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The wavefront of a light beam is given by an equation 2X +Y + Z =C , where C is an arbitrary constant the angle made by the direction of light with X axis is?

The wavefront of a light beam is given by an equation 2X +Y + Z =C , where C is an arbitrary constant the angle made by the direction of light with X axis is?

Grade:12th Pass

1 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
x + 2y + 3z = c 
is a equation of a plane 
the normal to the plane is 
N= (1,2,3) = i + 2j + 3k 
now we know the normal will point in the direction of motion 
A is the angle between N the direction of light and the y axis 
we know also 
unit vector in x direction is 
u = (1,0,0) = 1i 
so we now can dot product 
N dot u = |N| *|u| cos A 
we want to solve for cos A so divide by the magnitudes 
(N dot u)/|N| = cos A 
I didnt write |u| because its a unit vector so that is 1 length so basically doesnt matter 
cos A = (1i + 2j + 3k) dot (1i)/ sqrt(1^2 + 2^2 + 3^2) 
cos A = 1 /sqrt(14) 
thats the answer if you wish 

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