Final answer:
The first virtual image created by the convex mirror is located at approximately -3.64 cm from the mirror, and in theory, there is an infinite series of progressively fainter and closer images due to multiple reflections, but practical observation depends on alignment and mirror quality.
Step-by-step explanation:
To determine the location of the images formed by the convex mirror in this scenario, we must consider both the reflection from the plane mirror and the subsequent reflection from the convex mirror. For simplicity, we'll assume that each mirror obeys the law of reflection and the mirror equations, considering the virtual image as an object for the convex mirror reflection.
The light bulb placed 10 cm from the plane mirror will create a virtual image 10 cm behind the plane mirror (as virtual images in plane mirrors lie as far behind the mirror as the object is in front of it). This virtual image is at a distance of 30 cm + 10 cm = 40 cm from the convex mirror.
The radius of curvature for the convex mirror is given as 8 cm, which means the focal length (f) is -4 cm (since the focal length for a convex mirror is negative and half the radius of curvature).
Using the mirror equation 1/f = 1/do + 1/di (where do is the object distance and di is the image distance), we can calculate the location of the first image in the convex mirror.
1/-4 = 1/40 + 1/di
1/di = 1/-4 - 1/40 = -1/4 - 1/40 = -10/40 - 1/40 = -11/40
di = -40/11
The first image is located at a distance of approximately -3.64 cm from the convex mirror, which is a virtual image because it is behind the convex mirror.
As for other images, we must consider multiple reflections between the mirrors. In theory, an infinite series of images can form due to the light bouncing back and forth between the plane mirror and the convex mirror. However, each subsequent image would be fainter and closer to the focal point of the convex mirror, eventually becoming imperceptible.
It is important to note that the practical observation of images will significantly depend on the alignment and distances between the mirrors and the quality of the mirrors used.