Question

Image of an object approaching a convex mirror of radius of curvature 20m along its optical axis is observed to move $\dfrac{25}{3}m \ to \ \dfrac{50}{7}m$in 30 seconds. What is the speed of the object in km/h?
A. 3
B. 2
C. 3.5
D. 3.2

Answer 1

Hint: Speed of an object is defined as the ratio of distance travelled by it to the time taken to move the distance. When an object is moved in front of a convex mirror, the image also moves along with it. The velocity of an object could be obtained by dividing object distance corresponding to two given points with the time taken.
Formula used:
$\dfrac1f = \dfrac 1u + \dfrac 1v$

Complete answer:
First of all we shall find the position of image ‘u’ for the two point
For $v = \dfrac{25}{3}m$.
Given R = 20m for convex mirror. Thus $f = \dfrac R2 = \dfrac {20}{2} = 10m$
Now using: $\dfrac1f = \dfrac 1u + \dfrac 1v$
$\dfrac{1}{10} = \dfrac1u + \dfrac{1}{\dfrac{25}{3}}$
$\dfrac1u = \dfrac{1}{10} - \dfrac{3}{25}$
$\implies u = -50m$
For $v = \dfrac{50}{7}m$
$\dfrac1f = \dfrac 1u + \dfrac 1v$
$\dfrac{1}{10} = \dfrac1u + \dfrac{1}{\dfrac{50}{7}}$
$\dfrac1u = \dfrac{1}{10} - \dfrac{7}{50}$
$u = -25 m$
Hence the distance moved by the object must be $|-25-(-50)| = 25 m$
Thus speed of image = $\dfrac{25}{30} m/s = \dfrac56 \times \dfrac {18}{5} = 3 km/h$.

So, the correct answer is “Option A”.

Additional Information:
A convex mirror can be used to view over a large angle of sight. These types of mirrors are certainly used on highways and in cars. This is because a convex mirror produces a virtual image of the object and can cover a large area. A concave mirror can be used to produce enlarged and diminished images of any object depending upon the location of the object in front of it.

Note:
Ever wondered why its written “OBJECTS IN THE MIRROR ARE CLOSER THAT THEY APPEAR” on the side view mirror of any vehicle? It is because the mirror has to cover a wider view of the road so that the driver can drive safely, so here a convex mirror is used which always produces a diminished image so our brain starts thinking that they must be far as they’re looking diminished.