Question

A ray of light emanating from the point A (1,0,1) reflects from the plane mirror 2x +2y + z = 1 at the point B (0,0,1), then equation of the reflected ray is

• A. 8 - 72x = 9y + 8 = 18z - 10
• B. 8x = y = 3z - 2
• C. 8x = y = 2z - 2
• D. 8 + 2x = 9y + 8 = 2z + 10

Answer 1

Answer: (A), (C)

The correct options are
A 8 - 72x = 9y + 8 = 18z - 10
C 8x = y = 2z - 2

Image of A in the plane 2x +2y + z = 1 is given by
$\frac{x-1}{2}=\frac{y-0}{2}=\frac{z-1}{1}=-2\frac{2+0+1-1}{2^2+2^2+1^2}=-\frac{4}{9}$
$\therefore$ Coordinates of the image are $(\frac{1}{9},\frac{8}{9},\frac{5}{9})$
$\therefore$ Equation of the reflected ray is $\left(\frac{x-0}{1/9}\right)=\frac{y-0}{-8/9}=\frac{2-1}{-4/9}$
i.e $-8x=y=2z-2$ or $\frac{x-\frac{1}{9}}{1/9}=\frac{y+\frac{8}{9}}{-8/9}=\frac{2-\frac{5}{9}}{-4/9}$ i.e $8-72x=9y+8=18z-10$