An object is located 13.5 cm in front of a convex mirror, the image being 7.05 cm behind the mirror. a second object, twice as tall as the first one, is placed in front of the mirror, but at a different location. the image of this second object has the same height as the other image. how far in front of the mirror is the second object located?

Second object is located at 42.03 cm in front of mirror

Explanation:

In this question we have given,

object distance from convex mirror ,u=-13.5cm

Image distance from convex mirror,v=7.05cm

let focal length of convex mirror be f

we have to find the distance of second object from convex mirror

we know that u, v and f are related by following formula

.............(1)

put values of u and v in equation (1)

we got,

we have given that

second object is twice as tall as the first object

and image height of both objects are same

it means

.............(2)

we know that

therefore,

.................(3)

put values of v and u in equation 3

therefore from equation 2

we know that

.................(4)

put value of and in equation 4

we know that U,V and f are related by following formula

.............(5)

put values of f and U in equation 5

we got

Therefore,

U=-10.91\times 3.85

U=-42.03 cm

Second object is located at 42.03 cm in front of mirror

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