You unconsciously estimate the distance to an object from the angle it subtends in your field of view. This angle θ in radians is related to the linear height of the object h and to the distance d by θ = h/d. Assume that you are driving a car and another car, 1.50 m high, is 24.0 m behind you.
(a) Suppose your car has a flat passenger-side rearview mirror, 1.55 m from your eyes.
How far from your eyes is the image of the car following you?
(b) What angle does the image subtend in your field of view?
(c) What If? Suppose instead that your car has a convex rearview mirror with a radius of curvature of magnitude 2.00 m (Fig. P36.19). How far from your eyes is the image of the car behind you?
(d) What angle does the image subtend at your eyes?
(e) Based on its angular size, how far away does the following car appear to be?