13.1.16 | revision #19861 | Savchenko Solutions

Statement

13.1.16. A converging conical beam of light rays falls on a concave mirror. At what distance from the focus will the reflected rays intersect, if the mirror radius is $$80$$ cm, and the continuation of the rays intersects the main optical axis at a distance of $$40$$ cm from the mirror.

Solution

Conversely, we may ask where a light source should be placed in order that its image is formed $$40$$ cm behind the mirror. Using half the radius of curvature of the mirror as its focal length, we have

$u=\frac{vf}{v-f}=\frac{-40\cdot40}{-40-40}=20.$

Therefore, the object should be placed $$20$$ cm from the focal point toward the mirror.

Answer

$$20$$ cm from the focal point toward the mirror.