A mirror used for rear-view of an automobile has a focal length $\displaystyle 2.0$ m. If a car is located at $\displaystyle 8.0$ m from the mirror -

(a)

Find out the position of the image of this car as seen in the mirror.

(b)

Draw the ray-diagram for image formation by the rear-view mirror.

(a) \(\displaystyle \mathrm{f}=+2 \mathrm{~m} \quad \mathrm{u}=-8 \mathrm{~m}\) \[\begin{aligned} & \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ & \frac{1}{v}=\frac{1}{f}-\frac{1}{u} \\ & \frac{1}{v}=\frac{1}{2}+\frac{1}{8} \\ & v=\frac{8}{5}=1.6 \mathrm{~m} \end{aligned} \] The image is formed $\displaystyle 1.6$ m behind the mirror