Newton's formula

Another useful formula for calculating the image position for a curved mirror is Newton's formula.

The diagram shows the position of an object and its image formed by a concave mirror.

Let the distances of the object and image from the principal focus of the mirror be x and y respectively.

Then: Object distance (u) = f+x and Image distance (v) = f+y

Using the mirror formula 1/u + 1/v = 1/f we have: 1/[f+x] + 1/[f+y] = 1/f and simplifying this we get: