Question

An image of a car with height of 14 cm occurred in the mirror which is located at a T-intersection.if the car height is 140 cm and the radius of the curvature of the mirror is 60 cm, how far is the car from the mirror?​

Answer 1

The distance of the car from the mirror is 10 times the distance of the image of the car from the mirror

Step-by-step 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;

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

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

`The \ magnification,\, m = (h')/(h) = (v)/(u)`

Therefore, we get;

`The \ magnification,\, m = (14)/(140) = (v)/(u)`

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