The rear window in a car is approximately a rectangle, 2.0 m wide and 0.65 m high. The inside rearview mirror is 0.50 m from the driver's eyes, and 1.80 m from the rear window. 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

Question

Kolby Ray

Physics

27 February, 20:01

The rear window in a car is approximately a rectangle, 2.0 m wide and 0.65 m high. The inside rearview mirror is 0.50 m from the driver's eyes, and 1.80 m from the rear window. 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

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Ruchus · Answer 1

0.43 m

Explanation:

Angle of incident and angle of reflection is same.

tan Θh = L' / x (eye)

L' = Length of the window

x (eye) = Distance of the mirror from the eye

tan Θh = L / (x (eye) + xw)

xw = Distance of the mirror from the window

L' / x (eye) = L / (x (eye) + xw)

L' = L*x (eye) / (x (eye) + xw)

L' = (2*0.5) / (0.5 + 1.8)

L' = 0.43 m