Use of a smartphone camera to determine the focal length of a thin lens by finding the transverse magnification of the virtual image of an object

In this work we have determined the focal length of a concave lens by photographing the virtual image of an object by a smartphone camera. We have similarly determined the focal length of a convex lens by forming a virtual image of an object keeping it within the focal distance from the lens. When a photograph is taken by a smartphone, the transverse width of the image on the sensor of the camera in pixels can be read off by software available freely from the internet. By taking a photograph of the virtual image from two positions of the camera separated by a distance along the line of sight of the camera, we have determined the transverse width of the virtual image. From this we find the focal lengths of the lenses knowing the transverse width and the distance of the object from the lenses.