Final answer:
The question involves using the lens formula and mirror equation to determine the location of the image produced by a converging lens and reflecting off a plane mirror, as well as using the magnification formula to find the image size.
Step-by-step explanation:
The student's question pertains to light reflection from mirrors and involves calculations based on the ratios of side length between mirrors and focus on creating an image through a converging lens and a plane mirror.
To solve where the image would be when looking into the mirror for the given scenario (lamp height of 5 cm and 40 cm in front of a lens with focal length of 20 cm), one would apply the lens formula (1/f = 1/do + 1/di) and the mirror equation to find the image distance (di) created by the lens, and then consider the additional reflection from the plane mirror. The magnification formula (magnification = image height/object height) helps to determine the size of the image. By considering the optical principles of reflection and refraction, one can locate the image produced.