Question

A real object is located at the zero end of a meter stick. A concave mirror located at the 100 cm end of the meter stick forms an image of the object at the 70 cm position. A convex mirror placed at the 60 cm position forms a final image at the 10 cm point. What is the radius of curvature of the convex mirror?

Answer 1

Here, the image formed by the concave mirror will act as virtual object for convex mirror.
Thus,
For convex mirror,
Object distance, u =- (70-60) =-10 cm
Image distance, v =+ (60-10) =+50 cm
Using mirror formula,
$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
$=\frac{1}{(-10)}+\frac{1}{\left(50\right)}=-\frac{4}{50}$
Or $f=-\frac{50}{4}=-12.5cm$
Radius of curvature, $R=2f=2\times 12.5=25cm$