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The rear window in a car is approximately a rectangle, 1.3 m wide and 0.30 m high. The inside rear-view mirror is 0.50 m from the driver’s eyes and 1.50 m from the rear window. What are the minimum dimensions that the rear-view mirror should have 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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Answer:

Height of mirror 0.075 m

width of mirror 0.325 m  

Explanation:

given data

wide = 1.3 m

high = 0.30 m

driver’s eyes = 0.50 m

rear window = 1.50 m

solution

we take here height / width of the mirror  is

height / width   = [tex]\frac{h}{w}[/tex]   .................1

and

height /width of the window is

height /width  = [tex]\frac{h_w}{w_w}[/tex]   .................2

and

distance of eye / window by the mirror is

distance of eye / window = [tex]\frac{x_e}{x_w}[/tex]      .................3

so here

θ = θi  = θr    ....................4

and  tanθ for vertical is

tanθ  = [tex]\frac{h}{x_e}[/tex]  

tanθ  =  [tex]\frac{h_w}{(x_e + x_w)}[/tex]       ....................5

so

h =   [tex]h_w \times \frac{x_e}{(x_e + x_e)}[/tex]     ....................6

put  here value and we get

[tex]h = 0.30 \times \frac{0.50}{(0.50 + 1.50)}[/tex]  

h = 0.075 m

and

when we take here tanθ for horizontal than it will be

tanθ = [tex]\frac{w}{x_e}[/tex]    

tanθ = [tex]\frac{w_w}{(x_e + x_w)}[/tex]       .......................7

so

[tex]w = w_w \times \frac{x_e}{(x_e + x_w)}[/tex]         ....................8

put here value and we get

[tex]w = 1.3 \times \frac{0.50}{(0.50 + 1.50)}[/tex]  

w = 0.325 m

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