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

Answer 1

The correct option is A

$\frac{1}{8b}$

$y^2=\frac{x}{2b}$

Comparing with $y^2=4Px$ we get,

$4P=\frac{1}{2b}\Rightarrow P=\frac{1}{8b}$ is the focal length.