Answer:
The focal length of the convex mirror is 16 cm
Step-by-step explanation:
To find this, we need to use the principle of reversibility, which states that the path taken by a light ray from a point object to a mirror and back to the same point is the same as the path taken by a light ray from the mirror to the object and back to the mirror. In this case, the path of the light ray from the object to the convex mirror and back to the object is the same as the path of the light ray from the plane mirror to the convex mirror and back to the plane mirror.
We can use this principle to create a diagram showing the path of the light ray from the object to the convex mirror and back to the object. The object is located 40 cm from the convex mirror, and the plane mirror is located 32 cm from the object, so the distance from the object to the plane mirror is 40 - 32 = 8 cm. Since the images in the two mirrors coincide, the distance from the plane mirror to the convex mirror is also 8 cm. Therefore, the distance from the object to the plane mirror to the convex mirror and back to the object is 8 + 8 = 16 cm.
Since the focal length of a convex mirror is the distance from the mirror to the focus, which is the point where the light rays converge, the focal length of the convex mirror is 16 cm.