Question

The wave front of a light beam is given by the equation x + 2y + 3z = C, (where C is arbitrary constant) then the angle made by the direction of light with the y _¯ axis is-

• A. cos^–1$\frac{1}{\sqrt{14}}$
• B. sin^–1 $\frac{2}{\sqrt{14}}$
• C. cos^–1$\frac{2}{\sqrt{14}}$
• D. sin^–1 $\frac{3}{\sqrt{14}}$

Answer 1

Answer: (C)

cos^–1$\frac{2}{\sqrt{14}}$

Answer 2

Here direction of light is given by normal vector

\widehat{n} = \overset{̑}{i} + 2\overset{̑}{j} + 3\overset{̑}{k}

\ angle made by the $\widehat{n}$ with y– axis is given by

$\cos\beta = \frac{2}{\sqrt{1^{2} + 2^{2} + 3^{2}}} = \frac{2}{\sqrt{14}}$