The rear window in a car is approximately a rectangle, 2.1 m wide and 0.45 m high. The inside rearview mirror is 0.55 m from the driver's eyes, and 1.70 m from the rear window.
a) What is the minimum length for the rearview mirror if the driver is to be able to see the entire width and height of the rear window in the mirror without moving her head?
b) What is the minimum height for the rearview mirror if the driver is to be able to see the entire width and height of the rear window in the mirror without moving her head?
Answer:
The angle of incidence and the angle of reflection to the driver's eyes is the same. Thus, the convergence point of the mirror centre (if the light passed straight through it) will be 0.55m. (55cm) in front of the mirror.
(1.7 + 0.55) = 2.25 metres, or 225cm.
Half the window width is 1.05 metres, or 105cm.The angle of incidence is arctan (105/225) = 25 degrees (also isthe reflection angle).The half width of the mirror will be (55 x tan 25) = 25.6666cm., so mirror width is 51.3cm.
You can use the same process as above with 1/2 the window height, to find the angle of incidence/ reflection and the 1/2 height of the mirror, = 5.5cm.(11cm mirror height needed).
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