A car is moving with at a constant speed of 60 km h–1 on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km h–1. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 s till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?
The mirror formula is:
where f is the focal length, u is the object distance and v is the image distance. All quantities are measured with the Cartesian sign convention (the sign convention in NCERT).
Differentiating the mirror equation with respect to time , we get
Substitute 
and 
where s0 and si are the speed of the object and the image respectively.
Using the mirror equation,
Option (a):
Let the forward direction be positive.
Velocity of the car ahead with respect to ground, 
Velocity of the car at the rear with respect to the car ahead , 
Let the velocity of the car at the rear with respect to the ground be 
Now,
Hence, (a) is incorrect.
Option (b):
The speed of the image is not equal to the speed of the object. This is incorrect.
Option (c):
From the above equation, we can see that as the object distance decreases, the speed of the image increases. (Note that it is a convex mirror and f is positive). Hence, (c) is incorrect.
Option (d):
We have established that the speed of the image increases as the distance decreases. Thus, (d) is correct.