Results 1 to 5 of 5
Like Tree2Thanks
  • 1 Post By Soroban
  • 1 Post By skeeter

Math Help - reflecting telescope

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    Georgia
    Posts
    4

    reflecting telescope

    I think that the vertex is (0,0) and the focus is (0,25) but thats about all. Please include any formulas that should be used. I'm not sure how to approach this problem.


    -A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 25 feet and the distance across the top of the mirror is 66 inches, how deep is the mirror in the center?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,866
    Thanks
    745

    Re: reflecting telescope

    Hello, antiqua!

    Is there a typo in the units of measurements?
    As written, the answer is 0.075625 feet, less than an inch.


    \text{A reflecting telescope has a mirror shaped like a paraboloid of revolution.}
    \text{If the distance of the vertex to the focus is 25 feet}
    \text{and the distance across the top of the mirror is 66 } \rlap{/////}\text{inches}\;{\color{blue}\text{feet}},
    \text{how deep is the mirror in the center?}

    Code:
                  |
          * - - - + - - - *(33,?)
          :       |       :
          :       |       :
          :*     F|      *:
          :       ♥25     :
          : *     |     * :
          :  *    |    *  :
          :    *  |  *    :
      - - + - - - * - - - + - -
         -33      |      33
                  |
    We need the formula: . x^2 \,=\,4Py
    . . where P is the distance from the vertex to the focus.

    Since P = 25, the equation is: . x^2 \,=\,100y \quad\Rightarrow\quad y \:=\:\tfrac{1}{100}x^2

    When x = 33,\;y \:=\:\tfrac{1}{100}(33^2) \:=\:\frac{1089}{100} \:=\:10.89\text{ feet.}
    Thanks from antiqua
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2012
    From
    Georgia
    Posts
    4

    Re: reflecting telescope

    Hello Soroban,
    There isn't a typo that I know of. This was how the problem was given. What you have worked out, is that for the 66 inches or 66 feet?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,061
    Thanks
    900

    Re: reflecting telescope

    Quote Originally Posted by antiqua View Post
    Hello Soroban,
    There isn't a typo that I know of. This was how the problem was given. What you have worked out, is that for the 66 inches or 66 feet?
    note that he crossed out inches and used feet.

    change 66 inches to 5.5 ft ...

    y = \frac{x^2}{100}

    y = \frac{2.75^2}{100} = 0.075625 \, ft = 0.9075 \, in , a reasonable depth for a parabolic mirror in a reflector
    Thanks from antiqua
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2012
    From
    Georgia
    Posts
    4

    Thumbs up Re: reflecting telescope

    Oh, I see now. Thank you so much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Reflecting Graphs over Lines
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 29th 2010, 11:28 AM
  2. Reflecting a line in a plane
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 4th 2010, 10:48 AM
  3. Replies: 6
    Last Post: November 18th 2009, 07:35 PM
  4. Reflecting Telescope
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 16th 2008, 07:03 PM
  5. Two Circles Reflecting
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 4th 2008, 12:35 PM

Search Tags


/mathhelpforum @mathhelpforum