Answer:
The distance of the car from the mirror is 10 times the distance of the image of the car from the mirror
Explanation:
The parameters of the mirror image are;
The height of the car's image, h' = -14 cm (The image is inside the mirror and therefore, -ve)
The height of the car, h = 140 cm
The radius of curvature of the mirror, R = 60 cm
The mirror formula is given as follows;
[tex]\dfrac{1}{u} + \dfrac{1}{v} = \dfrac{1}{f}[/tex]
Where;
u = The distance of the car from the mirror
v = The distance of the image of the car from the mirror
f = The focus of the mirror ≈ R2
The focus of convex mirrors is negative, therefore, f = -62 cm/2 = -32
[tex]The \ magnification,\, m = \dfrac{h'}{h} = \dfrac{v}{u}[/tex]
Therefore, we get;
[tex]The \ magnification,\, m = \dfrac{14}{140} = \dfrac{v}{u}[/tex]
14·u = 140·v
∴ u = 140·v/14 = 10·v
The distance of the car from the mirror = 10 × The distance of the image of the car from the mirror