NEWTON'S FORMULA

If x1 is the distance of the object from the first focus of the lens, x2 is the distance of the image from the second focus, and f is the focal length, we have

$$u=−(f + x1)$$

$$v=f+x2$$ 

The lens formula is, 

$$\frac 1v− \frac 1u=\frac 1f$$

The lens Formula becomes

$$\frac {1}{f+x2} - \frac {1}{-(f+x1)} = \frac1f$$

$$\frac {1}{f+x2} + \frac {1}{f+x1} = \frac1f$$

 $$1f+x2−1−(f+x1)=1f or x1x2=f2 $$This is called Newton’s formula.

$${f+x1 + f+X2}f = {f^2+fx1+fx2+x1x2}$$