 7 - h) = (6 - h) (because PS = 13 m)
RS = PQ = 8 m

Consider triangle RY'E,
RE = (8 + 8) m = 16 m
(because ES = RS = 8 m, distance of image behind mirror equals to distance of object from mirror)
Y'E = YR = (13 - 1 - 3) m = 9 m

Since trangles RAS and RY'E are similar,
AS/RS = Y'E/RE
i.e. (6-h)/8 = 9/16
solve for h gives h = 1.5 m

The minimum length of the mirror is 1.5 m

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