A small object of height h is placed perpendicular to the principal axis of a convex mirror of focal length f at a distance x from the pole of the mirror. An observer is located on the principal axis at a distance L from the pole of the mirror. (Take x,f,L≫h).
(1) Calculate the angle α formed by the image at the eye of the observer.
(2) If the convex mirror is replaced by a plane mirror, with all other things remaining unchanged, calculate the angle β formed by the image at the eye.
(3) Justify the statement "objects are closer than they appear" written on the rear view mirror of your car.