Final answer:
The image formed when looking in the mirror will be located 55 cm from the lens.
Step-by-step explanation:
To find the location of the image when looking in the mirror, we need to consider the different components of the setup. The lamp is placed 40 cm in front of a converging lens of focal length 20 cm. There is also a plane mirror 15 cm behind the lens. First, we can use the lens equation 1/f = 1/di - 1/do to find the position of the image formed by the lens. Plugging in the values, we get 1/20 = 1/di - 1/40, which simplifies to di = 40 cm. Next, we can use the mirror equation 1/di' + 1/do' = 1/f to find the position of the final image formed by the mirror. Since the object distance is 40 cm (same as di), we can substitute this value into the equation and solve for di'. Therefore, the image formed by the mirror will be located 15 cm behind the mirror, at a distance of 55 cm from the lens.