Question

A ray of light along $x + \sqrt 3 y = \sqrt 3 $ gets reflected upon reaching the x-axis, an equation of the reflected ray is
$
  A.\sqrt 3 y = x + \sqrt 3 \\
  B.y = \sqrt 3 x - \sqrt 3 \\
  C.\sqrt {3y} = x - 1 \\
  D.y = x + \sqrt 3 \\
$

Answer 1

Hint: In order to solve this problem we need to use the concepts of plane mirrors that angle of incidence is equal to angle of reflection. We will draw figures and will draw the normal and will show the situation. To get the reflected equation we will just change the sign of the variable that is f(x) will be changed with f(-x) and the equation f(-x) is the equation of the reflected ray. Remember you have to change the sign of that variable on which reflection is taking place like here it is taking on x – axis. You can use this trick anywhere and get the right equation.

Complete step-by-step answer:
The figure representing the situation can be made as:

The given equation is $x + \sqrt 3 y = \sqrt 3 $
The above equation can also be written as:
$\sqrt 3 y = \sqrt 3 - x$
Let \[f(x) = \sqrt 3 y = \sqrt 3 - x\]
Here we will just change the sign of the variable that is f(x) will be changed with f(-x) and the equation f(-x) is the equation of the reflected ray. Remember you have to change the sign of that variable on which reflection is taking place like here it is taking on x – axis.
Then,
$ \Rightarrow f( - x) = \sqrt 3 y = \sqrt 3 - \left( { - x} \right) = \sqrt 3 + x$
So, the equation of reflected ray is,
$ \Rightarrow \sqrt 3 y = \sqrt 3 + x$
So, the correct option is A.

Note: When you get to solve such problems you can just use the technique above and get the equation of reflected ray. You can also solve this problem with the help of the line given and figure drawn that is you will find the slope of that line than you can find the angle of incident as well as reflected ray with the help of normal then you can get the slope of reflected ray and then you know that you have a point at which all the rays including normal is intersecting and then you got the point where y = 0 since the point is on x = axis after that you can find the equation of reflected ray if you know the slope and any point from which the line passes. Doing this will solve your problem and will give you the right answer.