Question

The rear window in a car is approximately a rectangle, 1.5 m wide and 0.70 m high. The inside rearview mirror is 0.60 m from the driver's eyes, and 2.00 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?

Answer 1

Answer:

Length of rear-view mirror = 0.3462 m

Step-by-step explanation:

• As per the attachment first thing we need to calculate is the angle of incidence of light "α" reflected from the rear view mirror to the eyes of the driver.

• As per the diagram the following calculations are:

• α = arctan(half length L of the rear view window / distance between the focus point and the centre of the rear view window).

• half length L of the rear view window = 1.5/2 = 0.75 m

• Distance between the focus point and the center of the rear view window = 0.6+2.0 = 2.6 m

hence,

• α = arctan(0.75/2.6)
• α = 16.091 degrees

Now the we will use α to calculate length of the rear view mirror.

length of the rear view mirror = 2 x 0.6 x tan(α)

length of the rear view mirror = 2 x 0.6 x tan(16.091)

length of the rear view mirror = 0.3462 m