Final answer:
The final image formed by the system is a virtual and upright image located at -14.48 cm behind the convex mirror with a height of 0.68 cm. The image is smaller compared to the original object.
Step-by-step explanation:
To find the location, orientation, and size of the final image formed by the system of a converging lens and a convex mirror, we can use a step-by-step approach. First, we need to find the image created by the converging lens using the lens formula: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the object distance, and di is the image distance.
For the converging lens with a focal length of 40 cm and an object placed 50 cm in front of it, the image distance di can be calculated as follows:
1/40 = 1/50 + 1/di
Di comes out to be 200 cm, indicating that the image is 200 cm on the other side of the lens, and it would be real and inverted since it is a converging lens and do > f. The magnification (m) can be calculated using the magnification formula: m = -di/do. Therefore, m = -200/50 = -4. This means the image is 4 times larger than the object, so the image height would be -8 cm (the negative sign indicates the image is inverted).
Now, this first image will act as an object for the convex mirror. Since the lens and mirror are 30 cm apart, the object distance for the mirror will be 200 cm - 30 cm = 170 cm. However, since this object distance is positive and the convention for mirrors takes object distances as negative, we actually use -170 cm. Using the mirror formula 1/f = 1/do + 1/di (with the convention that the focal length of convex mirrors is positive), we get:
1/15 = -1/170 + 1/di
Calculating di gives us -14.48 cm, which is behind the convex mirror, meaning the final image is virtual and upright. The magnification for the mirror can be calculated as m = -di/do, yielding m = -14.48/-170 = 0.085. Therefore, the final image size is 0.085 * -8 cm = -0.68 cm. Since the image is virtual and upright for the convex mirror and the original image was inverted, the final image will be upright relative to the original object.