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Chapter 10: Q. 72 (page 645)

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

Expert verified

The collected light be concentrated at 0.33 inch .

Step by step solution

01

. Given information .

Consider the given distance and depth .

02

Step 2. Standard form of parabola used .

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

03

Step 3. Find the distance .

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

Here $x = 2, y = 3$

$x^{2} = 4 a y 2^{2} = 4 a \cdot 3 a = 0 \cdot 33 i n c h$

Therefore the collected light will be concentrated at $0 \cdot 33 i n c h$ .

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