# A bus driver has the centre of a 20 cm wide plain mirror placed 50 cm in front of him. if the rear of the bus is 500 cm directly behind the plain mirror, how wide id the field of vision of the bus driver whenever he looks into the mirror while driving?

Jul 8, 2016

When viewed through the mirror the field of vision is said to be the area visible from the perspective of the observer .It actually depends on the visual angle at the the eye subtended by the two extreme points of the mirror. The field of vision increases with increase of visual angle
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So it depends on followings

• The position of with respect to the mirror
• The distance of observers' eye from the mirror
• The length of the mirror

The above figure explains the phenomenon of our problem
Where

• $M N \implies \text{Mirror of length of 20 cm}$
• $E \implies \text{Position of driver's eye}$
• $d = \text{ Distance from the center C of mirror MN} = 50 c m$

To get the field of vision when viewed through the mirror we are to draw the reflected rays coming to the eye of the observer being incident on two extreme points on the mirror , M and N as in our case .

Let at a distance of 500cm from the mirror the width of the field of vision be x , So the distance from point V will be (500+50)cm =550 cm
Now applying properties of similar triangle we can write

$\frac{x}{\text{MN"=550/"VC}}$

$\implies \frac{x}{20} = \frac{550}{50}$

$\implies x = 20 \times 11 = 220 c m$