1. ## 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?

2. ## Re: reflecting telescope

Hello, antiqua!

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

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

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

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

When $\displaystyle x = 33,\;y \:=\:\tfrac{1}{100}(33^2) \:=\:\frac{1089}{100} \:=\:10.89\text{ feet.}$

3. ## 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?

4. ## Re: reflecting telescope

Originally Posted by antiqua
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 ...

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

$\displaystyle y = \frac{2.75^2}{100} = 0.075625 \, ft = 0.9075 \, in$ , a reasonable depth for a parabolic mirror in a reflector

5. ## Re: reflecting telescope

Oh, I see now. Thank you so much!