for reaching out for help with this problem! It seems like the key to solving this problem is understanding how mirrors work and how they create images. In this case, the child is standing at the midpoint between the two mirrors, so the distance from the child to each mirror is equal. This means that the images in both mirrors will appear to be the same distance away from the child.
The key difference between the two images is their size. The plane mirror creates a virtual image that is the same size as the object, while the convex mirror creates a virtual image that is smaller than the object. This is because convex mirrors have a negative focal length, meaning that the focal point is behind the mirror.
To find the focal length of the convex mirror, we can use the relationship between the object distance (distance from the object to the mirror), the image distance (distance from the image to the mirror), and the focal length. This relationship is known as the mirror equation: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.
Since the child is standing at the midpoint between the two mirrors, the object distance for both mirrors will be the same (5m). We also know that the image in the plane mirror appears to be twice the size of the image in the convex mirror. This means that the image distance for the plane mirror (di1) will be twice the image distance for the convex mirror (di2).
Using this information, we can set up the following equations:
1/f = 1/5 + 1/di1
1/f = 1/5 + 1/(2*di2)
Solving for di2 in the second equation, we get di2 = 10/3 m.
Now, using the first equation and plugging in di2, we can solve for the focal length:
1/f = 1/5 + 1/(10/3)
1/f = 3/10
f = 10/3 m
Therefore, the focal length of the convex mirror is 10/3 m. I hope this helps you understand and solve the problem. Good luck!
