**Problem 6.86: A concave mirror forms an image, on a screen $2.00 \:m$ in front of the mirror, of a lamp $20.0 \:cm$ in front of the mirror. Find the radius of curvature of the mirror?**

**Solution:**

Here the object, that is the lamp is at a distance of $20.0 \:cm$ and the image on the screen is at $3.00 \:m$. Both image and object are on the same side of the mirror.

Object distance, $u\:=\:-20\:cm$ and image distance $v\:=\:-2\:m\:=\:-200\:cm$.

Let us use mirror equation $\frac{1}{f}\:=\:\frac{1}{v}\:+\:\frac{1}{u}$.

Therefore, $\frac{1}{f}\:=\:\frac{1}{-200}\:+\:\frac{1}{-20}\:=\:\frac{-11}{200}$.

Or focal length $f\:=\:\frac{-200}{11}$.

Radius of curvature is twice focal length.