Deduce the relation `f^(2) = ` ab , where 'a' and 'b' are the distance of an object and its real image from the principal focus and 'f' its focal length .

Explanation

Given, u = f + a, v = f + b
substituting the values in the mirror equation, we get `(1)/(f) = (1)/(u) + (1)/(v) = (1)/(f + a) + (1)/(f + b) `
`(1)/(f) = ((f + b) + (f + a ))/((f + a) (f + b)) = ( f + b + f + a)/(f^(2) + bf + af + ab)`
`f^(2) + bf + f^(2) + af = f^(2) + bf + af + ab " " therefore f^(2) = ab `