Question

The spherical side mirror on a car is convex and has a radius of curvature of 25 cm. Another car is following, 20 m behind the mirror. If the height of the car is 1.6 m, how tall is its image? (A) 5.0 cm (B) 2.0 cm (C) 4.0 cm (D) 0.99 cm

Answer 1

Answer:

(D) 0.99 cm

Explanation:

Given that the radius of curvature of the mirror is 25 cm.

And another car is following which is behind the mirror of 20 m.

$u=20m=2000cm$

Focal length is half of the radius of curvature and it is negative for convex lens.

Now the mirror formula.

$1/v+1/u=1/f$

So,

$1/v+1/2000=-1/(25/2)\\1/v=-1/2000-1/12.5\\v=-12.422cm$

Now

Magnification is,

$m=-v/u$

So,

$m=12.422/2000=0.00621$

So, Height of the image

$mh=0.00621\times 1.6 m\\mh=0.0099m\\mh=0.99cm$

Therefore, the image height is 0.99 cm.