A telescope at a mountaintop observatory has a d 400ln mirr

A telescope at a mountaintop observatory has a d = 400-ln. mirror, as shown in the figure. The mirror is constructed is a parabolic shape that collects light from the stars and focuses it at the prime focus, that is, the focus of the parabola. The mirror is 3.79 ln, deep at its centre. Find the focal length of this parabolic mirror, that is, the distance from the vertex to the focus. ()

Solution

d = 400 in

depth = 3.79 in

focal length = d^2 / 16* depth

focal length = 400^2 / 16*3.79 = 2638.5 inches