The Problem:
A motor car is fitted with a convex rear view mirror of focal length 20 cm. Another car, which is 2.1 m broad and 1.05 m high, is positioned 4 m behind the first car. We need to determine the size of the image of the second car as seen in the mirror of the first car.

Solution:

Step 1: Identify the Given Information
In order to solve the problem, we need to identify the given information:

- Focal length of the convex rear view mirror: 20 cm
- Distance between the two cars: 4 m
- Dimensions of the second car: 2.1 m (breadth) and 1.05 m (height)

Step 2: Calculate the Distance of the Second Car from the Mirror
Since the distance between the two cars is given as 4 m, we can calculate the distance of the second car from the mirror by subtracting the width of the second car from the total distance between the two cars.
Distance of the second car from the mirror = Total distance - Width of the second car
Distance of the second car from the mirror = 4 m - 2.1 m
Distance of the second car from the mirror = 1.9 m

Step 3: Calculate the Size of the Image
Now, we can use the mirror formula to calculate the size of the image of the second car.
Mirror Formula: 1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the image distance
- u is the object distance

In this case, the object distance (u) is the distance of the second car from the mirror, which we calculated as 1.9 m. Since the mirror is convex, the image formed will be virtual and erect. Therefore, the image distance (v) will be negative.
1/f = 1/v - 1/u
1/0.2 = 1/v - 1/1.9
5 = 1/v - 1/1.9
1/v = 5 + 1/1.9
1/v = (5 * 1.9 + 1) / 1.9
1/v = 10.5 / 1.9
v = 1.9 / 10.5
v ≈ 0.181 m

Step 4: Calculate the Size of the Image
Now, we can calculate the size of the image using the magnification formula.
Magnification (m) = -v / u
Magnification (m) = -0.181 / 1.9
Magnification (m) ≈ -0.095

Step 5: Interpret the Result
The negative magnification indicates that the image formed is inverted. Therefore, the size of the image of the second car as seen in the mirror of the first car is approximately 0.095 times the actual size of the second car.

Summary:
The size of the image of the second car, as seen in the convex rear view mirror of the first car, is approximately 0.095 times the actual size of the second car.