Passive auto-focusing is a key feature in digital cameras and smart-phones which uses the image sharpness information to capture focused images without any user intervention. This paper introduces a new sharpness function for achieving passive auto-focusing in digital cameras and smart-phones. It is shown that this sharpness function produces a peak when the image is in-focus and drops when the image goes out-of-focus and the amount of drop is proportional to the degree of defocus. A comparison is made between this introduced sharpness function and the commonly used sharpness functions in terms of focusing accuracy and focusing speed. The results obtained indicate that the introduced sharpness function possesses a comparable accuracy while it achieves faster focusing.