Question

A motor car is fitted with a rear view mirror of focal length 20 cm . A second motor car 2 m broads and 21.6 m high is 6 m away from the first car. Find the position of the second car as seen in the mirror of the first car.

Answer 1

Hint: In the question the focal length and the object distance is given we are asked to find the image distance. We can simply find it by applying the mirror formula and simply solving it by putting the values given.

Formulas used:
$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$

Complete step by step answer:

In the above diagram, F is the focal length.
Now, we know that the focal length(f) of the rear view mirror is 20cm (given in the question).
Now, it is given in the question that a second motor car is just 6m away from the first car so,
Here according to the question, car is the object,
Hence, object distance, u = -6m or -600cm
We have been asked to find the image distance in the rear view mirror,
So we know that,
From mirror formula,
$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$,
$\dfrac{1}{20}=\dfrac{1}{v}-\dfrac{1}{600}$, (replacing with the given value of focal length and the object distance).
$\dfrac{1}{v}=\dfrac{1}{20}+\dfrac{1}{600}$,
$\dfrac{1}{v}=\dfrac{30+1}{600}$,
\[\dfrac{1}{v}=\dfrac{31}{600}\],
\[v=\dfrac{600}{31}\],
V = 19.35cm (answer)
Hence, we can say that the position of the second car as seen in the mirror of the first car is 19.35 cm back according to the mirror.
Additional Information:
The rear view mirror of the car is a convex mirror. A convex mirror is generally given as they have a very wide field of view, so it helps the driver or whoever is operating the car to see a wider image. It is also used because convex mirrors give images that are erect and the size of image is also small.

Note:
In the formula $\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$, ‘f’ is the focal length, ‘v’ is the image distance and ‘u’ is the object distance. We see that in the question maximum of the values are given to find the answer with the help of mirror formula. We must remember to convert all the different units into one single unit while doing calculations. We are considering u = - 6 m as it is a convex mirror and according to ‘y’ sign convention.