Your smartphone's camera can be modeled using a thin lens placed in front of a sensor that automatically moves to ensure the image remains in focus.

a$)$ Develop a model of the lens$-$sensor system based on geometric optics and propose an equation for measuring the focal length of the lens from several images of an object of known size obtained at several distances.

b$)$ Estimate the focal length of the lens. Describe the methodology used clearly. Does it match your phone's specifications? It might be helpful to know the pixel size of your smartphone $($keywords: pixel size, pixel pitch$).$