1. ## refraction

A ray of light is sent along the line x-2y=8. After refraction across the line x+y=1 it enters the opposite side after turning by 15degrees away from the line x+y=1. find the equation of the line along which refracted ray travels.
please solve step by step.
and is there any standard method of doing these types of questions(refraction as well as reflection)?

2. Hi!

I did but I don't know if it is correct, could you give me the solution of the problem?
Are you sure that it is about refraction? Or is it about reflection??

I think you've to do this using the slope of the lines:
x+y=1 <=> y=1-x
so you know that the slope of this line is -1, and then you can use trigonometry: tg alfa = slope of the line <=> tg alfa = -1 <=> alfa = 135º

you said "it enters the opposite side after turning by 15degrees away from the line x+y=1", so you do: 135º+15º=150º

and then you have that the slope of the new line is tg 150º
and the equation of the new line is: y=tg 150ºx+1

3. Originally Posted by Gaurav
A ray of light is sent along the line x-2y=8. After refraction across the line x+y=1 it enters the opposite side after turning by 15degrees away from the line x+y=1. find the equation of the line along which refracted ray travels.
please solve step by step.
and is there any standard method of doing these types of questions(refraction as well as reflection)?
The intersection of the lines x - 2y = 8 and x + y = 1 gives you a point on the line of refraction.

You know the gradient of the line x + y = 1. and you're given the angle between the line of refraction and the line x + y = 1. So use the formula for the angle between two lines to get the gradient of the line of refraction.

Now you have a point and you have a gradient. So get the equation of the line.