Reflecting Telescope

magentarita · #1 $Old$ October 16th, 2008, 04:55 AM

A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 feet deep, where will the collected light be concentrated?

earboth · #2 $Old$ October 16th, 2008, 07:23 AM

Quote:

Originally Posted by magentarita $View Post$

A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 feet deep (ähemm! are you sure?) , where will the collected light be concentrated?

I assume that the paraboloid has an opening of 4'' and a depth of 3''. If so:

The cross-section of the paraboloid through the focus and the vertex of the paraboloid must be a parabola. Use a coordinate system where the vertex is V(0, 0) and the point P(3, 2) are located on the parabola.

The general equation of a parabola opening to the right is:

$y^2 = 2p\cdot x$

Use the coordinates of P to calculate p. (I've got $p = \frac23$ )

Then the focus F is the point where all parallel light rays will be concentrated. F has the coordinates $F\left(\frac p2\ ,\ 0\right)$

magentarita · #3 $Old$ October 16th, 2008, 08:03 PM

Quote:

Originally Posted by earboth $View Post$

I assume that the paraboloid has an opening of 4'' and a depth of 3''. If so:

The cross-section of the paraboloid through the focus and the vertex of the paraboloid must be a parabola. Use a coordinate system where the vertex is V(0, 0) and the point P(3, 2) are located on the parabola.

The general equation of a parabola opening to the right is:

$y^2 = 2p\cdot x$

Use the coordinates of P to calculate p. (I've got $p = \frac23$ )

Then the focus F is the point where all parallel light rays will be concentrated. F has the coordinates $F\left(\frac p2\ ,\ 0\right)$

Another great and helpful reply.