# Can someone help me with this hw problem

A child stands at the midpoint between two mirrors, which are separated by 10.0 m. One of the mirrors is a plane mirror, and the other mirrors is convex. The child looks at the two images and notices that her image in the plane mirror appears to be exactly twice as tall as her image in the convex mirror. This appearance is from her viewpoint - it does not represent the actuasl height of the images. The appearracne to the child will be based on two contributions - the actual height of the image in space and how far away the image is . Thus, acccoding to the child, the angle subtended by the image in the plane mirror is twice the angle subtended by the image in the convex mirror. what is the focal lenght of the convex mirror.

thanks

HallsofIvy
Homework Helper
The "actual" height of the image of the child in the plane mirror is the height of the child. The image appears to be 20 feet away (the mirror is ten feet away and the image appears to be 10 feet behind the mirror).

Let "f" be the focal length of the convex mirror and set up the formulas for size and distance to the image based on that. The apparent size of an image depends directly on the actual size of the image and inversely on the distance to the image (that's from "similar triangles"!).