Question

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?

Answer 1

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   = $\frac{h}{w}$   .................1

and

height /width of the window is

height /width  = $\frac{h_w}{w_w}$   .................2

and

distance of eye / window by the mirror is

distance of eye / window = $\frac{x_e}{x_w}$      .................3

so here

θ = θi  = θr    ....................4

and  tanθ for vertical is

tanθ  = $\frac{h}{x_e}$  

tanθ  =  $\frac{h_w}{(x_e + x_w)}$       ....................5

so

h =   $h_w \times \frac{x_e}{(x_e + x_e)}$     ....................6

put  here value and we get

$h = 0.30 \times \frac{0.50}{(0.50 + 1.50)}$  

h = 0.075 m

and

when we take here tanθ for horizontal than it will be

tanθ = $\frac{w}{x_e}$    

tanθ = $\frac{w_w}{(x_e + x_w)}$       .......................7

so

$w = w_w \times \frac{x_e}{(x_e + x_w)}$         ....................8

put here value and we get

$w = 1.3 \times \frac{0.50}{(0.50 + 1.50)}$  

w = 0.325 m