Question

A bus driver is reversing his bus at a speed $8m/s$. The rear view mirror of a bus is a plane mirror. The driver sees in his rear view mirror the image of a car parked behind his bus. The speed at which the image of the car appears to approach the driver will be
A. $2m/s$
B. $4m/s$
C. $8m/s$
D. $16m/s$

Answer 1

Hint: The Plane mirror has focal length equal to infinity and thus distance of image and object with respect to mirror is equal.
In this question the speed of the image of the car at which it approaches is asked with respect to the driver which means the observer.
And if the driver of the bus moves backwards with x speed, he sees in the plane mirror that the image of the car will approach him with 2x speed with respect to him. This is the relative observation.

Complete step by step answer:
The mirror in the bus is a plane mirror whose power is zero and focal length is infinite. The distance between object and image with respect to mirrors is the same.
Hence the speed with which the car will be seen by the bus driver is twice with which the bus itself is moving.
It is due to relative viewing as the image is being viewed by the driver in the plane mirror and he will observe it travelling twice the distance or speed to which the bus is moving backwards.
The speed by which the bus is moving backwards $8m/s$
And the speed by which the image of car is seen by the driver in the plane mirror is
$\Rightarrow 2\times 8=16m/s$

So, the correct answer is “Option D”.

Note: Law of reflection is seen in mirrors and law of refraction is seen in lenses.
Mirror formula is the fundamental formula in optics which relates the object distance, image distance and focal length in cases of spherical mirrors.
Lens maker's formula is another important formula which establishes the relation between the focal length of a lens to its refractive index and the radii of curvature of its two surfaces.