Question

A parallel beam of light ray parallel to the X-axis is incident on a parabolic reflecting surface $x=2b{y}^2$ as shown in the figure. After reflecting it passes through focal point $F$. The focal length of the reflecting surface is:

• A. $\frac{1}{8b}$
• B. $\frac{1}{4b}$
• C. $\frac{1}{b}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{8b}$

Since it is parabolic with general equation $y^2=4ax$ where $a=$focal length

Here $y^2-\frac{1}{2b}$

$4a=\frac{1}{2b}$

$a=\frac{1}{8b}$