Final answer:
To find the position of the second car as seen in the mirror of the first car, we use the mirror equation for convex mirrors, considering that the image formed will be virtual, reduced, and behind the mirror.
Step-by-step explanation:
The given problem is related to the application of the mirror equation for a convex mirror to determine the position of a virtual image formed by a second car as observed through the side mirror of a first car. The focal length (f) of the convex mirror is given to be 30 cm (note that focal lengths for convex mirrors are considered positive), and the object distance (do), which is the distance of the second car from the mirror, is given to be 5 m or 500 cm. Since the mirror is convex, we expect the image to be virtual, reduced in size, and located behind the mirror.
Using the mirror equation
1/f = 1/do + 1/di, where di is the image distance, we can calculate the position of the image of the second car. Since for a convex mirror the image distance (di) is always negative (indicating the image is virtual and behind the mirror), we can rewrite the equation as:
1/-30 = 1/500 + 1/di.
To find the image distance, we first take the reciprocal of both sides, which gives us:
-1/30 = 1/500 + 1/di, then we solve for 1/di giving us 1/di = -1/30 - 1/500. After finding a common denominator and simplifying, we get the value of di. The image position as seen in the mirror will be this calculated distance, negative indicating that it is virtual and behind the mirror.
Thus, the position of the second car as seen in the mirror of the first car will be found using the mirror equation and understanding that the image will be virtual, reduced, and situated behind the convex mirror.