Suppose you have a concave mirror with a radius of curvature of 71.4 cm. What is the focal length of mirror?

Question

If then you place an object very far from the mirror, what is the location of the image? What is the magnification of the image?

Answer 1

well its a concave mirror so it has a real focal point and the focal length is taken to be positive. The focal length "f" is related to the radius of curvature "r" by: f = 1/2r  so in your case the focal length is 35.7cm.

If you place an image very far away you could then imagine the light rays striking the mirror parallel to the central axis so then the rays would reflect off the mirror and go through the focal point.

There is a formula for for light rays that only make small angles with the central axis 1/p + 1/i = 1/f where p is the object distance, i is the image distance, and f is the focal length. Since you said the object is very far away we can say that 1/p = 0 and then we are left with 1/i = 1/f so i = f.

Magnification is given by m = -i/p. Like before p is very large so m can be taken as 0

Answer 2

F = R/2

Location is at the focus

Mag = 0