You are trying to photograph a bird sitting on a tree branch, but a tall hedge i
ID: 1324844 • Letter: Y
Question
You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking your view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. For what distance must you set the focus of the camera lens in order to snap a sharp picture of the bird's image?
You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking your view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. For what distance must you set the focus of the camera lens in order to snap a sharp picture of the bird's image?Explanation / Answer
The mirror is a plane mirror (plane, not plain). That means the mirror is flat, so it just reflects the light without having a focal distance or any tricks like that. Also, the angle between the plane of the mirror and the light coming from the bird will be equal to the angle between the plane of the mirror and the light going to the camera. So, understanding those physics facts, the distance required is just the path length of the light beam -- bird to mirror, mirror to you. And it's a problem in trigonometry. The problem doesn't say, but it appears that the plane of the mirror is parallel to the y axis. Change the picture temporarily so that the bird is at the intersection of the y axis and the red line between bird and mirror. So the y axis and the 2 red lines make an isosceles triangle. Draw a line from the mirror to the y axis at y = (1/2)*4.2 m = 2.1 m. That gives you 2 right triangles. One side is 4.4 m and another is 2.1 m. The 3rd side is a hypotenuse. You can calculate the length of the hypotenuse using your trig skills. Now, the bird isn't really at the y axis. It's 2.1 m from the plane of the mirror measured in the x direction. The component of the hypotenuse in the x direction is 4.4 m. So the path length between the bird and the mirror is the hyupotenuse length * 2.1/4.4
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