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 the focal point $F$. What is the focal length of the reflecting surface?

Answer 1

Step 1: Given data

1. A parallel beam of light ray parallel to the x-axis is incident on a parabolic reflecting surface$x=2b{y}^2$
2. After reflecting it passes through the focal point $F$.

Step 2: Formula Used

The general equation of a parabola is $y^2=4ax$, where $a$ is the focal length

Step 3: Calculating focus

We know, the general equation of a parabola is $y^2=4ax$, where $a$ is the focal length

Comparing it with the given equation $x=2b{y}^2$, we get

$$\begin{gathered} 4ax=\frac{x}{2b} \\ a=\frac{1}{8b} \end{gathered}$$

Therefore, the focal length of the reflecting surface is $\frac{1}{8b}$.