Question

Reflecting Telescope - 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 inches deep, where will the collected light be concentrated?

Short answer

The collected light be concentrated at 0.33 inch .

Step-by-step solution

. Given information .

Consider the given distance and depth .

Step 2. Standard form of parabola used .

The standard form of parabola is $x^2=4ay$the vertex of the parabola is at origin and the focus is on y parallel axis .

Step 3. Find the distance .

To find the distance of collected light substitute the values in equation of parabola .

Here $x=2,y=3$

$$\begin{gathered} x^2=4ay \\ {2}^2=4a·3 \\ a=0·33inch \end{gathered}$$

Therefore the collected light will be concentrated at $0·33inch$.