A convex mirror is on the exterior of the passenger side of many trucks (see the

Question

A convex mirror is on the exterior of the passenger side of many trucks (see the figure(Figure 1) ). If the focal length of such a mirror is -40.0 cm,

Part A) What will be the location of the image of a car that is 1.5 m high and 110 m behind the truck mirror?

Part B) What will be the height of the image of a car that is 1.5 m high and 110 m behind the truck mirror?

Part C) What will be the location of the image of a car that is 1.5 m high and 11.5 m behind the truck mirror?

Part D) What will be the height of the image of a car that is 1.5 m high and 11.5 m behind the truck mirror?

Explanation / Answer

f = -40 cm , do = 110 m, ho =1.5 m

part A: From mirror formula

(1/f) = (1/u) + (1/v)

-(1/40) = -(1/110) +(1/v)

v = -62.86 cm

image position is 62.86 cm from the mirror

Part B: from lateral magnification

hi/ho = -di/do

hi/1.5 = (62.86/110)

image height hi = 0.857 m

Part C:

f = -40 cm , do = -11.5 m, ho =1.5 m

From mirror formula

(1/f) = (1/u) + (1/v)

-(1/40) = -(1/11.5) +(1/v)

v = 16.14 cm

image position is 16.14 cm from the mirror

Part D: from lateral magnification

hi/ho = -di/do

hi/1.5 = (16.14/11.5)

image height hi = - 2.1 m

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