A convex mirror and a concave mirror face each other at

Solution

We are given a setup where a convex mirror and a concave mirror are placed facing each other, with a distance of 30 cm between them. A point object is placed midway, i.e., 15 cm from each mirror. We are asked to find the nature and position of the final image formed after double reflection — once from each mirror. 1.     First reflection — Concave mirror: o    Object is 15 cm from the concave mirror. o    Let’s assume focal length of concave mirror fc is greater than 15 cm. Then the object lies within the focal length, and the concave mirror forms a virtual, erect, and enlarged image behind the mirror (on the same side as the object). 2.     This virtual image becomes the object for the convex mirror: o    Since this image is closer to the convex mirror than the original object (because it’s virtual and behind the concave mirror), the convex mirror now sees this image as a real object placed in front of it. o    Convex mirrors always form virtual, erect, and diminished images, and these images are located behind the mirror. 3.     Second reflection — Convex mirror: o    The image formed by the convex mirror is virtual, and it appears to be between the two mirrors, but closer to the convex mirror. 4.     Now consider reverse path — object first reflects off convex mirror: o    Again, a virtual, erect, and diminished image is formed behind the convex mirror, acting as an object for the concave mirror. o    Since it’s behind the convex mirror (and hence in front of the concave mirror), the concave mirror now receives a virtual object, and the final image it forms will be real or virtual depending on distances. o    But in this symmetrical setup, the final image in both cases lies somewhere between the mirrors. Regardless of the order of reflection, the final image after two reflections (one from each mirror) is formed between the mirrors, and its nature may vary depending on focal lengths, but its position is guaranteed to lie between them.