The primary mirror in a space telescope has parabolic cross

The primary mirror in a space telescope has parabolic cross section. The diameter of the mirror is 1.8 m and the depth of the mirror is 0.00450 m. what is the equation of the cross section? What is the focal length of the mirror?

Solution

The standard equation of parabola:

y = a( x-h)^2 +k

if vertex is at origin( h, k) ----( 0, 0)

y = ax^2\'

Now ( x, y) on parabola = ( 1.8/2 , 0.00450 ).Plug this point in equation to get value of a:

0.00450 = a(0.9)^2

a =0.0055

a) y = 0.0055x^2 ( Equation of cross section)

b) Focal length = 1/4p = 1/4*0.0055 =1/0.022 = 45.45 mt