where \({n_2}\) and \({n_1}\) are the refractive indices of the material of the lens and of the surroundings respectively. For a double concave lens,
\(\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)\) is always negative.
Hence \(f\) is negative only when \({n_2} > {n_1}\)