A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 35 feet, If the distance across the top of the mirror is 56 inches, how deep is the mirror in the center?
2007-10-31 05:02:55 · 2 answers · asked by pitbulgurl 1 in Science & Mathematics ➔ Mathematics
Be careful here. You are given the focus distance in feet and the width of the mirror in inches. Change all dimensions to inches. If you mix the two dimensions you will get a mirror with a depth of more than 5 feet which would have a focus only a few inches from the vertex.T
The equation of a parabola with vertex at the origin, opening upward, with focus at (0,p) is 4py = x^2 or solving for y,
y = x^2/(4p). But we know p = 35 feet or 420 inches so
y = x^2 /(4 * 420) = x^2 / 1680.
Now we want to know the depth of the mirror which has a radius of 56/2 = 28 inches. So we want to find y for x = 28
Y(28) = 28^2 / 1680 = = 0.467 inches to three sig. figs.
2007-10-31 05:23:43 · answer #1 · answered by baja_tom 4 · 0⤊ 0⤋
The equation of the parabola is x^2 = 2py where where
p/2 = 35 feet, so 2p = 140. Thus equation is y= x^2/140.
Whe x =56/2 = 28 inches = 2 1/3 feet,
y = (2 1/3)^2/140 = .0388888 feet = .4666 inches
2007-10-31 05:38:16 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋