Question

A parallel beam of light ray parallel to the X-axis is incident on a parabolic reflecting surface x = 2by². After reflecting it passes through focal point F. The focal length of the reflecting surface is: -

(1) 1/8b
(2) 1/4b
(3) 1/b
(4) none of these​

Answer 1

Given :

The equation of parabolic surface is x = 2by²

To Find :

The focal length of the reflecting surface = ?

Solution :

• As the reflecting surface is a parabola, the general equation of the parabola having focal length a is

                $y^{2}=4ax\rightarrow Equation(1)$  

• From the equation of parabolic surface

                $x=2by^{2}$

                $y^{2}=\frac{x}{2b}$

• By substituting the value in equation(1)

                $\frac{x}{2b} =4ax$

                $\frac{1}{2b} =4a$

                $a=\frac{1}{8b}$

  The focal length of the reflecting surface is  b/8.