Question

the radius of curvature of a convex mirror is 20 cm.The size of the image formed is half to the size of the object. find the distance of the object and image

Answer 1

Dear Student,

$$\begin{gathered} magnification=\frac{1}{2} \\ \Rightarrow \frac{v}{u}=\frac{1}{2} \\ \Rightarrow v=\frac{1}{2}u \end{gathered}$$
In convex mirror the image and the object are on the two sides of the mirror.
So,$$\begin{gathered} \frac{1}{v}-\frac{1}{u}=-\frac{2}{r} \\ \Rightarrow \frac{2}{u}-\frac{1}{u}=-\frac{2}{20} \\ \Rightarrow u=-10cm \end{gathered}$$
Therefore
$v=5cm$
hence distance of object is 10 cm
distance of image is 5 cm